Merge branch 'dev_native' of https://github.com/prusa3d/Slic3r into dev_native

src/eigen/Eigen/src/SparseLU/SparseLU_panel_bmod.h

@@ -146,7 +146,7 @@ void SparseLUImpl<Scalar,StorageIndex>::panel_bmod(const Index m, const Index w,
       
       Index ldl = internal::first_multiple<Index>(nrow, PacketSize);
       Index offset = (PacketSize-internal::first_default_aligned(B.data(), PacketSize)) % PacketSize;
-      MappedMatrixBlock L(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
+      auto L = MappedMatrixBlock(tempv.data()+w*ldu+offset, nrow, u_cols, OuterStride<>(ldl));
       
       L.setZero();
       internal::sparselu_gemm<Scalar>(L.rows(), L.cols(), B.cols(), B.data(), B.outerStride(), U.data(), U.outerStride(), L.data(), L.outerStride());

src/igl/AABB.h

@@ -0,0 +1,413 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AABB_H
+#define IGL_AABB_H
+
+#include "Hit.h"
+#include "igl_inline.h"
+#include <Eigen/Core>
+#include <Eigen/Geometry>
+#include <vector>
+namespace igl
+{
+  // Implementation of semi-general purpose axis-aligned bounding box hierarchy.
+  // The mesh (V,Ele) is stored and managed by the caller and each routine here
+  // simply takes it as references (it better not change between calls).
+  //
+  // It's a little annoying that the Dimension is a template parameter and not
+  // picked up at run time from V. This leads to duplicated code for 2d/3d (up to
+  // dim).
+  template <typename DerivedV, int DIM>
+    class AABB 
+    {
+public:
+      typedef typename DerivedV::Scalar Scalar;
+      typedef Eigen::Matrix<Scalar,1,DIM> RowVectorDIMS;
+      typedef Eigen::Matrix<Scalar,DIM,1> VectorDIMS;
+      typedef Eigen::Matrix<Scalar,Eigen::Dynamic,DIM> MatrixXDIMS;
+      // Shared pointers are slower...
+      AABB * m_left;
+      AABB * m_right;
+      Eigen::AlignedBox<Scalar,DIM> m_box;
+      // -1 non-leaf
+      int m_primitive;
+      //Scalar m_low_sqr_d;
+      //int m_depth;
+      AABB():
+        m_left(NULL), m_right(NULL),
+        m_box(), m_primitive(-1)
+        //m_low_sqr_d(std::numeric_limits<double>::infinity()),
+        //m_depth(0)
+    {}
+      // http://stackoverflow.com/a/3279550/148668
+      AABB(const AABB& other):
+        m_left(other.m_left ? new AABB(*other.m_left) : NULL),
+        m_right(other.m_right ? new AABB(*other.m_right) : NULL),
+        m_box(other.m_box),
+        m_primitive(other.m_primitive)
+        //m_low_sqr_d(other.m_low_sqr_d),
+        //m_depth(std::max(
+        //   m_left ? m_left->m_depth + 1 : 0,
+        //   m_right ? m_right->m_depth + 1 : 0))
+        {
+        }
+      // copy-swap idiom
+      friend void swap(AABB& first, AABB& second)
+      {
+        // Enable ADL
+        using std::swap;
+        swap(first.m_left,second.m_left);
+        swap(first.m_right,second.m_right);
+        swap(first.m_box,second.m_box);
+        swap(first.m_primitive,second.m_primitive);
+        //swap(first.m_low_sqr_d,second.m_low_sqr_d);
+        //swap(first.m_depth,second.m_depth);
+      }
+      // Pass-by-value (aka copy)
+      AABB& operator=(AABB other)
+      {
+        swap(*this,other);
+        return *this;
+      }
+      AABB(AABB&& other):
+        // initialize via default constructor
+        AABB() 
+      {
+        swap(*this,other);
+      }
+      // Seems like there should have been an elegant solution to this using
+      // the copy-swap idiom above:
+      IGL_INLINE void deinit()
+      {
+        m_primitive = -1;
+        m_box = Eigen::AlignedBox<Scalar,DIM>();
+        delete m_left;
+        m_left = NULL;
+        delete m_right;
+        m_right = NULL;
+      }
+      ~AABB()
+      {
+        deinit();
+      }
+      // Build an Axis-Aligned Bounding Box tree for a given mesh and given
+      // serialization of a previous AABB tree.
+      //
+      // Inputs:
+      //   V  #V by dim list of mesh vertex positions. 
+      //   Ele  #Ele by dim+1 list of mesh indices into #V. 
+      //   bb_mins  max_tree by dim list of bounding box min corner positions
+      //   bb_maxs  max_tree by dim list of bounding box max corner positions
+      //   elements  max_tree list of element or (not leaf id) indices into Ele
+      //   i  recursive call index {0}
+      template <
+        typename DerivedEle, 
+        typename Derivedbb_mins, 
+        typename Derivedbb_maxs,
+        typename Derivedelements>
+        IGL_INLINE void init(
+            const Eigen::MatrixBase<DerivedV> & V,
+            const Eigen::MatrixBase<DerivedEle> & Ele, 
+            const Eigen::MatrixBase<Derivedbb_mins> & bb_mins,
+            const Eigen::MatrixBase<Derivedbb_maxs> & bb_maxs,
+            const Eigen::MatrixBase<Derivedelements> & elements,
+            const int i = 0);
+      // Wrapper for root with empty serialization
+      template <typename DerivedEle>
+      IGL_INLINE void init(
+          const Eigen::MatrixBase<DerivedV> & V,
+          const Eigen::MatrixBase<DerivedEle> & Ele);
+      // Build an Axis-Aligned Bounding Box tree for a given mesh.
+      //
+      // Inputs:
+      //   V  #V by dim list of mesh vertex positions. 
+      //   Ele  #Ele by dim+1 list of mesh indices into #V. 
+      //   SI  #Ele by dim list revealing for each coordinate where Ele's
+      //     barycenters would be sorted: SI(e,d) = i --> the dth coordinate of
+      //     the barycenter of the eth element would be placed at position i in a
+      //     sorted list.
+      //   I  #I list of indices into Ele of elements to include (for recursive
+      //     calls)
+      // 
+      template <typename DerivedEle, typename DerivedSI, typename DerivedI>
+      IGL_INLINE void init(
+          const Eigen::MatrixBase<DerivedV> & V,
+          const Eigen::MatrixBase<DerivedEle> & Ele, 
+          const Eigen::MatrixBase<DerivedSI> & SI,
+          const Eigen::MatrixBase<DerivedI>& I);
+      // Return whether at leaf node
+      IGL_INLINE bool is_leaf() const;
+      // Find the indices of elements containing given point: this makes sense
+      // when Ele is a co-dimension 0 simplex (tets in 3D, triangles in 2D).
+      //
+      // Inputs:
+      //   V  #V by dim list of mesh vertex positions. **Should be same as used to
+      //     construct mesh.**
+      //   Ele  #Ele by dim+1 list of mesh indices into #V. **Should be same as used to
+      //     construct mesh.**
+      //   q  dim row-vector query position
+      //   first  whether to only return first element containing q
+      // Returns:
+      //   list of indices of elements containing q
+      template <typename DerivedEle, typename Derivedq>
+      IGL_INLINE std::vector<int> find(
+          const Eigen::MatrixBase<DerivedV> & V,
+          const Eigen::MatrixBase<DerivedEle> & Ele, 
+          const Eigen::MatrixBase<Derivedq> & q,
+          const bool first=false) const;
+
+      // If number of elements m then total tree size should be 2*h where h is
+      // the deepest depth 2^ceil(log(#Ele*2-1))
+      IGL_INLINE int subtree_size() const;
+
+      // Serialize this class into 3 arrays (so we can pass it pack to matlab)
+      //
+      // Outputs:
+      //   bb_mins  max_tree by dim list of bounding box min corner positions
+      //   bb_maxs  max_tree by dim list of bounding box max corner positions
+      //   elements  max_tree list of element or (not leaf id) indices into Ele
+      //   i  recursive call index into these arrays {0}
+      template <
+        typename Derivedbb_mins, 
+        typename Derivedbb_maxs,
+        typename Derivedelements>
+        IGL_INLINE void serialize(
+            Eigen::PlainObjectBase<Derivedbb_mins> & bb_mins,
+            Eigen::PlainObjectBase<Derivedbb_maxs> & bb_maxs,
+            Eigen::PlainObjectBase<Derivedelements> & elements,
+            const int i = 0) const;
+      // Compute squared distance to a query point
+      //
+      // Inputs:
+      //   V  #V by dim list of vertex positions
+      //   Ele  #Ele by dim list of simplex indices
+      //   p  dim-long query point 
+      // Outputs:
+      //   i  facet index corresponding to smallest distances
+      //   c  closest point
+      // Returns squared distance
+      //
+      // Known bugs: currently assumes Elements are triangles regardless of
+      // dimension.
+      template <typename DerivedEle>
+      IGL_INLINE Scalar squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & p,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+//private:
+      // Compute squared distance to a query point
+      //
+      // Inputs:
+      //   V  #V by dim list of vertex positions
+      //   Ele  #Ele by dim list of simplex indices
+      //   p  dim-long query point 
+      //   low_sqr_d  lower bound on squared distance, specified maximum squared
+      //     distance 
+      //   up_sqr_d  current upper bounded on squared distance, current minimum
+      //     squared distance (only consider distances less than this), see
+      //     output.
+      // Outputs:
+      //   up_sqr_d  updated current minimum squared distance
+      //   i  facet index corresponding to smallest distances
+      //   c  closest point
+      // Returns squared distance
+      //
+      // Known bugs: currently assumes Elements are triangles regardless of
+      // dimension.
+      template <typename DerivedEle>
+      IGL_INLINE Scalar squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & p,
+        const Scalar low_sqr_d,
+        const Scalar up_sqr_d,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+      // Default low_sqr_d
+      template <typename DerivedEle>
+      IGL_INLINE Scalar squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & p,
+        const Scalar up_sqr_d,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+      // All hits
+      template <typename DerivedEle>
+      IGL_INLINE bool intersect_ray(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & origin,
+        const RowVectorDIMS & dir,
+        std::vector<igl::Hit> & hits) const;
+      // First hit
+      template <typename DerivedEle>
+      IGL_INLINE bool intersect_ray(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & origin,
+        const RowVectorDIMS & dir,
+        igl::Hit & hit) const;
+//private:
+      template <typename DerivedEle>
+      IGL_INLINE bool intersect_ray(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & origin,
+        const RowVectorDIMS & dir,
+        const Scalar min_t,
+        igl::Hit & hit) const;
+
+
+public:
+      // Compute the squared distance from all query points in P to the
+      // _closest_ points on the primitives stored in the AABB hierarchy for
+      // the mesh (V,Ele).
+      //
+      // Inputs:
+      //   V  #V by dim list of vertex positions
+      //   Ele  #Ele by dim list of simplex indices
+      //   P  #P by dim list of query points
+      // Outputs:
+      //   sqrD  #P list of squared distances
+      //   I  #P list of indices into Ele of closest primitives
+      //   C  #P by dim list of closest points
+      template <
+        typename DerivedEle,
+        typename DerivedP, 
+        typename DerivedsqrD, 
+        typename DerivedI, 
+        typename DerivedC>
+      IGL_INLINE void squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const Eigen::MatrixBase<DerivedP> & P,
+        Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+        Eigen::PlainObjectBase<DerivedI> & I,
+        Eigen::PlainObjectBase<DerivedC> & C) const;
+
+      // Compute the squared distance from all query points in P already stored
+      // in its own AABB hierarchy to the _closest_ points on the primitives
+      // stored in the AABB hierarchy for the mesh (V,Ele).
+      //
+      // Inputs:
+      //   V  #V by dim list of vertex positions
+      //   Ele  #Ele by dim list of simplex indices
+      //   other  AABB hierarchy of another set of primitives (must be points)
+      //   other_V  #other_V by dim list of query points
+      //   other_Ele  #other_Ele by ss list of simplex indices into other_V
+      //     (must be simple list of points: ss == 1)
+      // Outputs:
+      //   sqrD  #P list of squared distances
+      //   I  #P list of indices into Ele of closest primitives
+      //   C  #P by dim list of closest points
+      template < 
+        typename DerivedEle,
+        typename Derivedother_V,
+        typename Derivedother_Ele,
+        typename DerivedsqrD, 
+        typename DerivedI, 
+        typename DerivedC>
+      IGL_INLINE void squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const AABB<Derivedother_V,DIM> & other,
+        const Eigen::MatrixBase<Derivedother_V> & other_V,
+        const Eigen::MatrixBase<Derivedother_Ele> & other_Ele, 
+        Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+        Eigen::PlainObjectBase<DerivedI> & I,
+        Eigen::PlainObjectBase<DerivedC> & C) const;
+private:
+      template < 
+        typename DerivedEle,
+        typename Derivedother_V,
+        typename Derivedother_Ele,
+        typename DerivedsqrD, 
+        typename DerivedI, 
+        typename DerivedC>
+      IGL_INLINE Scalar squared_distance_helper(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const AABB<Derivedother_V,DIM> * other,
+        const Eigen::MatrixBase<Derivedother_V> & other_V,
+        const Eigen::MatrixBase<Derivedother_Ele>& other_Ele, 
+        const Scalar up_sqr_d,
+        Eigen::PlainObjectBase<DerivedsqrD> & sqrD,
+        Eigen::PlainObjectBase<DerivedI> & I,
+        Eigen::PlainObjectBase<DerivedC> & C) const;
+      // Compute the squared distance to the primitive in this node: assumes
+      // that this is indeed a leaf node.
+      //
+      // Inputs:
+      //   V  #V by dim list of vertex positions
+      //   Ele  #Ele by dim list of simplex indices
+      //   p  dim-long query point
+      //   sqr_d  current minimum distance for this query, see output
+      //   i  current index into Ele of closest point, see output
+      //   c  dim-long current closest point, see output
+      // Outputs:
+      //   sqr_d   minimum of initial value and squared distance to this
+      //     primitive
+      //   i  possibly updated index into Ele of closest point
+      //   c  dim-long possibly updated closest point
+      template <typename DerivedEle>
+      IGL_INLINE void leaf_squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & p,
+        const Scalar low_sqr_d,
+        Scalar & sqr_d,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+      // Default low_sqr_d
+      template <typename DerivedEle>
+      IGL_INLINE void leaf_squared_distance(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedEle> & Ele, 
+        const RowVectorDIMS & p,
+        Scalar & sqr_d,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+      // If new distance (sqr_d_candidate) is less than current distance
+      // (sqr_d), then update this distance and its associated values
+      // _in-place_:
+      //
+      // Inputs:
+      //   p  dim-long query point (only used in DEBUG mode)
+      //   sqr_d  candidate minimum distance for this query, see output
+      //   i  candidate index into Ele of closest point, see output
+      //   c  dim-long candidate closest point, see output
+      //   sqr_d  current minimum distance for this query, see output
+      //   i  current index into Ele of closest point, see output
+      //   c  dim-long current closest point, see output
+      // Outputs:
+      //   sqr_d   minimum of initial value and squared distance to this
+      //     primitive
+      //   i  possibly updated index into Ele of closest point
+      //   c  dim-long possibly updated closest point
+      IGL_INLINE void set_min(
+        const RowVectorDIMS & p,
+        const Scalar sqr_d_candidate,
+        const int i_candidate,
+        const RowVectorDIMS & c_candidate,
+        Scalar & sqr_d,
+        int & i,
+        Eigen::PlainObjectBase<RowVectorDIMS> & c) const;
+public:
+      EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+    };
+}
+
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "AABB.cpp"
+#endif
+
+#endif

src/igl/ARAPEnergyType.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ARAPENERGYTYPE_H
+#define IGL_ARAPENERGYTYPE_H
+namespace igl
+{
+  //     ARAP_ENERGY_TYPE_SPOKES  "As-rigid-as-possible Surface Modeling" by [Sorkine and
+  //       Alexa 2007], rotations defined at vertices affecting incident edges,
+  //       default
+  //     ARAP_ENERGY_TYPE_SPOKES-AND-RIMS  Adapted version of "As-rigid-as-possible Surface
+  //       Modeling" by [Sorkine and Alexa 2007] presented in section 4.2 of or
+  //       "A simple geometric model for elastic deformation" by [Chao et al.
+  //       2010], rotations defined at vertices affecting incident edges and
+  //       opposite edges
+  //     ARAP_ENERGY_TYPE_ELEMENTS  "A local-global approach to mesh parameterization" by
+  //       [Liu et al.  2010] or "A simple geometric model for elastic
+  //       deformation" by [Chao et al.  2010], rotations defined at elements
+  //       (triangles or tets) 
+  //     ARAP_ENERGY_TYPE_DEFAULT  Choose one automatically: spokes and rims
+  //       for surfaces, elements for planar meshes and tets (not fully
+  //       supported)
+  enum ARAPEnergyType
+  {
+    ARAP_ENERGY_TYPE_SPOKES = 0,
+    ARAP_ENERGY_TYPE_SPOKES_AND_RIMS = 1,
+    ARAP_ENERGY_TYPE_ELEMENTS = 2,
+    ARAP_ENERGY_TYPE_DEFAULT = 3,
+    NUM_ARAP_ENERGY_TYPES = 4
+  };
+}
+#endif

src/igl/AtA_cached.cpp

@@ -0,0 +1,130 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2017 Daniele Panozzo <daniele.panozzo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "AtA_cached.h"
+
+#include <iostream>
+#include <vector>
+#include <utility>
+
+template <typename Scalar>
+IGL_INLINE void igl::AtA_cached_precompute(
+    const Eigen::SparseMatrix<Scalar>& A,
+    igl::AtA_cached_data& data,
+    Eigen::SparseMatrix<Scalar>& AtA)
+{
+  // 1 Compute At (this could be avoided, but performance-wise it will not make a difference)
+  std::vector<std::vector<int> > Col_RowPtr;
+  std::vector<std::vector<int> > Col_IndexPtr;
+
+  Col_RowPtr.resize(A.cols());
+  Col_IndexPtr.resize(A.cols());
+
+  for (unsigned k=0; k<A.outerSize(); ++k)
+  {
+    unsigned outer_index = *(A.outerIndexPtr()+k);
+    unsigned next_outer_index = (k+1 == A.outerSize()) ? A.nonZeros() : *(A.outerIndexPtr()+k+1); 
+    
+    for (unsigned l=outer_index; l<next_outer_index; ++l)
+    {
+      int col = k;
+      int row = *(A.innerIndexPtr()+l);
+      int value_index = l;
+      assert(col < A.cols());
+      assert(col >= 0);
+      assert(row < A.rows());
+      assert(row >= 0);
+      assert(value_index >= 0);
+      assert(value_index < A.nonZeros());
+
+      Col_RowPtr[col].push_back(row);
+      Col_IndexPtr[col].push_back(value_index);
+    }
+  }
+
+  Eigen::SparseMatrix<Scalar> At = A.transpose();
+  At.makeCompressed();
+  AtA = At * A;
+  AtA.makeCompressed();
+
+  assert(AtA.isCompressed());
+
+  // If weights are not provided, use 1
+  if (data.W.size() == 0)
+    data.W = Eigen::VectorXd::Ones(A.rows());
+  assert(data.W.size() == A.rows());
+
+  data.I_outer.reserve(AtA.outerSize());
+  data.I_row.reserve(2*AtA.nonZeros());
+  data.I_col.reserve(2*AtA.nonZeros());
+  data.I_w.reserve(2*AtA.nonZeros());
+
+  // 2 Construct the rules
+  for (unsigned k=0; k<AtA.outerSize(); ++k)
+  {
+    unsigned outer_index = *(AtA.outerIndexPtr()+k);
+    unsigned next_outer_index = (k+1 == AtA.outerSize()) ? AtA.nonZeros() : *(AtA.outerIndexPtr()+k+1); 
+    
+    for (unsigned l=outer_index; l<next_outer_index; ++l)
+    {
+      int col = k;
+      int row = *(AtA.innerIndexPtr()+l);
+      int value_index = l;
+      assert(col < AtA.cols());
+      assert(col >= 0);
+      assert(row < AtA.rows());
+      assert(row >= 0);
+      assert(value_index >= 0);
+      assert(value_index < AtA.nonZeros());
+
+      data.I_outer.push_back(data.I_row.size());
+
+      // Find correspondences
+      unsigned i=0;
+      unsigned j=0;
+      while (i<Col_RowPtr[row].size() && j<Col_RowPtr[col].size())
+      {
+          if (Col_RowPtr[row][i] == Col_RowPtr[col][j])
+          {
+            data.I_row.push_back(Col_IndexPtr[row][i]);
+            data.I_col.push_back(Col_IndexPtr[col][j]);
+            data.I_w.push_back(Col_RowPtr[col][j]);
+            ++i;
+            ++j;
+          } else 
+          if (Col_RowPtr[row][i] > Col_RowPtr[col][j])
+            ++j;
+          else
+            ++i;
+
+      }
+    }
+  }
+  data.I_outer.push_back(data.I_row.size()); // makes it more efficient to iterate later on
+
+  igl::AtA_cached(A,data,AtA);
+}
+
+template <typename Scalar>
+IGL_INLINE void igl::AtA_cached(
+    const Eigen::SparseMatrix<Scalar>& A,
+    const igl::AtA_cached_data& data,
+    Eigen::SparseMatrix<Scalar>& AtA)
+{
+  for (unsigned i=0; i<data.I_outer.size()-1; ++i)
+  {
+    *(AtA.valuePtr() + i) = 0;
+    for (unsigned j=data.I_outer[i]; j<data.I_outer[i+1]; ++j)
+      *(AtA.valuePtr() + i) += *(A.valuePtr() + data.I_row[j]) * data.W[data.I_w[j]] * *(A.valuePtr() + data.I_col[j]);
+  }
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+template void igl::AtA_cached<double>(Eigen::SparseMatrix<double, 0, int> const&, igl::AtA_cached_data const&, Eigen::SparseMatrix<double, 0, int>&);
+template void igl::AtA_cached_precompute<double>(Eigen::SparseMatrix<double, 0, int> const&, igl::AtA_cached_data&, Eigen::SparseMatrix<double, 0, int>&);
+#endif

src/igl/AtA_cached.h

@@ -0,0 +1,70 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2017 Daniele Panozzo <daniele.panozzo@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ATA_CACHED_H
+#define IGL_ATA_CACHED_H
+#include "igl_inline.h"
+#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+namespace igl
+{  
+  struct AtA_cached_data
+  {
+    // Weights
+    Eigen::VectorXd W;
+
+    // Flatten composition rules
+    std::vector<int> I_row;
+    std::vector<int> I_col;
+    std::vector<int> I_w;
+
+    // For each entry of AtA, points to the beginning
+    // of the composition rules
+    std::vector<int> I_outer;
+  };
+
+  // Computes At * W * A, where A is sparse and W is diagonal. Divides the 
+  // construction in two phases, one
+  // for fixing the sparsity pattern, and one to populate it with values. Compared to
+  // evaluating it directly, this version is slower for the first time (since it requires a
+  // precomputation), but faster to the subsequent evaluations.
+  //
+  // Input:
+  //   A m x n sparse matrix
+  //   data stores the precomputed sparsity pattern, data.W contains the optional diagonal weights (stored as a dense vector). If W is not provided, it is replaced by the identity.
+  // Outputs:
+  //   AtA  m by m matrix computed as AtA * W * A
+  //
+  // Example:
+  // AtA_data = igl::AtA_cached_data();
+  // AtA_data.W = W;
+  // if (s.AtA.rows() == 0)
+  //   igl::AtA_cached_precompute(s.A,s.AtA_data,s.AtA);
+  // else
+  //   igl::AtA_cached(s.A,s.AtA_data,s.AtA);
+  template <typename Scalar>
+  IGL_INLINE void AtA_cached_precompute(
+    const Eigen::SparseMatrix<Scalar>& A,
+    AtA_cached_data& data,
+    Eigen::SparseMatrix<Scalar>& AtA
+    );
+
+  template <typename Scalar>
+  IGL_INLINE void AtA_cached(
+    const Eigen::SparseMatrix<Scalar>& A,
+    const AtA_cached_data& data,
+    Eigen::SparseMatrix<Scalar>& AtA
+    );
+  
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "AtA_cached.cpp"
+#endif
+
+#endif

src/igl/C_STR.h

@@ -0,0 +1,18 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_C_STR_H
+#define IGL_C_STR_H
+// http://stackoverflow.com/a/2433143/148668
+// Suppose you have a function:
+//   void func(const char * c);
+// Then you can write:
+//   func(C_STR("foo"<<1<<"bar"));
+#include <sstream>
+#include <string>
+#define C_STR(X) static_cast<std::ostringstream&>(std::ostringstream().flush() << X).str().c_str()
+#endif

src/igl/Camera.h

@@ -0,0 +1,359 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_CAMERA_H
+#define IGL_CAMERA_H
+
+// you're idiot, M$!
+#if defined(_WIN32)
+#undef far
+#undef near
+#endif
+
+#include <Eigen/Geometry>
+#include <Eigen/Core>
+#include <PI.h>
+
+#define IGL_CAMERA_MIN_ANGLE 5.0
+namespace igl
+{
+
+  // A simple camera class. The camera stores projection parameters (field of
+  // view angle, aspect ratio, near and far clips) as well as a rigid
+  // transformation *of the camera as if it were also a scene object*. Thus, the
+  // **inverse** of this rigid transformation is the modelview transformation.
+  class Camera
+  {
+    public:
+      // On windows you might need: -fno-delayed-template-parsing
+      //static constexpr double IGL_CAMERA_MIN_ANGLE = 5.;
+      //  m_angle  Field of view angle in degrees {45}
+      //  m_aspect  Aspect ratio {1}
+      //  m_near  near clipping plane {1e-2}
+      //  m_far  far clipping plane {100}
+      //  m_at_dist  distance of looking at point {1}
+      //  m_orthographic  whether to use othrographic projection {false}
+      //  m_rotation_conj  Conjugate of rotation part of rigid transformation of
+      //    camera {identity}. Note: we purposefully store the conjugate because
+      //    this is what TW_TYPE_QUAT4D is expecting.
+      //  m_translation  Translation part of rigid transformation of camera
+      //    {(0,0,1)}
+      double m_angle, m_aspect, m_near, m_far, m_at_dist;
+      bool m_orthographic;
+      Eigen::Quaterniond m_rotation_conj;
+      Eigen::Vector3d m_translation;
+    public:
+      inline Camera();
+      inline virtual ~Camera(){}
+      // Return projection matrix that takes relative camera coordinates and
+      // transforms it to viewport coordinates
+      //
+      // Note:
+      //
+      //     if(m_angle > 0)
+      //     {
+      //       gluPerspective(m_angle,m_aspect,m_near,m_at_dist+m_far);
+      //     }else
+      //     {
+      //       gluOrtho(-0.5*aspect,0.5*aspect,-0.5,0.5,m_at_dist+m_near,m_far);
+      //     }
+      //
+      // Is equivalent to
+      //
+      //     glMultMatrixd(projection().data());
+      //
+      inline Eigen::Matrix4d projection() const;
+      // Return an Affine transformation (rigid actually) that 
+      // takes relative coordinates and tramsforms them into world 3d
+      // coordinates: moves the camera into the scene.
+      inline Eigen::Affine3d affine() const;
+      // Return an Affine transformation (rigid actually) that puts the takes a
+      // world 3d coordinate and transforms it into the relative camera
+      // coordinates: moves the scene in front of the camera.
+      //
+      // Note:
+      //
+      //     gluLookAt(
+      //       eye()(0), eye()(1), eye()(2),
+      //       at()(0), at()(1), at()(2),
+      //       up()(0), up()(1), up()(2));
+      //
+      // Is equivalent to
+      //
+      //     glMultMatrixd(camera.inverse().matrix().data());
+      //
+      // See also: affine, eye, at, up
+      inline Eigen::Affine3d inverse() const;
+      // Returns world coordinates position of center or "eye" of camera.
+      inline Eigen::Vector3d eye() const;
+      // Returns world coordinate position of a point "eye" is looking at.
+      inline Eigen::Vector3d at() const;
+      // Returns world coordinate unit vector of "up" vector
+      inline Eigen::Vector3d up() const;
+      // Return top right corner of unit plane in relative coordinates, that is
+      // (w/2,h/2,1)
+      inline Eigen::Vector3d unit_plane() const;
+      // Move dv in the relative coordinate frame of the camera (move the FPS)
+      //
+      // Inputs:
+      //   dv  (x,y,z) displacement vector
+      //
+      inline void dolly(const Eigen::Vector3d & dv);
+      // "Scale zoom": Move `eye`, but leave `at`
+      //
+      // Input:
+      //   s  amount to scale distance to at
+      inline void push_away(const double s);
+      // Aka "Hitchcock", "Vertigo", "Spielberg" or "Trombone" zoom:
+      // simultaneously dolly while changing angle so that `at` not only stays
+      // put in relative coordinates but also projected coordinates. That is
+      //
+      // Inputs:
+      //   da  change in angle in degrees
+      inline void dolly_zoom(const double da);
+      // Turn around eye so that rotation is now q
+      //
+      // Inputs:
+      //   q  new rotation as quaternion
+      inline void turn_eye(const Eigen::Quaterniond & q);
+      // Orbit around at so that rotation is now q
+      //
+      // Inputs:
+      //   q  new rotation as quaternion
+      inline void orbit(const Eigen::Quaterniond & q);
+      // Rotate and translate so that camera is situated at "eye" looking at "at"
+      // with "up" pointing up.
+      //
+      // Inputs:
+      //   eye  (x,y,z) coordinates of eye position
+      //   at   (x,y,z) coordinates of at position
+      //   up   (x,y,z) coordinates of up vector
+      inline void look_at(
+        const Eigen::Vector3d & eye,
+        const Eigen::Vector3d & at,
+        const Eigen::Vector3d & up);
+    // Needed any time Eigen Structures are used as class members
+    // http://eigen.tuxfamily.org/dox-devel/group__TopicStructHavingEigenMembers.html
+    public:
+        EIGEN_MAKE_ALIGNED_OPERATOR_NEW
+  };
+}
+
+// Implementation
+#include "PI.h"
+#include "EPS.h"
+#include <cmath>
+#include <iostream>
+#include <cassert>
+
+inline igl::Camera::Camera():
+  m_angle(45.0),m_aspect(1),m_near(1e-2),m_far(100),m_at_dist(1),
+  m_orthographic(false),
+  m_rotation_conj(1,0,0,0),
+  m_translation(0,0,1)
+{
+}
+
+inline Eigen::Matrix4d igl::Camera::projection() const
+{
+  Eigen::Matrix4d P;
+  using namespace std;
+  const double far = m_at_dist + m_far;
+  const double near = m_near;
+  // http://stackoverflow.com/a/3738696/148668
+  if(m_orthographic)
+  {
+    const double f = 0.5;
+    const double left = -f*m_aspect;
+    const double right = f*m_aspect;
+    const double bottom = -f;
+    const double top = f;
+    const double tx = (right+left)/(right-left);
+    const double ty = (top+bottom)/(top-bottom);
+    const double tz = (far+near)/(far-near);
+    const double z_fix = 0.5 /m_at_dist / tan(m_angle*0.5 * (igl::PI/180.) );
+    P<<
+      z_fix*2./(right-left), 0, 0, -tx,
+      0, z_fix*2./(top-bottom), 0, -ty,
+      0, 0, -z_fix*2./(far-near),  -tz,
+      0, 0, 0, 1;
+  }else
+  {
+    const double yScale = tan(PI*0.5 - 0.5*m_angle*PI/180.);
+    // http://stackoverflow.com/a/14975139/148668
+    const double xScale = yScale/m_aspect;
+    P<< 
+      xScale, 0, 0, 0,
+      0, yScale, 0, 0,
+      0, 0, -(far+near)/(far-near), -1,
+      0, 0, -2.*near*far/(far-near), 0;
+    P = P.transpose().eval();
+  }
+  return P;
+}
+
+inline Eigen::Affine3d igl::Camera::affine() const
+{
+  using namespace Eigen;
+  Affine3d t = Affine3d::Identity();
+  t.rotate(m_rotation_conj.conjugate());
+  t.translate(m_translation);
+  return t;
+}
+
+inline Eigen::Affine3d igl::Camera::inverse() const
+{
+  using namespace Eigen;
+  Affine3d t = Affine3d::Identity();
+  t.translate(-m_translation);
+  t.rotate(m_rotation_conj);
+  return t;
+}
+
+inline Eigen::Vector3d igl::Camera::eye() const
+{
+  using namespace Eigen;
+  return affine() * Vector3d(0,0,0);
+}
+
+inline Eigen::Vector3d igl::Camera::at() const
+{
+  using namespace Eigen;
+  return affine() * (Vector3d(0,0,-1)*m_at_dist);
+}
+
+inline Eigen::Vector3d igl::Camera::up() const
+{
+  using namespace Eigen;
+  Affine3d t = Affine3d::Identity();
+  t.rotate(m_rotation_conj.conjugate());
+  return t * Vector3d(0,1,0);
+}
+
+inline Eigen::Vector3d igl::Camera::unit_plane() const
+{
+  // Distance of center pixel to eye
+  const double d = 1.0;
+  const double a = m_aspect;
+  const double theta = m_angle*PI/180.;
+  const double w =
+    2.*sqrt(-d*d/(a*a*pow(tan(0.5*theta),2.)-1.))*a*tan(0.5*theta);
+  const double h = w/a;
+  return Eigen::Vector3d(w*0.5,h*0.5,-d);
+}
+
+inline void igl::Camera::dolly(const Eigen::Vector3d & dv)
+{
+  m_translation += dv;
+}
+
+inline void igl::Camera::push_away(const double s)
+{
+  using namespace Eigen;
+#ifndef NDEBUG
+  Vector3d old_at = at();
+#endif
+  const double old_at_dist = m_at_dist;
+  m_at_dist = old_at_dist * s;
+  dolly(Vector3d(0,0,1)*(m_at_dist - old_at_dist));
+  assert((old_at-at()).squaredNorm() < DOUBLE_EPS);
+}
+
+inline void igl::Camera::dolly_zoom(const double da)
+{
+  using namespace std;
+  using namespace Eigen;
+#ifndef NDEBUG
+  Vector3d old_at = at();
+#endif
+  const double old_angle = m_angle;
+  if(old_angle + da < IGL_CAMERA_MIN_ANGLE)
+  {
+    m_orthographic = true;
+  }else if(old_angle + da > IGL_CAMERA_MIN_ANGLE)
+  {
+    m_orthographic = false;
+  }
+  if(!m_orthographic)
+  {
+    m_angle += da;
+    m_angle = min(89.,max(IGL_CAMERA_MIN_ANGLE,m_angle));
+    // change in distance
+    const double s = 
+      (2.*tan(old_angle/2./180.*igl::PI)) /
+      (2.*tan(m_angle/2./180.*igl::PI)) ;
+    const double old_at_dist = m_at_dist;
+    m_at_dist = old_at_dist * s;
+    dolly(Vector3d(0,0,1)*(m_at_dist - old_at_dist));
+    assert((old_at-at()).squaredNorm() < DOUBLE_EPS);
+  }
+}
+
+inline void igl::Camera::turn_eye(const Eigen::Quaterniond & q)
+{
+  using namespace Eigen;
+  Vector3d old_eye = eye();
+  // eye should be fixed
+  //
+  // eye_1 = R_1 * t_1 = eye_0
+  // t_1 = R_1' * eye_0
+  m_rotation_conj = q.conjugate();
+  m_translation = m_rotation_conj * old_eye;
+  assert((old_eye - eye()).squaredNorm() < DOUBLE_EPS);
+}
+
+inline void igl::Camera::orbit(const Eigen::Quaterniond & q)
+{
+  using namespace Eigen;
+  Vector3d old_at = at();
+  // at should be fixed
+  //
+  // at_1 = R_1 * t_1 - R_1 * z = at_0
+  // t_1 = R_1' * (at_0 + R_1 * z)
+  m_rotation_conj = q.conjugate();
+  m_translation = 
+    m_rotation_conj * 
+      (old_at + 
+         m_rotation_conj.conjugate() * Vector3d(0,0,1) * m_at_dist);
+  assert((old_at - at()).squaredNorm() < DOUBLE_EPS);
+}
+
+inline void igl::Camera::look_at(
+  const Eigen::Vector3d & eye,
+  const Eigen::Vector3d & at,
+  const Eigen::Vector3d & up)
+{
+  using namespace Eigen;
+  using namespace std;
+  // http://www.opengl.org/sdk/docs/man2/xhtml/gluLookAt.xml
+  // Normalize vector from at to eye
+  Vector3d F = eye-at;
+  m_at_dist = F.norm();
+  F.normalize();
+  // Project up onto plane orthogonal to F and normalize
+  assert(up.cross(F).norm() > DOUBLE_EPS && "(eye-at) x up ≈ 0");
+  const Vector3d proj_up = (up-(up.dot(F))*F).normalized();
+  Quaterniond a,b;
+  a.setFromTwoVectors(Vector3d(0,0,-1),-F);
+  b.setFromTwoVectors(a*Vector3d(0,1,0),proj_up);
+  m_rotation_conj = (b*a).conjugate();
+  m_translation = m_rotation_conj * eye;
+  //cout<<"m_at_dist: "<<m_at_dist<<endl;
+  //cout<<"proj_up: "<<proj_up.transpose()<<endl;
+  //cout<<"F: "<<F.transpose()<<endl;
+  //cout<<"eye(): "<<this->eye().transpose()<<endl;
+  //cout<<"at(): "<<this->at().transpose()<<endl;
+  //cout<<"eye()-at(): "<<(this->eye()-this->at()).normalized().transpose()<<endl;
+  //cout<<"eye-this->eye(): "<<(eye-this->eye()).squaredNorm()<<endl;
+  assert(           (eye-this->eye()).squaredNorm() < DOUBLE_EPS);
+  //assert((F-(this->eye()-this->at()).normalized()).squaredNorm() < 
+  //  DOUBLE_EPS);
+  assert(           (at-this->at()).squaredNorm() < DOUBLE_EPS);
+  //assert(        (proj_up-this->up()).squaredNorm() < DOUBLE_EPS);
+}
+
+#endif

src/igl/EPS.cpp

@@ -0,0 +1,30 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "EPS.h"
+
+template <> IGL_INLINE float igl::EPS()
+{
+  return igl::FLOAT_EPS;
+}
+template <> IGL_INLINE double igl::EPS()
+{
+  return igl::DOUBLE_EPS;
+}
+
+template <> IGL_INLINE float igl::EPS_SQ()
+{
+  return igl::FLOAT_EPS_SQ;
+}
+template <> IGL_INLINE double igl::EPS_SQ()
+{
+  return igl::DOUBLE_EPS_SQ;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#endif

src/igl/EPS.h

@@ -0,0 +1,32 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_EPS_H
+#define IGL_EPS_H
+#include "igl_inline.h"
+namespace igl
+{
+  // Define a standard value for double epsilon
+  const double DOUBLE_EPS    = 1.0e-14;
+  const double DOUBLE_EPS_SQ = 1.0e-28;
+  const float FLOAT_EPS    = 1.0e-7;
+  const float FLOAT_EPS_SQ = 1.0e-14;
+  // Function returning EPS for corresponding type
+  template <typename S_type> IGL_INLINE S_type EPS();
+  template <typename S_type> IGL_INLINE S_type EPS_SQ();
+  // Template specializations for float and double
+  template <> IGL_INLINE float EPS<float>();
+  template <> IGL_INLINE double EPS<double>();
+  template <> IGL_INLINE float EPS_SQ<float>();
+  template <> IGL_INLINE double EPS_SQ<double>();
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "EPS.cpp"
+#endif
+
+#endif

src/igl/HalfEdgeIterator.cpp

@@ -0,0 +1,158 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Daniele Panozzo <daniele.panozzo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "HalfEdgeIterator.h"
+
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::HalfEdgeIterator(
+    const Eigen::PlainObjectBase<DerivedF>& _F,
+    const Eigen::PlainObjectBase<DerivedFF>& _FF,
+    const Eigen::PlainObjectBase<DerivedFFi>& _FFi,
+    int _fi,
+    int _ei,
+    bool _reverse
+)
+: fi(_fi), ei(_ei), reverse(_reverse), F(_F), FF(_FF), FFi(_FFi)
+{}
+
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE void igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::flipF()
+{
+  if (isBorder())
+    return;
+
+  int fin = (FF)(fi,ei);
+  int ein = (FFi)(fi,ei);
+
+  fi = fin;
+  ei = ein;
+  reverse = !reverse;
+}
+
+
+// Change Edge
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE void igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::flipE()
+{
+  if (!reverse)
+    ei = (ei+2)%3; // ei-1
+  else
+    ei = (ei+1)%3;
+
+  reverse = !reverse;
+}
+
+// Change Vertex
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE void igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::flipV()
+{
+  reverse = !reverse;
+}
+
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE bool igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::isBorder()
+{
+  return (FF)(fi,ei) == -1;
+}
+
+/*!
+ * Returns the next edge skipping the border
+ *      _________
+ *     /\ c | b /\
+ *    /  \  |  /  \
+ *   / d  \ | / a  \
+ *  /______\|/______\
+ *          v
+ * In this example, if a and d are of-border and the pos is iterating counterclockwise, this method iterate through the faces incident on vertex v,
+ * producing the sequence a, b, c, d, a, b, c, ...
+ */
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE bool igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::NextFE()
+{
+  if ( isBorder() ) // we are on a border
+  {
+    do
+    {
+      flipF();
+      flipE();
+    } while (!isBorder());
+    flipE();
+    return false;
+  }
+  else
+  {
+    flipF();
+    flipE();
+    return true;
+  }
+}
+
+// Get vertex index
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE int igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::Vi()
+{
+  assert(fi >= 0);
+  assert(fi < F.rows());
+  assert(ei >= 0);
+  assert(ei <= 2);
+
+  if (!reverse)
+    return (F)(fi,ei);
+  else
+    return (F)(fi,(ei+1)%3);
+}
+
+// Get face index
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE int igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::Fi()
+{
+  return fi;
+}
+
+// Get edge index
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE int igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::Ei()
+{
+  return ei;
+}
+
+
+template <typename DerivedF, typename DerivedFF, typename DerivedFFi>
+IGL_INLINE bool igl::HalfEdgeIterator<DerivedF,DerivedFF,DerivedFFi>::operator==(HalfEdgeIterator& p2)
+{
+  return
+      (
+          (fi == p2.fi) &&
+              (ei == p2.ei) &&
+              (reverse == p2.reverse) &&
+              (F   == p2.F) &&
+              (FF  == p2.FF) &&
+              (FFi == p2.FFi)
+      );
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template      igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>   >::HalfEdgeIterator(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, int, int, bool);
+template igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >::HalfEdgeIterator(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, int, int, bool);
+template bool igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::NextFE();
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::Ei();
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::Ei();
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>   >::Ei();
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>   >::Fi();
+template bool igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>  ,Eigen::Matrix<int, -1, 3, 0, -1, 3>   >::NextFE();
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::Vi();
+template      igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::HalfEdgeIterator(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, int, int, bool);
+template int  igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::Fi();
+template void igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::flipE();
+template void igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::flipF();
+template void igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::flipV();
+template bool igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >::operator==(igl::HalfEdgeIterator<Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1>,Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template int igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >::Fi();
+template bool igl::HalfEdgeIterator<Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >::NextFE();
+#endif

src/igl/HalfEdgeIterator.h

@@ -0,0 +1,114 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Daniele Panozzo <daniele.panozzo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_HALFEDGEITERATOR_H
+#define IGL_HALFEDGEITERATOR_H
+
+#include <Eigen/Core>
+
+#include <vector>
+#include <igl/igl_inline.h>
+
+// This file violates many of the libigl style guidelines.
+
+namespace igl
+{
+  // HalfEdgeIterator - Fake halfedge for fast and easy navigation
+  // on triangle meshes with vertex_triangle_adjacency and
+  // triangle_triangle adjacency
+  //
+  // Note: this is different to classical Half Edge data structure.
+  //    Instead, it follows cell-tuple in [Brisson, 1989]
+  //    "Representing geometric structures in d dimensions: topology and order."
+  //    This class can achieve local navigation similar to half edge in OpenMesh
+  //    But the logic behind each atom operation is different.
+  //    So this should be more properly called TriangleTupleIterator.
+  //
+  // Each tuple contains information on (face, edge, vertex)
+  //    and encoded by (face, edge \in {0,1,2}, bool reverse)
+  //
+  // Inputs:
+  //    F #F by 3 list of "faces"
+  //    FF #F by 3 list of triangle-triangle adjacency.
+  //    FFi #F by 3 list of FF inverse. For FF and FFi, refer to
+  //        "triangle_triangle_adjacency.h"
+  // Usages:
+  //    FlipF/E/V changes solely one actual face/edge/vertex resp.
+  //    NextFE iterates through one-ring of a vertex robustly.
+  //
+  template <
+    typename DerivedF,
+    typename DerivedFF,
+    typename DerivedFFi>
+  class HalfEdgeIterator
+  {
+  public:
+    // Init the HalfEdgeIterator by specifying Face,Edge Index and Orientation
+    IGL_INLINE HalfEdgeIterator(
+        const Eigen::PlainObjectBase<DerivedF>& _F,
+        const Eigen::PlainObjectBase<DerivedFF>& _FF,
+        const Eigen::PlainObjectBase<DerivedFFi>& _FFi,
+        int _fi,
+        int _ei,
+        bool _reverse = false
+        );
+
+    // Change Face
+    IGL_INLINE void flipF();
+
+    // Change Edge
+    IGL_INLINE void flipE();
+
+    // Change Vertex
+    IGL_INLINE void flipV();
+
+    IGL_INLINE bool isBorder();
+
+    /*!
+     * Returns the next edge skipping the border
+     *      _________
+     *     /\ c | b /\
+     *    /  \  |  /  \
+     *   / d  \ | / a  \
+     *  /______\|/______\
+     *          v
+     * In this example, if a and d are of-border and the pos is iterating
+     counterclockwise, this method iterate through the faces incident on vertex
+     v,
+     * producing the sequence a, b, c, d, a, b, c, ...
+     */
+    IGL_INLINE bool NextFE();
+
+    // Get vertex index
+    IGL_INLINE int Vi();
+
+    // Get face index
+    IGL_INLINE int Fi();
+
+    // Get edge index
+    IGL_INLINE int Ei();
+
+    IGL_INLINE bool operator==(HalfEdgeIterator& p2);
+
+  private:
+    int fi;
+    int ei;
+    bool reverse;
+
+    // All the same type? This is likely to break.
+    const Eigen::PlainObjectBase<DerivedF> & F;
+    const Eigen::PlainObjectBase<DerivedFF> & FF;
+    const Eigen::PlainObjectBase<DerivedFFi> & FFi;
+  };
+
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "HalfEdgeIterator.cpp"
+#endif
+
+#endif

src/igl/Hit.h

@@ -0,0 +1,25 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//               2014 Christian Schüller <schuellchr@gmail.com> 
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_HIT_H
+#define IGL_HIT_H
+
+namespace igl
+{
+  // Reimplementation of the embree::Hit struct from embree1.0
+  // 
+  // TODO: template on floating point type
+  struct Hit
+  {
+    int id; // primitive id
+    int gid; // geometry id
+    float u,v; // barycentric coordinates
+    float t; // distance = direction*t to intersection
+  };
+}
+#endif 

src/igl/IO

@@ -0,0 +1,28 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_IO
+#define IGL_IO
+// Input and output functions
+#include "read_triangle_mesh.h"
+#include "readDMAT.h"
+#include "readMESH.h"
+#include "readNODE.h"
+#include "readOBJ.h"
+#include "readOFF.h"
+#include "readTGF.h"
+#include "readWRL.h"
+#include "readCSV.h"
+#include "file_contents_as_string.h"
+#include "write_triangle_mesh.h"
+#include "writeDMAT.h"
+#include "writeMESH.h"
+#include "writeOBJ.h"
+#include "writeOFF.h"
+#include "writeTGF.h"
+
+#endif

src/igl/IndexComparison.h

@@ -0,0 +1,117 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_INDEXCOMPARISON_H
+#define IGL_INDEXCOMPARISON_H
+#include <iostream>
+namespace igl{
+  // Comparison struct used by sort
+  // http://bytes.com/topic/c/answers/132045-sort-get-index
+
+  // For use with functions like std::sort
+  template<class T> struct IndexLessThan
+  {
+    IndexLessThan(const T arr) : arr(arr) {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      return arr[a] < arr[b];
+    }
+    const T arr;
+  };
+
+  // For use with functions like std::unique
+  template<class T> struct IndexEquals
+  {
+    IndexEquals(const T arr) : arr(arr) {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      return arr[a] == arr[b];
+    }
+    const T arr;
+  };
+
+  // For use with functions like std::sort
+  template<class T> struct IndexVectorLessThan
+  {
+    IndexVectorLessThan(const T & vec) : vec ( vec) {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      return vec(a) < vec(b);
+    }
+    const T & vec;
+  };
+
+  // For use with functions like std::sort
+  template<class T> struct IndexDimLessThan
+  {
+    IndexDimLessThan(const T & mat,const int & dim, const int & j) : 
+      mat(mat),
+      dim(dim),
+      j(j)
+    {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      if(dim == 1)
+      {
+        return mat(a,j) < mat(b,j);
+      }else
+      {
+        return mat(j,a) < mat(j,b);
+      }
+    }
+    const T & mat;
+    const int & dim;
+    const int & j;
+  };
+
+  // For use with functions like std::sort
+  template<class T> struct IndexRowLessThan
+  {
+    IndexRowLessThan(const T & mat) : mat ( mat) {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      const int cols = mat.cols();
+      // Lexicographical order
+      for(int j = 0;j<cols;j++)
+      {
+        if(mat(a,j) > mat(b,j))
+        {
+          return false;
+        } else if(mat(a,j) < mat(b,j))
+        {
+          return true;
+        }
+      }
+      // equality is false
+      return false;
+    }
+    const T & mat;
+  };
+
+  // For use with functions like std::sort
+  template<class T> struct IndexRowEquals
+  {
+    IndexRowEquals(const T & mat) : mat ( mat) {}
+    bool operator()(const size_t a, const size_t b) const
+    {
+      const int cols = mat.cols();
+      // Lexicographical order
+      for(int j = 0;j<cols;j++)
+      {
+        if(mat(a,j) !=  mat(b,j))
+        {
+          return false;
+        }
+      }
+      return true;
+    }
+    const T & mat;
+  };
+
+}
+
+#endif

src/igl/LinSpaced.h

@@ -0,0 +1,61 @@
+#ifndef IGL_LINSPACED_H
+#define IGL_LINSPACED_H
+#include <Eigen/Core>
+// This function is not intended to be a permanent function of libigl. Rather
+// it is a "drop-in" workaround for documented bug in Eigen:
+// http://eigen.tuxfamily.org/bz/show_bug.cgi?id=1383
+//
+// Replace: 
+//
+//     Eigen::VectorXi::LinSpaced(size,low,high);
+//
+// With:
+//
+//     igl::LinSpaced<Eigen::VectorXi>(size,low,high);
+//
+// Specifcally, this version will _always_ return an empty vector if size==0,
+// regardless of the values for low and high. If size != 0, then this simply
+// returns the result of Eigen::Derived::LinSpaced.
+//
+// Until this bug is fixed, we should also avoid calls to the member function
+// `.setLinSpaced`. This means replacing:
+//
+//     a.setLinSpaced(size,low,high);
+//
+// with
+//
+//     a = igl::LinSpaced<decltype(a) >(size,low,high);
+//
+namespace igl
+{
+  template <typename Derived>
+  //inline typename Eigen::DenseBase< Derived >::RandomAccessLinSpacedReturnType 
+  inline Derived LinSpaced(
+    typename Derived::Index size,
+    const typename Derived::Scalar & low,
+    const typename Derived::Scalar & high);
+}
+
+// Implementation
+
+template <typename Derived>
+//inline typename Eigen::DenseBase< Derived >::RandomAccessLinSpacedReturnType 
+inline Derived
+igl::LinSpaced(
+  typename Derived::Index size,
+  const typename Derived::Scalar & low,
+  const typename Derived::Scalar & high)
+{
+  if(size == 0)
+  {
+    // Force empty vector with correct "RandomAccessLinSpacedReturnType" type.
+    return Derived::LinSpaced(0,0,1);
+  }else if(high < low)
+  {
+    return low-Derived::LinSpaced(size,low-low,low-high).array();
+  }else{
+    return Derived::LinSpaced(size,low,high);
+  }
+}
+
+#endif

src/igl/MeshBooleanType.h

@@ -0,0 +1,23 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_MESH_BOOLEAN_TYPE_H
+#define IGL_MESH_BOOLEAN_TYPE_H
+namespace igl
+{
+  enum MeshBooleanType
+  {
+    MESH_BOOLEAN_TYPE_UNION = 0,
+    MESH_BOOLEAN_TYPE_INTERSECT = 1,
+    MESH_BOOLEAN_TYPE_MINUS = 2,
+    MESH_BOOLEAN_TYPE_XOR = 3,
+    MESH_BOOLEAN_TYPE_RESOLVE = 4,
+    NUM_MESH_BOOLEAN_TYPES = 5
+  };
+};
+
+#endif

src/igl/NormalType.h

@@ -0,0 +1,27 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_NORMALTYPE_H
+#define IGL_NORMALTYPE_H
+
+namespace igl
+{
+  // PER_VERTEX_NORMALS  Normals computed per vertex based on incident faces
+  // PER_FACE_NORMALS  Normals computed per face
+  // PER_CORNER_NORMALS  Normals computed per corner (aka wedge) based on
+  //   incident faces without sharp edge
+  enum NormalType
+  {
+    PER_VERTEX_NORMALS,
+    PER_FACE_NORMALS,
+    PER_CORNER_NORMALS
+  };
+#  define NUM_NORMAL_TYPE 3
+}
+
+#endif
+

src/igl/ONE.h

@@ -0,0 +1,22 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ONE_H
+#define IGL_ONE_H
+namespace igl
+{
+  // Often one needs a reference to a dummy variable containing one as its
+  // value, for example when using AntTweakBar's
+  // TwSetParam( "3D View", "opened", TW_PARAM_INT32, 1, &INT_ONE);
+  const char CHAR_ONE = 1;
+  const int INT_ONE = 1;
+  const unsigned int UNSIGNED_INT_ONE = 1;
+  const double DOUBLE_ONE = 1;
+  const float FLOAT_ONE = 1;
+}
+#endif
+

src/igl/PI.h

@@ -0,0 +1,19 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_PI_H
+#define IGL_PI_H
+namespace igl
+{
+  // Use standard mathematical constants' M_PI if available
+#ifdef M_PI
+  const double PI = M_PI;
+#else
+  const double PI = 3.1415926535897932384626433832795;
+#endif
+}
+#endif

src/igl/REDRUM.h

@@ -0,0 +1,55 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_REDRUM_H
+#define IGL_REDRUM_H
+
+// Q: These should probably be inside the igl namespace. What's the correct
+// way to do that?
+// A: I guess the right way is to not use a macro but a proper function with
+// streams as input and output.
+
+// ANSI color codes for formatting iostream style output
+
+#ifdef IGL_REDRUM_NOOP
+
+// Bold Red, etc.
+#define NORUM(X)     X
+#define REDRUM(X)     X
+#define GREENRUM(X)   X
+#define YELLOWRUM(X)  X
+#define BLUERUM(X)    X
+#define MAGENTARUM(X) X
+#define CYANRUM(X)    X
+// Regular Red, etc.
+#define REDGIN(X)     X
+#define GREENGIN(X)   X
+#define YELLOWGIN(X)  X
+#define BLUEGIN(X)    X
+#define MAGENTAGIN(X) X
+#define CYANGIN(X)    X
+
+#else
+
+// Bold Red, etc.
+#define NORUM(X)       ""<<X<<""
+#define REDRUM(X)      "\e[1m\e[31m"<<X<<"\e[m"
+#define GREENRUM(X)    "\e[1m\e[32m"<<X<<"\e[m"
+#define YELLOWRUM(X)   "\e[1m\e[33m"<<X<<"\e[m"
+#define BLUERUM(X)     "\e[1m\e[34m"<<X<<"\e[m"
+#define MAGENTARUM(X)  "\e[1m\e[35m"<<X<<"\e[m"
+#define CYANRUM(X)     "\e[1m\e[36m"<<X<<"\e[m"
+// Regular Red, etc.
+#define REDGIN(X)      "\e[31m"<<X<<"\e[m"
+#define GREENGIN(X)    "\e[32m"<<X<<"\e[m"
+#define YELLOWGIN(X)   "\e[33m"<<X<<"\e[m"
+#define BLUEGIN(X)     "\e[34m"<<X<<"\e[m"
+#define MAGENTAGIN(X)  "\e[35m"<<X<<"\e[m"
+#define CYANGIN(X)     "\e[36m"<<X<<"\e[m"
+#endif
+
+#endif 

src/igl/STR.h

@@ -0,0 +1,18 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_STR_H
+#define IGL_STR_H
+// http://stackoverflow.com/a/2433143/148668
+#include <string>
+#include <sstream>
+// Suppose you have a function:
+//   void func(std::string c);
+// Then you can write:
+//   func(STR("foo"<<1<<"bar"));
+#define STR(X) static_cast<std::ostringstream&>(std::ostringstream().flush() << X).str()
+#endif 

src/igl/Singular_Value_Decomposition_Givens_QR_Factorization_Kernel.hpp

@@ -0,0 +1,128 @@
+//#####################################################################
+// Copyright (c) 2010-2011, Eftychios Sifakis.
+//
+// Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+//   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+//   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
+//     other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
+// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//#####################################################################
+
+//###########################################################
+// Compute the Givens half-angle, construct the Givens quaternion and the rotation sine/cosine (for the full angle)
+//###########################################################
+
+#ifdef _WIN32
+  #undef max
+  #undef min
+#endif
+
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=SANPIVOT.f*SANPIVOT.f;)                                ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(VANPIVOT,VANPIVOT);)                             ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(VANPIVOT,VANPIVOT);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=(Ssh.f>=Ssmall_number.f)?0xffffffff:0;)               ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_cmpge_ps(Vsh,Vsmall_number);)                           ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_cmp_ps(Vsh,Vsmall_number, _CMP_GE_OS);) //ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_cmpge_ps(Vsh,Vsmall_number);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=Ssh.ui&SANPIVOT.ui;)                                  ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_and_ps(Vsh,VANPIVOT);)                                  ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_and_ps(Vsh,VANPIVOT);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=0.;)                                                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_xor_ps(Vtmp5,Vtmp5);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_xor_ps(Vtmp5,Vtmp5);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=Stmp5.f-SAPIVOT.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vch=_mm_sub_ps(Vtmp5,VAPIVOT);)                                 ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_sub_ps(Vtmp5,VAPIVOT);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=std::max(Sch.f,SAPIVOT.f);)                            ENABLE_SSE_IMPLEMENTATION(Vch=_mm_max_ps(Vch,VAPIVOT);)                                   ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_max_ps(Vch,VAPIVOT);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=std::max(Sch.f,Ssmall_number.f);)                      ENABLE_SSE_IMPLEMENTATION(Vch=_mm_max_ps(Vch,Vsmall_number);)                             ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_max_ps(Vch,Vsmall_number);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp5.ui=(SAPIVOT.f>=Stmp5.f)?0xffffffff:0;)                 ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_cmpge_ps(VAPIVOT,Vtmp5);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_cmp_ps(VAPIVOT,Vtmp5, _CMP_GE_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_cmpge_ps(VAPIVOT,Vtmp5);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sch.f*Sch.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vch,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vch,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                     ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f*Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vtmp1,Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=Sch.f+Stmp1.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vch=_mm_add_ps(Vch,Vtmp1);)                                     ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_add_ps(Vch,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=~Stmp5.ui&Ssh.ui;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_andnot_ps(Vtmp5,Vsh);)                                ENABLE_AVX_IMPLEMENTATION(Vtmp1=Vch;)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=~Stmp5.ui&Sch.ui;)                                  ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_andnot_ps(Vtmp5,Vch);)                                ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_blendv_ps(Vsh,Vch,Vtmp5);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=Stmp5.ui&Sch.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vch=_mm_and_ps(Vtmp5,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_blendv_ps(Vtmp1,Vsh,Vtmp5);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=Stmp5.ui&Ssh.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_and_ps(Vtmp5,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=Sch.ui|Stmp1.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vch=_mm_or_ps(Vch,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=Ssh.ui|Stmp2.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_or_ps(Vsh,Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sch.f*Sch.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vch,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vch,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp1.f+Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(Vtmp1,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=rsqrt(Stmp2.f);)                                     ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_rsqrt_ps(Vtmp2);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_rsqrt_ps(Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp1.f*Sone_half.f;)                                ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vtmp1,Vone_half);)                             ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vtmp1,Vone_half);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f*Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp1,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp2.f*Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vtmp2,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vtmp2,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f+Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_add_ps(Vtmp1,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_add_ps(Vtmp1,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Stmp1.f-Stmp3.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_sub_ps(Vtmp1,Vtmp3);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_sub_ps(Vtmp1,Vtmp3);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=Sch.f*Stmp1.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vch=_mm_mul_ps(Vch,Vtmp1);)                                     ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_mul_ps(Vch,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Stmp1.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vtmp1);)                                     ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Sch.f*Sch.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vc=_mm_mul_ps(Vch,Vch);)                                        ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_mul_ps(Vch,Vch);)ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Ssh.f*Ssh.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vs=_mm_mul_ps(Vsh,Vsh);)                                        ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Sc.f-Ss.f;)                                             ENABLE_SSE_IMPLEMENTATION(Vc=_mm_sub_ps(Vc,Vs);)                                          ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_sub_ps(Vc,Vs);)
+ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Ssh.f*Sch.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vs=_mm_mul_ps(Vsh,Vch);)                                        ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_mul_ps(Vsh,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Ss.f+Ss.f;)                                             ENABLE_SSE_IMPLEMENTATION(Vs=_mm_add_ps(Vs,Vs);)                                          ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_add_ps(Vs,Vs);)
+
+//###########################################################
+// Rotate matrix A
+//###########################################################
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SA11.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VA11);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VA11);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SA21.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VA21);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VA21);)
+ENABLE_SCALAR_IMPLEMENTATION(SA11.f=Sc.f*SA11.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA11=_mm_mul_ps(Vc,VA11);)                                      ENABLE_AVX_IMPLEMENTATION(VA11=_mm256_mul_ps(Vc,VA11);)
+ENABLE_SCALAR_IMPLEMENTATION(SA21.f=Sc.f*SA21.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA21=_mm_mul_ps(Vc,VA21);)                                      ENABLE_AVX_IMPLEMENTATION(VA21=_mm256_mul_ps(Vc,VA21);)
+ENABLE_SCALAR_IMPLEMENTATION(SA11.f=SA11.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA11=_mm_add_ps(VA11,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VA11=_mm256_add_ps(VA11,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SA21.f=SA21.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA21=_mm_sub_ps(VA21,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VA21=_mm256_sub_ps(VA21,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SA12.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VA12);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VA12);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SA22.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VA22);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VA22);)
+ENABLE_SCALAR_IMPLEMENTATION(SA12.f=Sc.f*SA12.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA12=_mm_mul_ps(Vc,VA12);)                                      ENABLE_AVX_IMPLEMENTATION(VA12=_mm256_mul_ps(Vc,VA12);)
+ENABLE_SCALAR_IMPLEMENTATION(SA22.f=Sc.f*SA22.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA22=_mm_mul_ps(Vc,VA22);)                                      ENABLE_AVX_IMPLEMENTATION(VA22=_mm256_mul_ps(Vc,VA22);)
+ENABLE_SCALAR_IMPLEMENTATION(SA12.f=SA12.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA12=_mm_add_ps(VA12,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VA12=_mm256_add_ps(VA12,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SA22.f=SA22.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA22=_mm_sub_ps(VA22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VA22=_mm256_sub_ps(VA22,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SA13.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VA13);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VA13);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SA23.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VA23);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VA23);)
+ENABLE_SCALAR_IMPLEMENTATION(SA13.f=Sc.f*SA13.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA13=_mm_mul_ps(Vc,VA13);)                                      ENABLE_AVX_IMPLEMENTATION(VA13=_mm256_mul_ps(Vc,VA13);)
+ENABLE_SCALAR_IMPLEMENTATION(SA23.f=Sc.f*SA23.f;)                                         ENABLE_SSE_IMPLEMENTATION(VA23=_mm_mul_ps(Vc,VA23);)                                      ENABLE_AVX_IMPLEMENTATION(VA23=_mm256_mul_ps(Vc,VA23);)
+ENABLE_SCALAR_IMPLEMENTATION(SA13.f=SA13.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA13=_mm_add_ps(VA13,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VA13=_mm256_add_ps(VA13,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SA23.f=SA23.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VA23=_mm_sub_ps(VA23,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VA23=_mm256_sub_ps(VA23,Vtmp1);)
+
+//###########################################################
+// Update matrix U
+//###########################################################
+
+#ifdef COMPUTE_U_AS_MATRIX
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SU11.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VU11);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VU11);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SU12.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VU12);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VU12);)
+ENABLE_SCALAR_IMPLEMENTATION(SU11.f=Sc.f*SU11.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU11=_mm_mul_ps(Vc,VU11);)                                      ENABLE_AVX_IMPLEMENTATION(VU11=_mm256_mul_ps(Vc,VU11);)
+ENABLE_SCALAR_IMPLEMENTATION(SU12.f=Sc.f*SU12.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU12=_mm_mul_ps(Vc,VU12);)                                      ENABLE_AVX_IMPLEMENTATION(VU12=_mm256_mul_ps(Vc,VU12);)
+ENABLE_SCALAR_IMPLEMENTATION(SU11.f=SU11.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU11=_mm_add_ps(VU11,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VU11=_mm256_add_ps(VU11,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SU12.f=SU12.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU12=_mm_sub_ps(VU12,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VU12=_mm256_sub_ps(VU12,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SU21.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VU21);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VU21);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SU22.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VU22);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VU22);)
+ENABLE_SCALAR_IMPLEMENTATION(SU21.f=Sc.f*SU21.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU21=_mm_mul_ps(Vc,VU21);)                                      ENABLE_AVX_IMPLEMENTATION(VU21=_mm256_mul_ps(Vc,VU21);)
+ENABLE_SCALAR_IMPLEMENTATION(SU22.f=Sc.f*SU22.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU22=_mm_mul_ps(Vc,VU22);)                                      ENABLE_AVX_IMPLEMENTATION(VU22=_mm256_mul_ps(Vc,VU22);)
+ENABLE_SCALAR_IMPLEMENTATION(SU21.f=SU21.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU21=_mm_add_ps(VU21,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VU21=_mm256_add_ps(VU21,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SU22.f=SU22.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU22=_mm_sub_ps(VU22,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VU22=_mm256_sub_ps(VU22,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SU31.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VU31);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VU31);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SU32.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VU32);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VU32);)
+ENABLE_SCALAR_IMPLEMENTATION(SU31.f=Sc.f*SU31.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU31=_mm_mul_ps(Vc,VU31);)                                      ENABLE_AVX_IMPLEMENTATION(VU31=_mm256_mul_ps(Vc,VU31);)
+ENABLE_SCALAR_IMPLEMENTATION(SU32.f=Sc.f*SU32.f;)                                         ENABLE_SSE_IMPLEMENTATION(VU32=_mm_mul_ps(Vc,VU32);)                                      ENABLE_AVX_IMPLEMENTATION(VU32=_mm256_mul_ps(Vc,VU32);)
+ENABLE_SCALAR_IMPLEMENTATION(SU31.f=SU31.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU31=_mm_add_ps(VU31,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VU31=_mm256_add_ps(VU31,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SU32.f=SU32.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VU32=_mm_sub_ps(VU32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VU32=_mm256_sub_ps(VU32,Vtmp1);)
+#endif

src/igl/Singular_Value_Decomposition_Jacobi_Conjugation_Kernel.hpp

@@ -0,0 +1,118 @@
+//#####################################################################
+// Copyright (c) 2010-2011, Eftychios Sifakis.
+//
+// Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+//   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+//   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
+//     other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
+// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//#####################################################################
+
+//###########################################################
+// Compute the Givens angle (and half-angle) 
+//###########################################################
+
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=SS21.f*Sone_half.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(VS21,Vone_half);)                                ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(VS21,Vone_half);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=SS11.f-SS22.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_sub_ps(VS11,VS22);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_sub_ps(VS11,VS22);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=(Stmp2.f>=Stiny_number.f)?0xffffffff:0;)            ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_cmpge_ps(Vtmp2,Vtiny_number);)                        ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_cmp_ps(Vtmp2,Vtiny_number, _CMP_GE_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_cmpge_ps(Vtmp2,Vtiny_number);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=Stmp1.ui&Ssh.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_and_ps(Vtmp1,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_and_ps(Vtmp1,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=Stmp1.ui&Stmp5.ui;)                                   ENABLE_SSE_IMPLEMENTATION(Vch=_mm_and_ps(Vtmp1,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_blendv_ps(Vone,Vtmp5,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=~Stmp1.ui&Sone.ui;)                                 ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_andnot_ps(Vtmp1,Vone);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=Sch.ui|Stmp2.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vch=_mm_or_ps(Vch,Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ssh.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vsh,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sch.f*Sch.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vch,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vch,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f+Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp1,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=rsqrt(Stmp3.f);)                                     ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_rsqrt_ps(Vtmp3);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_rsqrt_ps(Vtmp3);)
+
+#ifdef USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION
+ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Stmp4.f*Sone_half.f;)                                   ENABLE_SSE_IMPLEMENTATION(Vs=_mm_mul_ps(Vtmp4,Vone_half);)                                ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_mul_ps(Vtmp4,Vone_half);)
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Stmp4.f*Ss.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vc=_mm_mul_ps(Vtmp4,Vs);)                                       ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_mul_ps(Vtmp4,Vs);)
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Stmp4.f*Sc.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vc=_mm_mul_ps(Vtmp4,Vc);)                                       ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_mul_ps(Vtmp4,Vc);)
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Stmp3.f*Sc.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vc=_mm_mul_ps(Vtmp3,Vc);)                                       ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_mul_ps(Vtmp3,Vc);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f+Ss.f;)                                       ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_add_ps(Vtmp4,Vs);)                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_add_ps(Vtmp4,Vs);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Sc.f;)                                       ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vc);)                                    ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vc);)
+#endif
+
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Stmp4.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vtmp4,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vtmp4,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.f=Stmp4.f*Sch.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vch=_mm_mul_ps(Vtmp4,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_mul_ps(Vtmp4,Vch);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Sfour_gamma_squared.f*Stmp1.f;)                      ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vfour_gamma_squared,Vtmp1);)                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vfour_gamma_squared,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.ui=(Stmp2.f<=Stmp1.f)?0xffffffff:0;)                   ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_cmple_ps(Vtmp2,Vtmp1);)                               ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_cmp_ps(Vtmp2,Vtmp1, _CMP_LE_OS);) //ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_cmple_ps(Vtmp2,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Ssine_pi_over_eight.ui&Stmp1.ui;)                   ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_and_ps(Vsine_pi_over_eight,Vtmp1);)                   ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_blendv_ps(Vsh,Vsine_pi_over_eight,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=~Stmp1.ui&Ssh.ui;)                                    ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_andnot_ps(Vtmp1,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.ui=Ssh.ui|Stmp2.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_or_ps(Vsh,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.ui=Scosine_pi_over_eight.ui&Stmp1.ui;)                 ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_and_ps(Vcosine_pi_over_eight,Vtmp1);)                 ENABLE_AVX_IMPLEMENTATION(Vch=_mm256_blendv_ps(Vch,Vcosine_pi_over_eight,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=~Stmp1.ui&Sch.ui;)                                    ENABLE_SSE_IMPLEMENTATION(Vch=_mm_andnot_ps(Vtmp1,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Sch.ui=Sch.ui|Stmp2.ui;)                                     ENABLE_SSE_IMPLEMENTATION(Vch=_mm_or_ps(Vch,Vtmp2);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ssh.f*Ssh.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vsh,Vsh);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vsh,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Sch.f*Sch.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vch,Vch);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vch,Vch);)
+ENABLE_SCALAR_IMPLEMENTATION(Sc.f=Stmp2.f-Stmp1.f;)                                       ENABLE_SSE_IMPLEMENTATION(Vc=_mm_sub_ps(Vtmp2,Vtmp1);)                                    ENABLE_AVX_IMPLEMENTATION(Vc=_mm256_sub_ps(Vtmp2,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Sch.f*Ssh.f;)                                           ENABLE_SSE_IMPLEMENTATION(Vs=_mm_mul_ps(Vch,Vsh);)                                        ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_mul_ps(Vch,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Ss.f=Ss.f+Ss.f;)                                             ENABLE_SSE_IMPLEMENTATION(Vs=_mm_add_ps(Vs,Vs);)                                          ENABLE_AVX_IMPLEMENTATION(Vs=_mm256_add_ps(Vs,Vs);)
+
+//###########################################################
+// Perform the actual Givens conjugation
+//###########################################################
+
+#ifndef USE_ACCURATE_RSQRT_IN_JACOBI_CONJUGATION
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Stmp1.f+Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_add_ps(Vtmp1,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_add_ps(Vtmp1,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SS33.f=SS33.f*Stmp3.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS33=_mm_mul_ps(VS33,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(VS33=_mm256_mul_ps(VS33,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(SS31.f=SS31.f*Stmp3.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS31=_mm_mul_ps(VS31,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(VS31=_mm256_mul_ps(VS31,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(SS32.f=SS32.f*Stmp3.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS32=_mm_mul_ps(VS32,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(VS32=_mm256_mul_ps(VS32,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(SS33.f=SS33.f*Stmp3.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS33=_mm_mul_ps(VS33,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(VS33=_mm256_mul_ps(VS33,Vtmp3);)
+#endif
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ss.f*SS31.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vs,VS31);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vs,VS31);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*SS32.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,VS32);)                                     ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,VS32);)
+ENABLE_SCALAR_IMPLEMENTATION(SS31.f=Sc.f*SS31.f;)                                         ENABLE_SSE_IMPLEMENTATION(VS31=_mm_mul_ps(Vc,VS31);)                                      ENABLE_AVX_IMPLEMENTATION(VS31=_mm256_mul_ps(Vc,VS31);)
+ENABLE_SCALAR_IMPLEMENTATION(SS32.f=Sc.f*SS32.f;)                                         ENABLE_SSE_IMPLEMENTATION(VS32=_mm_mul_ps(Vc,VS32);)                                      ENABLE_AVX_IMPLEMENTATION(VS32=_mm256_mul_ps(Vc,VS32);)
+ENABLE_SCALAR_IMPLEMENTATION(SS31.f=Stmp2.f+SS31.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS31=_mm_add_ps(Vtmp2,VS31);)                                   ENABLE_AVX_IMPLEMENTATION(VS31=_mm256_add_ps(Vtmp2,VS31);)
+ENABLE_SCALAR_IMPLEMENTATION(SS32.f=SS32.f-Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS32=_mm_sub_ps(VS32,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VS32=_mm256_sub_ps(VS32,Vtmp1);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ss.f*Ss.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vs,Vs);)                                       ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vs,Vs);)         
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=SS22.f*Stmp2.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(VS22,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(VS22,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=SS11.f*Stmp2.f;)                                     ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(VS11,Vtmp2);)                                  ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(VS11,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sc.f*Sc.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vc,Vc);)                                       ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vc,Vc);)
+ENABLE_SCALAR_IMPLEMENTATION(SS11.f=SS11.f*Stmp4.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS11=_mm_mul_ps(VS11,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(VS11=_mm256_mul_ps(VS11,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(SS22.f=SS22.f*Stmp4.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS22=_mm_mul_ps(VS22,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(VS22=_mm256_mul_ps(VS22,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(SS11.f=SS11.f+Stmp1.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS11=_mm_add_ps(VS11,Vtmp1);)                                   ENABLE_AVX_IMPLEMENTATION(VS11=_mm256_add_ps(VS11,Vtmp1);)
+ENABLE_SCALAR_IMPLEMENTATION(SS22.f=SS22.f+Stmp3.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS22=_mm_add_ps(VS22,Vtmp3);)                                   ENABLE_AVX_IMPLEMENTATION(VS22=_mm256_add_ps(VS22,Vtmp3);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Stmp4.f-Stmp2.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_sub_ps(Vtmp4,Vtmp2);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_sub_ps(Vtmp4,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=SS21.f+SS21.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_add_ps(VS21,VS21);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_add_ps(VS21,VS21);)
+ENABLE_SCALAR_IMPLEMENTATION(SS21.f=SS21.f*Stmp4.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS21=_mm_mul_ps(VS21,Vtmp4);)                                   ENABLE_AVX_IMPLEMENTATION(VS21=_mm256_mul_ps(VS21,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp4.f=Sc.f*Ss.f;)                                          ENABLE_SSE_IMPLEMENTATION(Vtmp4=_mm_mul_ps(Vc,Vs);)                                       ENABLE_AVX_IMPLEMENTATION(Vtmp4=_mm256_mul_ps(Vc,Vs);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Stmp2.f*Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vtmp2,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vtmp2,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp5.f=Stmp5.f*Stmp4.f;)                                    ENABLE_SSE_IMPLEMENTATION(Vtmp5=_mm_mul_ps(Vtmp5,Vtmp4);)                                 ENABLE_AVX_IMPLEMENTATION(Vtmp5=_mm256_mul_ps(Vtmp5,Vtmp4);)
+ENABLE_SCALAR_IMPLEMENTATION(SS11.f=SS11.f+Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS11=_mm_add_ps(VS11,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VS11=_mm256_add_ps(VS11,Vtmp2);)
+ENABLE_SCALAR_IMPLEMENTATION(SS21.f=SS21.f-Stmp5.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS21=_mm_sub_ps(VS21,Vtmp5);)                                   ENABLE_AVX_IMPLEMENTATION(VS21=_mm256_sub_ps(VS21,Vtmp5);)
+ENABLE_SCALAR_IMPLEMENTATION(SS22.f=SS22.f-Stmp2.f;)                                      ENABLE_SSE_IMPLEMENTATION(VS22=_mm_sub_ps(VS22,Vtmp2);)                                   ENABLE_AVX_IMPLEMENTATION(VS22=_mm256_sub_ps(VS22,Vtmp2);)
+
+//###########################################################
+// Compute the cumulative rotation, in quaternion form
+//###########################################################
+
+ENABLE_SCALAR_IMPLEMENTATION(Stmp1.f=Ssh.f*Sqvvx.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vtmp1=_mm_mul_ps(Vsh,Vqvvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp1=_mm256_mul_ps(Vsh,Vqvvx);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp2.f=Ssh.f*Sqvvy.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vtmp2=_mm_mul_ps(Vsh,Vqvvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp2=_mm256_mul_ps(Vsh,Vqvvy);)
+ENABLE_SCALAR_IMPLEMENTATION(Stmp3.f=Ssh.f*Sqvvz.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vtmp3=_mm_mul_ps(Vsh,Vqvvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vtmp3=_mm256_mul_ps(Vsh,Vqvvz);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssh.f=Ssh.f*Sqvs.f;)                                         ENABLE_SSE_IMPLEMENTATION(Vsh=_mm_mul_ps(Vsh,Vqvs);)                                      ENABLE_AVX_IMPLEMENTATION(Vsh=_mm256_mul_ps(Vsh,Vqvs);)
+
+ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sch.f*Sqvs.f;)                                        ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_mul_ps(Vch,Vqvs);)                                     ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_mul_ps(Vch,Vqvs);)
+ENABLE_SCALAR_IMPLEMENTATION(Sqvvx.f=Sch.f*Sqvvx.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vqvvx=_mm_mul_ps(Vch,Vqvvx);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvvx=_mm256_mul_ps(Vch,Vqvvx);)
+ENABLE_SCALAR_IMPLEMENTATION(Sqvvy.f=Sch.f*Sqvvy.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vqvvy=_mm_mul_ps(Vch,Vqvvy);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvvy=_mm256_mul_ps(Vch,Vqvvy);)
+ENABLE_SCALAR_IMPLEMENTATION(Sqvvz.f=Sch.f*Sqvvz.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vqvvz=_mm_mul_ps(Vch,Vqvvz);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvvz=_mm256_mul_ps(Vch,Vqvvz);)
+
+ENABLE_SCALAR_IMPLEMENTATION(SQVVZ.f=SQVVZ.f+Ssh.f;)                                      ENABLE_SSE_IMPLEMENTATION(VQVVZ=_mm_add_ps(VQVVZ,Vsh);)                                   ENABLE_AVX_IMPLEMENTATION(VQVVZ=_mm256_add_ps(VQVVZ,Vsh);)
+ENABLE_SCALAR_IMPLEMENTATION(Sqvs.f=Sqvs.f-STMP3.f;)                                      ENABLE_SSE_IMPLEMENTATION(Vqvs=_mm_sub_ps(Vqvs,VTMP3);)                                   ENABLE_AVX_IMPLEMENTATION(Vqvs=_mm256_sub_ps(Vqvs,VTMP3);)
+ENABLE_SCALAR_IMPLEMENTATION(SQVVX.f=SQVVX.f+STMP2.f;)                                    ENABLE_SSE_IMPLEMENTATION(VQVVX=_mm_add_ps(VQVVX,VTMP2);)                                 ENABLE_AVX_IMPLEMENTATION(VQVVX=_mm256_add_ps(VQVVX,VTMP2);)
+ENABLE_SCALAR_IMPLEMENTATION(SQVVY.f=SQVVY.f-STMP1.f;)                                    ENABLE_SSE_IMPLEMENTATION(VQVVY=_mm_sub_ps(VQVVY,VTMP1);)                                 ENABLE_AVX_IMPLEMENTATION(VQVVY=_mm256_sub_ps(VQVVY,VTMP1);)

src/igl/Singular_Value_Decomposition_Kernel_Declarations.hpp

@@ -0,0 +1,137 @@
+//#####################################################################
+// Copyright (c) 2010-2011, Eftychios Sifakis.
+//
+// Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+//   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+//   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
+//     other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
+// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//#####################################################################
+
+//###########################################################
+// Local variable declarations
+//###########################################################
+
+#ifdef PRINT_DEBUGGING_OUTPUT
+
+#ifdef USE_SSE_IMPLEMENTATION
+    float buf[4];
+    float A11,A21,A31,A12,A22,A32,A13,A23,A33;
+    float S11,S21,S31,S22,S32,S33;
+#ifdef COMPUTE_V_AS_QUATERNION
+    float QVS,QVVX,QVVY,QVVZ;
+#endif
+#ifdef COMPUTE_V_AS_MATRIX
+    float V11,V21,V31,V12,V22,V32,V13,V23,V33;
+#endif
+#ifdef COMPUTE_U_AS_QUATERNION
+    float QUS,QUVX,QUVY,QUVZ;
+#endif
+#ifdef COMPUTE_U_AS_MATRIX
+    float U11,U21,U31,U12,U22,U32,U13,U23,U33;
+#endif
+#endif
+
+#ifdef USE_AVX_IMPLEMENTATION
+    float buf[8];
+    float A11,A21,A31,A12,A22,A32,A13,A23,A33;
+    float S11,S21,S31,S22,S32,S33;
+#ifdef COMPUTE_V_AS_QUATERNION
+    float QVS,QVVX,QVVY,QVVZ;
+#endif
+#ifdef COMPUTE_V_AS_MATRIX
+    float V11,V21,V31,V12,V22,V32,V13,V23,V33;
+#endif
+#ifdef COMPUTE_U_AS_QUATERNION
+    float QUS,QUVX,QUVY,QUVZ;
+#endif
+#ifdef COMPUTE_U_AS_MATRIX
+    float U11,U21,U31,U12,U22,U32,U13,U23,U33;
+#endif
+#endif
+
+#endif
+
+const float Four_Gamma_Squared=sqrt(8.)+3.;
+const float Sine_Pi_Over_Eight=.5*sqrt(2.-sqrt(2.));
+const float Cosine_Pi_Over_Eight=.5*sqrt(2.+sqrt(2.));
+
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sfour_gamma_squared;)       ENABLE_SSE_IMPLEMENTATION(__m128 Vfour_gamma_squared;)                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vfour_gamma_squared;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssine_pi_over_eight;)       ENABLE_SSE_IMPLEMENTATION(__m128 Vsine_pi_over_eight;)                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vsine_pi_over_eight;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Scosine_pi_over_eight;)     ENABLE_SSE_IMPLEMENTATION(__m128 Vcosine_pi_over_eight;)                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vcosine_pi_over_eight;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sone_half;)                 ENABLE_SSE_IMPLEMENTATION(__m128 Vone_half;)                                              ENABLE_AVX_IMPLEMENTATION(__m256 Vone_half;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sone;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vone;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vone;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stiny_number;)              ENABLE_SSE_IMPLEMENTATION(__m128 Vtiny_number;)                                           ENABLE_AVX_IMPLEMENTATION(__m256 Vtiny_number;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssmall_number;)             ENABLE_SSE_IMPLEMENTATION(__m128 Vsmall_number;)                                          ENABLE_AVX_IMPLEMENTATION(__m256 Vsmall_number;)
+
+ENABLE_SCALAR_IMPLEMENTATION(Sfour_gamma_squared.f=Four_Gamma_Squared;)                   ENABLE_SSE_IMPLEMENTATION(Vfour_gamma_squared=_mm_set1_ps(Four_Gamma_Squared);)           ENABLE_AVX_IMPLEMENTATION(Vfour_gamma_squared=_mm256_set1_ps(Four_Gamma_Squared);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssine_pi_over_eight.f=Sine_Pi_Over_Eight;)                   ENABLE_SSE_IMPLEMENTATION(Vsine_pi_over_eight=_mm_set1_ps(Sine_Pi_Over_Eight);)           ENABLE_AVX_IMPLEMENTATION(Vsine_pi_over_eight=_mm256_set1_ps(Sine_Pi_Over_Eight);)
+ENABLE_SCALAR_IMPLEMENTATION(Scosine_pi_over_eight.f=Cosine_Pi_Over_Eight;)               ENABLE_SSE_IMPLEMENTATION(Vcosine_pi_over_eight=_mm_set1_ps(Cosine_Pi_Over_Eight);)       ENABLE_AVX_IMPLEMENTATION(Vcosine_pi_over_eight=_mm256_set1_ps(Cosine_Pi_Over_Eight);)
+ENABLE_SCALAR_IMPLEMENTATION(Sone_half.f=.5;)                                             ENABLE_SSE_IMPLEMENTATION(Vone_half=_mm_set1_ps(.5);)                                     ENABLE_AVX_IMPLEMENTATION(Vone_half=_mm256_set1_ps(.5);)
+ENABLE_SCALAR_IMPLEMENTATION(Sone.f=1.;)                                                  ENABLE_SSE_IMPLEMENTATION(Vone=_mm_set1_ps(1.);)                                          ENABLE_AVX_IMPLEMENTATION(Vone=_mm256_set1_ps(1.);)
+ENABLE_SCALAR_IMPLEMENTATION(Stiny_number.f=1.e-20;)                                      ENABLE_SSE_IMPLEMENTATION(Vtiny_number=_mm_set1_ps(1.e-20);)                              ENABLE_AVX_IMPLEMENTATION(Vtiny_number=_mm256_set1_ps(1.e-20);)
+ENABLE_SCALAR_IMPLEMENTATION(Ssmall_number.f=1.e-12;)                                     ENABLE_SSE_IMPLEMENTATION(Vsmall_number=_mm_set1_ps(1.e-12);)                             ENABLE_AVX_IMPLEMENTATION(Vsmall_number=_mm256_set1_ps(1.e-12);)
+
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va11;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va21;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va31;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va12;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va22;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va32;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va13;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va23;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sa33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Va33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Va33;)
+
+#ifdef COMPUTE_V_AS_MATRIX
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv11;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv21;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv31;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv12;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv22;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv32;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv13;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv23;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sv33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vv33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vv33;)
+#endif
+
+#ifdef COMPUTE_V_AS_QUATERNION
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvs;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vqvs;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqvs;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvx;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvx;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvy;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvy;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sqvvz;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vqvvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vqvvz;)
+#endif
+
+#ifdef COMPUTE_U_AS_MATRIX
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su11;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu11;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu11;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su21;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu21;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu21;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su31;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu31;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu31;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su12;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu12;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu12;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su22;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu22;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu22;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su32;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu32;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu32;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su13;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu13;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu13;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su23;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu23;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu23;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Su33;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vu33;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vu33;)
+#endif
+
+#ifdef COMPUTE_U_AS_QUATERNION
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squs;)                      ENABLE_SSE_IMPLEMENTATION(__m128 Vqus;)                                                   ENABLE_AVX_IMPLEMENTATION(__m256 Vqus;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvx;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvx;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvx;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvy;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvy;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvy;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Squvz;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vquvz;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vquvz;)
+#endif
+
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sc;)                        ENABLE_SSE_IMPLEMENTATION(__m128 Vc;)                                                     ENABLE_AVX_IMPLEMENTATION(__m256 Vc;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ss;)                        ENABLE_SSE_IMPLEMENTATION(__m128 Vs;)                                                     ENABLE_AVX_IMPLEMENTATION(__m256 Vs;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Sch;)                       ENABLE_SSE_IMPLEMENTATION(__m128 Vch;)                                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vch;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Ssh;)                       ENABLE_SSE_IMPLEMENTATION(__m128 Vsh;)                                                    ENABLE_AVX_IMPLEMENTATION(__m256 Vsh;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp1;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp1;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp1;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp2;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp2;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp2;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp3;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp3;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp3;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp4;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp4;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp4;)
+ENABLE_SCALAR_IMPLEMENTATION(union {float f;unsigned int ui;} Stmp5;)                     ENABLE_SSE_IMPLEMENTATION(__m128 Vtmp5;)                                                  ENABLE_AVX_IMPLEMENTATION(__m256 Vtmp5;)

src/igl/Singular_Value_Decomposition_Preamble.hpp

@@ -0,0 +1,78 @@
+//#####################################################################
+// Copyright (c) 2010-2011, Eftychios Sifakis.
+//
+// Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
+//   * Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
+//   * Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or
+//     other materials provided with the distribution.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING,
+// BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT
+// SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
+// DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+// NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+//#####################################################################
+
+#ifdef PRINT_DEBUGGING_OUTPUT
+#include <iomanip>
+#include <iostream>
+#endif
+
+// Prevent warnings
+#ifdef ENABLE_SCALAR_IMPLEMENTATION
+#  undef ENABLE_SCALAR_IMPLEMENTATION
+#endif
+#ifdef ENABLE_SSE_IMPLEMENTATION
+#  undef ENABLE_SSE_IMPLEMENTATION
+#endif
+#ifdef ENABLE_AVX_IMPLEMENTATION
+#  undef ENABLE_AVX_IMPLEMENTATION
+#endif
+
+#ifdef USE_SCALAR_IMPLEMENTATION
+#define ENABLE_SCALAR_IMPLEMENTATION(X) X
+#else
+#define ENABLE_SCALAR_IMPLEMENTATION(X)
+#endif
+
+#ifdef USE_SSE_IMPLEMENTATION
+#define ENABLE_SSE_IMPLEMENTATION(X) X
+#else
+#define ENABLE_SSE_IMPLEMENTATION(X)
+#endif
+
+#ifdef USE_AVX_IMPLEMENTATION
+#include <immintrin.h>
+#define ENABLE_AVX_IMPLEMENTATION(X) X
+#else
+// Stefan: removed include. Why does it import MMX instructions, shouldn't this be under the #ifdef USE_SSE_IMPLEMENTATION above?
+//#include <xmmintrin.h>
+#define ENABLE_AVX_IMPLEMENTATION(X)
+#endif
+
+#ifdef USE_SCALAR_IMPLEMENTATION
+// Alec: Why is this using sse intrinsics if it's supposed to be the scalar
+// implementation?
+#ifdef __SSE__
+#include <mmintrin.h>
+// Changed to inline
+inline float rsqrt(const float f)
+{
+    float buf[4];
+    buf[0]=f;
+    __m128 v=_mm_loadu_ps(buf);
+    v=_mm_rsqrt_ss(v);
+    _mm_storeu_ps(buf,v);
+    return buf[0];
+}
+#else
+#include <cmath>
+inline float rsqrt(const float f)
+{
+  return 1./sqrtf(f);
+}
+#endif
+#endif
+
+

src/igl/SolverStatus.h

@@ -0,0 +1,23 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_SOLVER_STATUS_H
+#define IGL_SOLVER_STATUS_H
+namespace igl
+{
+  enum SolverStatus
+  {
+    // Good
+    SOLVER_STATUS_CONVERGED = 0,
+    // OK
+    SOLVER_STATUS_MAX_ITER = 1,
+    // Bad
+    SOLVER_STATUS_ERROR = 2,
+    NUM_SOLVER_STATUSES = 3,
+  };
+};
+#endif

src/igl/SortableRow.h

@@ -0,0 +1,70 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_SORTABLE_ROW_H
+#define IGL_SORTABLE_ROW_H
+
+// Simple class to contain a rowvector which allows rowwise sorting and
+// reordering
+#include <Eigen/Core>
+
+namespace igl
+{
+  // Templates:
+  //   T  should be a matrix that implements .size(), and operator(int i)
+  template <typename T>
+  class SortableRow
+  {
+    public:
+      T data;
+    public:
+      SortableRow():data(){};
+      SortableRow(const T & data):data(data){};
+      bool operator<(const SortableRow & that) const
+      {
+        // Get reference so that I can use parenthesis
+        const SortableRow<T> & THIS = *this;
+        // Lexicographical
+        int minc = (THIS.data.size() < that.data.size()? 
+            THIS.data.size() : that.data.size());
+        // loop over columns
+        for(int i = 0;i<minc;i++)
+        {
+          if(THIS.data(i) == that.data(i))
+          {
+            continue;
+          }
+          return THIS.data(i) < that.data(i);
+        }
+        // All characters the same, comes done to length
+        return THIS.data.size()<that.data.size();
+      };
+      bool operator==(const SortableRow & that) const
+      {
+        // Get reference so that I can use parenthesis
+        const SortableRow<T> & THIS = *this;
+        if(THIS.data.size() != that.data.size())
+        {
+          return false;
+        }
+        for(int i = 0;i<THIS.data.size();i++)
+        {
+          if(THIS.data(i) != that.data(i))
+          {
+            return false;
+          }
+        }
+        return true;
+      };
+      bool operator!=(const SortableRow & that) const
+      {
+        return !(*this == that);
+      };
+  };
+}
+
+#endif

src/igl/Timer.h

@@ -0,0 +1,179 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+// High Resolution Timer.
+//
+// Resolution on Mac (clock tick)
+// Resolution on Linux (1 us not tested)
+// Resolution on Windows (clock tick not tested)
+
+#ifndef IGL_TIMER_H
+#define IGL_TIMER_H
+
+#ifdef WIN32   // Windows system specific
+#include <windows.h>
+#elif __APPLE__ // Unix based system specific
+#include <mach/mach_time.h> // for mach_absolute_time
+#else
+#include <sys/time.h>
+#endif
+#include <cstddef>
+
+namespace igl
+{
+  class Timer
+  {
+  public:
+    // default constructor
+    Timer():
+      stopped(0),
+#ifdef WIN32
+      frequency(),
+      startCount(),
+      endCount()
+#elif __APPLE__
+      startCount(0),
+      endCount(0)
+#else
+      startCount(),
+      endCount()
+#endif
+    {
+#ifdef WIN32
+      QueryPerformanceFrequency(&frequency);
+      startCount.QuadPart = 0;
+      endCount.QuadPart = 0;
+#elif __APPLE__
+      startCount = 0;
+      endCount = 0;
+#else
+      startCount.tv_sec = startCount.tv_usec = 0;
+      endCount.tv_sec = endCount.tv_usec = 0;
+#endif
+
+      stopped = 0;
+    }
+    // default destructor
+    ~Timer()                     
+    {
+
+    }
+
+#ifdef __APPLE__
+    //Raw mach_absolute_times going in, difference in seconds out
+    double subtractTimes( uint64_t endTime, uint64_t startTime )
+    {
+      uint64_t difference = endTime - startTime;
+      static double conversion = 0.0;
+
+      if( conversion == 0.0 )
+      {
+        mach_timebase_info_data_t info;
+        kern_return_t err = mach_timebase_info( &info );
+
+        //Convert the timebase into seconds
+        if( err == 0  )
+          conversion = 1e-9 * (double) info.numer / (double) info.denom;
+      }
+
+      return conversion * (double) difference;
+    }
+#endif
+
+    // start timer
+    void   start()               
+    {
+      stopped = 0; // reset stop flag
+#ifdef WIN32
+      QueryPerformanceCounter(&startCount);
+#elif __APPLE__
+      startCount = mach_absolute_time();
+#else
+      gettimeofday(&startCount, NULL);
+#endif
+
+    }
+
+    // stop the timer
+    void   stop()                
+    {
+      stopped = 1; // set timer stopped flag
+
+#ifdef WIN32
+      QueryPerformanceCounter(&endCount);
+#elif __APPLE__
+      endCount = mach_absolute_time();
+#else
+      gettimeofday(&endCount, NULL);
+#endif
+
+    }
+    // get elapsed time in second
+    double getElapsedTime()      
+    {
+      return this->getElapsedTimeInSec();
+    }
+    // get elapsed time in second (same as getElapsedTime)
+    double getElapsedTimeInSec() 
+    {
+      return this->getElapsedTimeInMicroSec() * 0.000001;
+    }
+
+    // get elapsed time in milli-second
+    double getElapsedTimeInMilliSec()
+    {
+      return this->getElapsedTimeInMicroSec() * 0.001;
+    }
+    // get elapsed time in micro-second
+    double getElapsedTimeInMicroSec()          
+    {
+      double startTimeInMicroSec = 0;
+      double endTimeInMicroSec = 0;
+
+#ifdef WIN32
+      if(!stopped)
+        QueryPerformanceCounter(&endCount);
+
+      startTimeInMicroSec = 
+        startCount.QuadPart * (1000000.0 / frequency.QuadPart);
+      endTimeInMicroSec = endCount.QuadPart * (1000000.0 / frequency.QuadPart);
+#elif __APPLE__
+      if (!stopped)
+        endCount = mach_absolute_time();
+
+      return subtractTimes(endCount,startCount)/1e-6;
+#else
+      if(!stopped)
+        gettimeofday(&endCount, NULL);
+
+      startTimeInMicroSec = 
+        (startCount.tv_sec * 1000000.0) + startCount.tv_usec;
+      endTimeInMicroSec = (endCount.tv_sec * 1000000.0) + endCount.tv_usec;
+#endif
+
+      return endTimeInMicroSec - startTimeInMicroSec;
+    }
+
+  private:
+    // stop flag 
+    int    stopped;               
+#ifdef WIN32
+    // ticks per second
+    LARGE_INTEGER frequency;      
+    LARGE_INTEGER startCount;     
+    LARGE_INTEGER endCount;       
+#elif __APPLE__
+    uint64_t startCount;           
+    uint64_t endCount;             
+#else
+    timeval startCount;           
+    timeval endCount;             
+#endif
+  };
+}
+#endif // TIMER_H_DEF
+

src/igl/Viewport.h

@@ -0,0 +1,69 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_VIEWPORT_H
+#define IGL_VIEWPORT_H
+
+namespace igl
+{
+  // Simple Viewport class for an opengl context. Handles reshaping and mouse.
+  struct Viewport
+  {
+    int x,y,width,height;
+    // Constructors
+    Viewport(
+      const int x=0, 
+      const int y=0, 
+      const int width=0,
+      const int height=0):
+      x(x),
+      y(y),
+      width(width),
+      height(height)
+    {
+    };
+    virtual ~Viewport(){}
+    void reshape(
+      const int x, 
+      const int y, 
+      const int width,
+      const int height)
+    {
+      this->x = x;
+      this->y = y;
+      this->width = width;
+      this->height = height;
+    };
+    // Given mouse_x,mouse_y on the entire window return mouse_x, mouse_y in
+    // this viewport.
+    //
+    // Inputs:
+    //   my  mouse y-coordinate
+    //   wh  window height
+    // Returns y-coordinate in viewport
+    int mouse_y(const int my,const int wh)
+    {
+      return my - (wh - height - y);
+    }
+    // Inputs:
+    //   mx  mouse x-coordinate
+    // Returns x-coordinate in viewport
+    int mouse_x(const int mx)
+    {
+      return mx - x;
+    }
+    // Returns whether point (mx,my) is in extend of Viewport
+    bool inside(const int mx, const int my) const
+    {
+      return 
+        mx >= x && my >= y && 
+        mx < x+width && my < y+height;
+    }
+  };
+}
+
+#endif

src/igl/WindingNumberAABB.h

@@ -0,0 +1,377 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+
+// # MUTUAL DEPENDENCY ISSUE FOR HEADER ONLY VERSION
+// MUST INCLUDE winding_number.h first before guard:
+#include "winding_number.h"
+
+#ifndef IGL_WINDINGNUMBERAABB_H
+#define IGL_WINDINGNUMBERAABB_H
+#include "WindingNumberTree.h"
+
+namespace igl
+{
+  template <
+    typename Point,
+    typename DerivedV, 
+    typename DerivedF >
+  class WindingNumberAABB : public WindingNumberTree<Point,DerivedV,DerivedF>
+  {
+    protected:
+      Point min_corner;
+      Point max_corner;
+      typename DerivedV::Scalar total_positive_area;
+    public: 
+      enum SplitMethod
+      {
+        CENTER_ON_LONGEST_AXIS = 0,
+        MEDIAN_ON_LONGEST_AXIS = 1,
+        NUM_SPLIT_METHODS = 2
+      } split_method;
+    public:
+      inline WindingNumberAABB():
+        total_positive_area(std::numeric_limits<typename DerivedV::Scalar>::infinity()),
+        split_method(MEDIAN_ON_LONGEST_AXIS)
+      {}
+      inline WindingNumberAABB(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedF> & F);
+      inline WindingNumberAABB(
+        const WindingNumberTree<Point,DerivedV,DerivedF> & parent,
+        const Eigen::MatrixBase<DerivedF> & F);
+      // Initialize some things
+      inline void set_mesh(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedF> & F);
+      inline void init();
+      inline bool inside(const Point & p) const;
+      inline virtual void grow();
+      // Compute min and max corners
+      inline void compute_min_max_corners();
+      inline typename DerivedV::Scalar max_abs_winding_number(const Point & p) const;
+      inline typename DerivedV::Scalar max_simple_abs_winding_number(const Point & p) const;
+  };
+}
+
+// Implementation
+
+#include "winding_number.h"
+
+#include "barycenter.h"
+#include "median.h"
+#include "doublearea.h"
+#include "per_face_normals.h"
+
+#include <limits>
+#include <vector>
+#include <iostream>
+
+// Minimum number of faces in a hierarchy element (this is probably dependent
+// on speed of machine and compiler optimization)
+#ifndef WindingNumberAABB_MIN_F
+#  define WindingNumberAABB_MIN_F 100
+#endif
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberAABB<Point,DerivedV,DerivedF>::set_mesh(
+    const Eigen::MatrixBase<DerivedV> & V,
+    const Eigen::MatrixBase<DerivedF> & F)
+{
+  igl::WindingNumberTree<Point,DerivedV,DerivedF>::set_mesh(V,F);
+  init();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberAABB<Point,DerivedV,DerivedF>::init()
+{
+  using namespace Eigen;
+  assert(max_corner.size() == 3);
+  assert(min_corner.size() == 3);
+  compute_min_max_corners();
+  Eigen::Matrix<typename DerivedV::Scalar,Eigen::Dynamic,1> dblA;
+  doublearea(this->getV(),this->getF(),dblA);
+  total_positive_area = dblA.sum()/2.0;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberAABB<Point,DerivedV,DerivedF>::WindingNumberAABB(
+  const Eigen::MatrixBase<DerivedV> & V,
+  const Eigen::MatrixBase<DerivedF> & F):
+  WindingNumberTree<Point,DerivedV,DerivedF>(V,F),
+  min_corner(),
+  max_corner(),
+  total_positive_area(
+    std::numeric_limits<typename DerivedV::Scalar>::infinity()),
+  split_method(MEDIAN_ON_LONGEST_AXIS)
+{
+  init();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberAABB<Point,DerivedV,DerivedF>::WindingNumberAABB(
+  const WindingNumberTree<Point,DerivedV,DerivedF> & parent,
+  const Eigen::MatrixBase<DerivedF> & F):
+  WindingNumberTree<Point,DerivedV,DerivedF>(parent,F),
+  min_corner(),
+  max_corner(),
+  total_positive_area(
+    std::numeric_limits<typename DerivedV::Scalar>::infinity()),
+  split_method(MEDIAN_ON_LONGEST_AXIS)
+{
+  init();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberAABB<Point,DerivedV,DerivedF>::grow()
+{
+  using namespace std;
+  using namespace Eigen;
+  // Clear anything that already exists
+  this->delete_children();
+
+  //cout<<"cap.rows(): "<<this->getcap().rows()<<endl;
+  //cout<<"F.rows(): "<<this->getF().rows()<<endl;
+
+  // Base cases
+  if(
+    this->getF().rows() <= (WindingNumberAABB_MIN_F>0?WindingNumberAABB_MIN_F:0) ||
+    (this->getcap().rows() - 2) >= this->getF().rows())
+  {
+    // Don't grow
+    return;
+  }
+
+  // Compute longest direction
+  int max_d = -1;
+  typename DerivedV::Scalar max_len = 
+    -numeric_limits<typename DerivedV::Scalar>::infinity();
+  for(int d = 0;d<min_corner.size();d++)
+  {
+    if( (max_corner[d] - min_corner[d]) > max_len )
+    {
+      max_len = (max_corner[d] - min_corner[d]);
+      max_d = d;
+    }
+  }
+  // Compute facet barycenters
+  Eigen::Matrix<typename DerivedV::Scalar,Eigen::Dynamic,Eigen::Dynamic> BC;
+  barycenter(this->getV(),this->getF(),BC);
+
+
+  // Blerg, why is selecting rows so difficult
+
+  typename DerivedV::Scalar split_value;
+  // Split in longest direction
+  switch(split_method)
+  {
+    case MEDIAN_ON_LONGEST_AXIS:
+      // Determine median
+      median(BC.col(max_d),split_value);
+      break;
+    default:
+      assert(false);
+    case CENTER_ON_LONGEST_AXIS:
+      split_value = 0.5*(max_corner[max_d] + min_corner[max_d]);
+      break;
+  }
+  //cout<<"c: "<<0.5*(max_corner[max_d] + min_corner[max_d])<<" "<<
+  //  "m: "<<split_value<<endl;;
+
+  vector<int> id( this->getF().rows());
+  for(int i = 0;i<this->getF().rows();i++)
+  {
+    if(BC(i,max_d) <= split_value)
+    {
+      id[i] = 0; //left
+    }else
+    {
+      id[i] = 1; //right
+    }
+  }
+
+  const int lefts = (int) count(id.begin(),id.end(),0);
+  const int rights = (int) count(id.begin(),id.end(),1);
+  if(lefts == 0 || rights == 0)
+  {
+    // badly balanced base case (could try to recut)
+    return;
+  }
+  assert(lefts+rights == this->getF().rows());
+  DerivedF leftF(lefts,  this->getF().cols());
+  DerivedF rightF(rights,this->getF().cols());
+  int left_i = 0;
+  int right_i = 0;
+  for(int i = 0;i<this->getF().rows();i++)
+  {
+    if(id[i] == 0)
+    {
+      leftF.row(left_i++) = this->getF().row(i);
+    }else if(id[i] == 1)
+    {
+      rightF.row(right_i++) = this->getF().row(i);
+    }else
+    {
+      assert(false);
+    }
+  }
+  assert(right_i == rightF.rows());
+  assert(left_i == leftF.rows());
+  // Finally actually grow children and Recursively grow
+  WindingNumberAABB<Point,DerivedV,DerivedF> * leftWindingNumberAABB = 
+    new WindingNumberAABB<Point,DerivedV,DerivedF>(*this,leftF);
+  leftWindingNumberAABB->grow();
+  this->children.push_back(leftWindingNumberAABB);
+  WindingNumberAABB<Point,DerivedV,DerivedF> * rightWindingNumberAABB = 
+    new WindingNumberAABB<Point,DerivedV,DerivedF>(*this,rightF);
+  rightWindingNumberAABB->grow();
+  this->children.push_back(rightWindingNumberAABB);
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline bool igl::WindingNumberAABB<Point,DerivedV,DerivedF>::inside(const Point & p) const
+{
+  assert(p.size() == max_corner.size());
+  assert(p.size() == min_corner.size());
+  for(int i = 0;i<p.size();i++)
+  {
+    //// Perfect matching is **not** robust
+    //if( p(i) < min_corner(i) || p(i) >= max_corner(i))
+    // **MUST** be conservative
+    if( p(i) < min_corner(i) || p(i) > max_corner(i))
+    {
+      return false;
+    }
+  }
+  return true;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberAABB<Point,DerivedV,DerivedF>::compute_min_max_corners()
+{
+  using namespace std;
+  // initialize corners
+  for(int d = 0;d<min_corner.size();d++)
+  {
+    min_corner[d] =  numeric_limits<typename Point::Scalar>::infinity();
+    max_corner[d] = -numeric_limits<typename Point::Scalar>::infinity();
+  }
+
+  this->center = Point(0,0,0);
+  // Loop over facets
+  for(int i = 0;i<this->getF().rows();i++)
+  {
+    for(int j = 0;j<this->getF().cols();j++)
+    {
+      for(int d = 0;d<min_corner.size();d++)
+      {
+        min_corner[d] = 
+          this->getV()(this->getF()(i,j),d) < min_corner[d] ?  
+            this->getV()(this->getF()(i,j),d) : min_corner[d];
+        max_corner[d] = 
+          this->getV()(this->getF()(i,j),d) > max_corner[d] ?  
+            this->getV()(this->getF()(i,j),d) : max_corner[d];
+      }
+      // This is biased toward vertices incident on more than one face, but
+      // perhaps that's good
+      this->center += this->getV().row(this->getF()(i,j));
+    }
+  }
+  // Average
+  this->center.array() /= this->getF().size();
+
+  //cout<<"min_corner: "<<this->min_corner.transpose()<<endl;
+  //cout<<"Center: "<<this->center.transpose()<<endl;
+  //cout<<"max_corner: "<<this->max_corner.transpose()<<endl;
+  //cout<<"Diag center: "<<((this->max_corner + this->min_corner)*0.5).transpose()<<endl;
+  //cout<<endl;
+
+  this->radius = (max_corner-min_corner).norm()/2.0;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar
+igl::WindingNumberAABB<Point,DerivedV,DerivedF>::max_abs_winding_number(const Point & p) const
+{
+  using namespace std;
+  // Only valid if not inside
+  if(inside(p))
+  {
+    return numeric_limits<typename DerivedV::Scalar>::infinity();
+  }
+  // Q: we know the total positive area so what's the most this could project
+  // to? Remember it could be layered in the same direction.
+  return numeric_limits<typename DerivedV::Scalar>::infinity();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+  igl::WindingNumberAABB<Point,DerivedV,DerivedF>::max_simple_abs_winding_number(
+  const Point & p) const
+{
+  using namespace std;
+  using namespace Eigen;
+  // Only valid if not inside
+  if(inside(p))
+  {
+    return numeric_limits<typename DerivedV::Scalar>::infinity();
+  }
+  // Max simple is the same as sum of positive winding number contributions of
+  // bounding box
+
+  // begin precomputation
+  //MatrixXd BV((int)pow(2,3),3);
+  typedef
+    Eigen::Matrix<typename DerivedV::Scalar,Eigen::Dynamic,Eigen::Dynamic>
+    MatrixXS;
+  typedef
+    Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,Eigen::Dynamic>
+    MatrixXF;
+  MatrixXS BV((int)(1<<3),3);
+  BV <<
+    min_corner[0],min_corner[1],min_corner[2],
+    min_corner[0],min_corner[1],max_corner[2],
+    min_corner[0],max_corner[1],min_corner[2],
+    min_corner[0],max_corner[1],max_corner[2],
+    max_corner[0],min_corner[1],min_corner[2],
+    max_corner[0],min_corner[1],max_corner[2],
+    max_corner[0],max_corner[1],min_corner[2],
+    max_corner[0],max_corner[1],max_corner[2];
+  MatrixXF BF(2*2*3,3);
+  BF <<
+    0,6,4,
+    0,2,6,
+    0,3,2,
+    0,1,3,
+    2,7,6,
+    2,3,7,
+    4,6,7,
+    4,7,5,
+    0,4,5,
+    0,5,1,
+    1,5,7,
+    1,7,3;
+  MatrixXS BFN;
+  per_face_normals(BV,BF,BFN);
+  // end of precomputation
+
+  // Only keep those with positive dot products
+  MatrixXF PBF(BF.rows(),BF.cols());
+  int pbfi = 0;
+  Point p2c = 0.5*(min_corner+max_corner)-p;
+  for(int i = 0;i<BFN.rows();i++)
+  {
+    if(p2c.dot(BFN.row(i)) > 0)
+    {
+      PBF.row(pbfi++) = BF.row(i);
+    }
+  }
+  PBF.conservativeResize(pbfi,PBF.cols());
+  return igl::winding_number(BV,PBF,p);
+}
+
+#endif

src/igl/WindingNumberMethod.h

@@ -0,0 +1,23 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_WINDINGNUMBERMETHOD_H
+#define IGL_WINDINGNUMBERMETHOD_H
+namespace igl
+{
+  // EXACT_WINDING_NUMBER_METHOD  exact hierarchical evaluation
+  // APPROX_SIMPLE_WINDING_NUMBER_METHOD  poor approximation
+  // APPROX_CACHE_WINDING_NUMBER_METHOD  another poor approximation
+  enum WindingNumberMethod
+  {
+    EXACT_WINDING_NUMBER_METHOD = 0,
+    APPROX_SIMPLE_WINDING_NUMBER_METHOD = 1,
+    APPROX_CACHE_WINDING_NUMBER_METHOD = 2,
+    NUM_WINDING_NUMBER_METHODS = 3
+  };
+}
+#endif

src/igl/WindingNumberTree.h

@@ -0,0 +1,503 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_WINDINGNUMBERTREE_H
+#define IGL_WINDINGNUMBERTREE_H
+#include <list>
+#include <map>
+#include <Eigen/Dense>
+#include "WindingNumberMethod.h"
+
+namespace igl
+{
+  // Space partitioning tree for computing winding number hierarchically.
+  //
+  // Templates:
+  //   Point  type for points in space, e.g. Eigen::Vector3d
+  template <
+    typename Point,
+    typename DerivedV, 
+    typename DerivedF >
+  class WindingNumberTree
+  {
+    public:
+      // Method to use (see enum above)
+      //static double min_max_w;
+      static std::map< 
+        std::pair<const WindingNumberTree*,const WindingNumberTree*>, 
+        typename DerivedV::Scalar>
+          cached;
+      // This is only need to fill in references, it should never actually be touched
+      // and shouldn't cause race conditions. (This is a hack, but I think it's "safe")
+      static DerivedV dummyV;
+    protected:
+      WindingNumberMethod method;
+      const WindingNumberTree * parent;
+      std::list<WindingNumberTree * > children;
+      typedef 
+        Eigen::Matrix<typename DerivedV::Scalar,Eigen::Dynamic,Eigen::Dynamic>
+        MatrixXS;
+      typedef 
+        Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,Eigen::Dynamic>
+        MatrixXF;
+      //// List of boundary edges (recall edges are vertices in 2d)
+      //const Eigen::MatrixXi boundary;
+      // Base mesh vertices
+      DerivedV & V;
+      // Base mesh vertices with duplicates removed
+      MatrixXS SV;
+      // Facets in this bounding volume
+      MatrixXF F;
+      // Tessellated boundary curve
+      MatrixXF cap;
+      // Upper Bound on radius of enclosing ball
+      typename DerivedV::Scalar radius;
+      // (Approximate) center (of mass)
+      Point center;
+    public:
+      inline WindingNumberTree();
+      // For root
+      inline WindingNumberTree(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedF> & F);
+      // For chilluns 
+      inline WindingNumberTree(
+        const WindingNumberTree<Point,DerivedV,DerivedF> & parent,
+        const Eigen::MatrixBase<DerivedF> & F);
+      inline virtual ~WindingNumberTree();
+      inline void delete_children();
+      inline virtual void set_mesh(
+        const Eigen::MatrixBase<DerivedV> & V,
+        const Eigen::MatrixBase<DerivedF> & F);
+      // Set method
+      inline void set_method( const WindingNumberMethod & m);
+    public:
+      inline const DerivedV & getV() const;
+      inline const MatrixXF & getF() const;
+      inline const MatrixXF & getcap() const;
+      // Grow the Tree recursively
+      inline virtual void grow();
+      // Determine whether a given point is inside the bounding 
+      //
+      // Inputs:
+      //   p  query point 
+      // Returns true if the point p is inside this bounding volume
+      inline virtual bool inside(const Point & p) const;
+      // Compute the (partial) winding number of a given point p
+      // According to method
+      //  
+      // Inputs:
+      //   p  query point 
+      // Returns winding number 
+      inline typename DerivedV::Scalar winding_number(const Point & p) const;
+      // Same as above, but always computes winding number using exact method
+      // (sum over every facet)
+      inline typename DerivedV::Scalar winding_number_all(const Point & p) const;
+      // Same as above, but always computes using sum over tessllated boundary
+      inline typename DerivedV::Scalar winding_number_boundary(const Point & p) const;
+      //// Same as winding_number above, but if max_simple_abs_winding_number is
+      //// less than some threshold min_max_w just return 0 (colloquially the "fast
+      //// multipole method)
+      ////
+      ////
+      //// Inputs:
+      ////   p  query point 
+      ////   min_max_w  minimum max simple w to be processed
+      //// Returns approximate winding number
+      //double winding_number_approx_simple(
+      //  const Point & p, 
+      //  const double min_max_w);
+      // Print contents of Tree
+      //
+      // Optional input:
+      //   tab  tab to show depth
+      inline void print(const char * tab="");
+      // Determine max absolute winding number
+      //
+      // Inputs:
+      //   p  query point 
+      // Returns max winding number of 
+      inline virtual typename DerivedV::Scalar max_abs_winding_number(const Point & p) const; 
+      // Same as above, but stronger assumptions on (V,F). Assumes (V,F) is a
+      // simple polyhedron
+      inline virtual typename DerivedV::Scalar max_simple_abs_winding_number(const Point & p) const;
+      // Compute or read cached winding number for point p with respect to mesh
+      // in bounding box, recursing according to approximation criteria
+      //
+      // Inputs:
+      //   p  query point 
+      //   that  WindingNumberTree containing mesh w.r.t. which we're computing w.n.
+      // Returns cached winding number
+      inline virtual typename DerivedV::Scalar cached_winding_number(const WindingNumberTree & that, const Point & p) const;
+  };
+}
+
+// Implementation
+
+#include "WindingNumberTree.h"
+#include "winding_number.h"
+#include "triangle_fan.h"
+#include "exterior_edges.h"
+
+#include <igl/PI.h>
+#include <igl/remove_duplicate_vertices.h>
+
+#include <iostream>
+#include <limits>
+
+//template <typename Point, typename DerivedV, typename DerivedF>
+//WindingNumberMethod WindingNumberTree<Point,DerivedV,DerivedF>::method = EXACT_WINDING_NUMBER_METHOD;
+//template <typename Point, typename DerivedV, typename DerivedF>
+//double WindingNumberTree<Point,DerivedV,DerivedF>::min_max_w = 0;
+template <typename Point, typename DerivedV, typename DerivedF>
+std::map< std::pair<const igl::WindingNumberTree<Point,DerivedV,DerivedF>*,const igl::WindingNumberTree<Point,DerivedV,DerivedF>*>, typename DerivedV::Scalar>
+  igl::WindingNumberTree<Point,DerivedV,DerivedF>::cached;
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberTree<Point,DerivedV,DerivedF>::WindingNumberTree():
+  method(EXACT_WINDING_NUMBER_METHOD),
+  parent(NULL),
+  V(dummyV),
+  SV(),
+  F(),
+  //boundary(igl::boundary_facets<Eigen::MatrixXi,Eigen::MatrixXi>(F))
+  cap(),
+  radius(std::numeric_limits<typename DerivedV::Scalar>::infinity()),
+  center(0,0,0)
+{
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberTree<Point,DerivedV,DerivedF>::WindingNumberTree(
+  const Eigen::MatrixBase<DerivedV> & _V,
+  const Eigen::MatrixBase<DerivedF> & _F):
+  method(EXACT_WINDING_NUMBER_METHOD),
+  parent(NULL),
+  V(dummyV),
+  SV(),
+  F(),
+  //boundary(igl::boundary_facets<Eigen::MatrixXi,Eigen::MatrixXi>(F))
+  cap(),
+  radius(std::numeric_limits<typename DerivedV::Scalar>::infinity()),
+  center(0,0,0)
+{
+  set_mesh(_V,_F);
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberTree<Point,DerivedV,DerivedF>::set_mesh(
+    const Eigen::MatrixBase<DerivedV> & _V,
+    const Eigen::MatrixBase<DerivedF> & _F)
+{
+  using namespace std;
+  // Remove any exactly duplicate vertices
+  // Q: Can this ever increase the complexity of the boundary?
+  // Q: Would we gain even more by remove almost exactly duplicate vertices?
+  MatrixXF SF,SVI,SVJ;
+  igl::remove_duplicate_vertices(_V,_F,0.0,SV,SVI,SVJ,F);
+  triangle_fan(igl::exterior_edges(F),cap);
+  V = SV;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberTree<Point,DerivedV,DerivedF>::WindingNumberTree(
+  const igl::WindingNumberTree<Point,DerivedV,DerivedF> & parent,
+  const Eigen::MatrixBase<DerivedF> & _F):
+  method(parent.method),
+  parent(&parent),
+  V(parent.V),
+  SV(),
+  F(_F),
+  cap(triangle_fan(igl::exterior_edges(_F)))
+{
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline igl::WindingNumberTree<Point,DerivedV,DerivedF>::~WindingNumberTree()
+{
+  delete_children();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberTree<Point,DerivedV,DerivedF>::delete_children()
+{
+  using namespace std;
+  // Delete children
+  typename list<WindingNumberTree<Point,DerivedV,DerivedF>* >::iterator cit = children.begin();
+  while(cit != children.end())
+  {
+    // clear the memory of this item
+    delete (* cit);
+    // erase from list, returns next element in iterator
+    cit = children.erase(cit);
+  }
+}
+      
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberTree<Point,DerivedV,DerivedF>::set_method(const WindingNumberMethod & m)
+{
+  this->method = m;
+  for(auto child : children)
+  {
+    child->set_method(m);
+  }
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline const DerivedV & igl::WindingNumberTree<Point,DerivedV,DerivedF>::getV() const
+{
+  return V;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline const typename igl::WindingNumberTree<Point,DerivedV,DerivedF>::MatrixXF& 
+  igl::WindingNumberTree<Point,DerivedV,DerivedF>::getF() const
+{
+  return F;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline const typename igl::WindingNumberTree<Point,DerivedV,DerivedF>::MatrixXF& 
+  igl::WindingNumberTree<Point,DerivedV,DerivedF>::getcap() const
+{
+  return cap;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberTree<Point,DerivedV,DerivedF>::grow()
+{
+  // Don't grow
+  return;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline bool igl::WindingNumberTree<Point,DerivedV,DerivedF>::inside(const Point & /*p*/) const
+{
+  return true;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+igl::WindingNumberTree<Point,DerivedV,DerivedF>::winding_number(const Point & p) const
+{
+  using namespace std;
+  //cout<<"+"<<boundary.rows();
+  // If inside then we need to be careful
+  if(inside(p))
+  {
+    // If not a leaf then recurse
+    if(children.size()>0)
+    {
+      // Recurse on each child and accumulate
+      typename DerivedV::Scalar sum = 0;
+      for(
+        typename list<WindingNumberTree<Point,DerivedV,DerivedF>* >::const_iterator cit = children.begin();
+        cit != children.end();
+        cit++)
+      {
+        switch(method)
+        {
+          case EXACT_WINDING_NUMBER_METHOD:
+            sum += (*cit)->winding_number(p);
+            break;
+          case APPROX_SIMPLE_WINDING_NUMBER_METHOD:
+          case APPROX_CACHE_WINDING_NUMBER_METHOD:
+            //if((*cit)->max_simple_abs_winding_number(p) > min_max_w)
+            //{
+              sum += (*cit)->winding_number(p);
+            //}
+            break;
+          default:
+            assert(false);
+            break;
+        }
+      }
+      return sum;
+    }else
+    {
+      return winding_number_all(p);
+    }
+  }else{
+    // Otherwise we can just consider boundary
+    // Q: If we using the "multipole" method should we also subdivide the
+    // boundary case?
+    if((cap.rows() - 2) < F.rows())
+    {
+      switch(method)
+      {
+        case EXACT_WINDING_NUMBER_METHOD:
+          return winding_number_boundary(p);
+        case APPROX_SIMPLE_WINDING_NUMBER_METHOD:
+        {
+          typename DerivedV::Scalar dist = (p-center).norm();
+          // Radius is already an overestimate of inside
+          if(dist>1.0*radius)
+          {
+            return 0;
+          }else
+          {
+            return winding_number_boundary(p);
+          }
+        }
+        case APPROX_CACHE_WINDING_NUMBER_METHOD:
+        {
+          return parent->cached_winding_number(*this,p);
+        }
+        default: assert(false);break;
+      }
+    }else
+    {
+      // doesn't pay off to use boundary
+      return winding_number_all(p);
+    }
+  }
+  return 0;
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+  igl::WindingNumberTree<Point,DerivedV,DerivedF>::winding_number_all(const Point & p) const
+{
+  return igl::winding_number(V,F,p);
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+igl::WindingNumberTree<Point,DerivedV,DerivedF>::winding_number_boundary(const Point & p) const
+{
+  using namespace Eigen;
+  using namespace std;
+  return igl::winding_number(V,cap,p);
+}
+
+//template <typename Point, typename DerivedV, typename DerivedF>
+//inline double igl::WindingNumberTree<Point,DerivedV,DerivedF>::winding_number_approx_simple(
+//  const Point & p, 
+//  const double min_max_w)
+//{
+//  using namespace std;
+//  if(max_simple_abs_winding_number(p) > min_max_w)
+//  {
+//    return winding_number(p);
+//  }else
+//  {
+//    cout<<"Skipped! "<<max_simple_abs_winding_number(p)<<"<"<<min_max_w<<endl;
+//    return 0;
+//  }
+//}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline void igl::WindingNumberTree<Point,DerivedV,DerivedF>::print(const char * tab)
+{
+  using namespace std;
+  // Print all facets
+  cout<<tab<<"["<<endl<<F<<endl<<"]";
+  // Print children
+  for(
+      typename list<WindingNumberTree<Point,DerivedV,DerivedF>* >::iterator cit = children.begin();
+      cit != children.end();
+      cit++)
+  {
+    cout<<","<<endl;
+    (*cit)->print((string(tab)+"").c_str());
+  }
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+igl::WindingNumberTree<Point,DerivedV,DerivedF>::max_abs_winding_number(const Point & /*p*/) const
+{
+  return std::numeric_limits<typename DerivedV::Scalar>::infinity();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+igl::WindingNumberTree<Point,DerivedV,DerivedF>::max_simple_abs_winding_number(
+  const Point & /*p*/) const
+{
+  using namespace std;
+  return numeric_limits<typename DerivedV::Scalar>::infinity();
+}
+
+template <typename Point, typename DerivedV, typename DerivedF>
+inline typename DerivedV::Scalar 
+igl::WindingNumberTree<Point,DerivedV,DerivedF>::cached_winding_number(
+  const igl::WindingNumberTree<Point,DerivedV,DerivedF> & that,
+  const Point & p) const
+{
+  using namespace std;
+  // Simple metric for `is_far`
+  //
+  //   this             that
+  //                   --------
+  //   -----          /   |    \ .
+  //  /  r  \        /    R     \ .
+  // | p !   |      |     !      |
+  //  \_____/        \          /
+  //                  \________/
+  //
+  // 
+  // a = angle formed by trapazoid formed by raising sides with lengths r and R
+  // at respective centers.
+  //
+  // a = atan2(R-r,d), where d is the distance between centers
+
+  // That should be bigger (what about parent? what about sister?)
+  bool is_far = this->radius<that.radius;
+  if(is_far)
+  {
+    typename DerivedV::Scalar a = atan2(
+      that.radius - this->radius,
+      (that.center - this->center).norm());
+    assert(a>0);
+    is_far = (a<PI/8.0);
+  }
+
+  if(is_far)
+  {
+    // Not implemented yet
+    pair<const WindingNumberTree*,const WindingNumberTree*> this_that(this,&that);
+    // Need to compute it for first time?
+    if(cached.count(this_that)==0)
+    {
+      cached[this_that] = 
+        that.winding_number_boundary(this->center);
+    }
+    return cached[this_that];
+  }else if(children.size() == 0)
+  {
+    // not far and hierarchy ended too soon: can't use cache
+    return that.winding_number_boundary(p);
+  }else
+  {
+    for(
+      typename list<WindingNumberTree<Point,DerivedV,DerivedF>* >::const_iterator cit = children.begin();
+      cit != children.end();
+      cit++)
+    {
+      if((*cit)->inside(p))
+      {
+        return (*cit)->cached_winding_number(that,p);
+      }
+    }
+    // Not inside any children? This can totally happen because bounding boxes
+    // are set to bound contained facets. So sibilings may overlap and their
+    // union may not contain their parent (though, their union is certainly a
+    // subset of their parent).
+    assert(false);
+  }
+  return 0;
+}
+
+// Explicit instantiation of static variable
+template <
+  typename Point,
+  typename DerivedV, 
+  typename DerivedF >
+DerivedV igl::WindingNumberTree<Point,DerivedV,DerivedF>::dummyV;
+
+#endif

src/igl/ZERO.h

@@ -0,0 +1,21 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ZERO_H
+#define IGL_ZERO_H
+namespace igl
+{
+  // Often one needs a reference to a dummy variable containing zero as its
+  // value, for example when using AntTweakBar's
+  // TwSetParam( "3D View", "opened", TW_PARAM_INT32, 1, &INT_ZERO);
+  const char CHAR_ZERO = 0;
+  const int INT_ZERO = 0;
+  const unsigned int UNSIGNED_INT_ZERO = 0;
+  const double DOUBLE_ZERO = 0;
+  const float FLOAT_ZERO = 0;
+}
+#endif

src/igl/active_set.cpp

@@ -0,0 +1,370 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "active_set.h"
+#include "min_quad_with_fixed.h"
+#include "slice.h"
+#include "slice_into.h"
+#include "cat.h"
+//#include "matlab_format.h"
+
+#include <iostream>
+#include <limits>
+#include <algorithm>
+
+template <
+  typename AT,
+  typename DerivedB,
+  typename Derivedknown,
+  typename DerivedY,
+  typename AeqT,
+  typename DerivedBeq,
+  typename AieqT,
+  typename DerivedBieq,
+  typename Derivedlx,
+  typename Derivedux,
+  typename DerivedZ
+  >
+IGL_INLINE igl::SolverStatus igl::active_set(
+  const Eigen::SparseMatrix<AT>& A,
+  const Eigen::PlainObjectBase<DerivedB> & B,
+  const Eigen::PlainObjectBase<Derivedknown> & known,
+  const Eigen::PlainObjectBase<DerivedY> & Y,
+  const Eigen::SparseMatrix<AeqT>& Aeq,
+  const Eigen::PlainObjectBase<DerivedBeq> & Beq,
+  const Eigen::SparseMatrix<AieqT>& Aieq,
+  const Eigen::PlainObjectBase<DerivedBieq> & Bieq,
+  const Eigen::PlainObjectBase<Derivedlx> & p_lx,
+  const Eigen::PlainObjectBase<Derivedux> & p_ux,
+  const igl::active_set_params & params,
+  Eigen::PlainObjectBase<DerivedZ> & Z
+  )
+{
+//#define ACTIVE_SET_CPP_DEBUG
+#if defined(ACTIVE_SET_CPP_DEBUG) && !defined(_MSC_VER)
+#  warning "ACTIVE_SET_CPP_DEBUG"
+#endif
+  using namespace Eigen;
+  using namespace std;
+  SolverStatus ret = SOLVER_STATUS_ERROR;
+  const int n = A.rows();
+  assert(n == A.cols() && "A must be square");
+  // Discard const qualifiers
+  //if(B.size() == 0)
+  //{
+  //  B = DerivedB::Zero(n,1);
+  //}
+  assert(n == B.rows() && "B.rows() must match A.rows()");
+  assert(B.cols() == 1 && "B must be a column vector");
+  assert(Y.cols() == 1 && "Y must be a column vector");
+  assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.cols() == n);
+  assert((Aeq.size() == 0 && Beq.size() == 0) || Aeq.rows() == Beq.rows());
+  assert((Aeq.size() == 0 && Beq.size() == 0) || Beq.cols() == 1);
+  assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.cols() == n);
+  assert((Aieq.size() == 0 && Bieq.size() == 0) || Aieq.rows() == Bieq.rows());
+  assert((Aieq.size() == 0 && Bieq.size() == 0) || Bieq.cols() == 1);
+  Eigen::Matrix<typename Derivedlx::Scalar,Eigen::Dynamic,1> lx;
+  Eigen::Matrix<typename Derivedux::Scalar,Eigen::Dynamic,1> ux;
+  if(p_lx.size() == 0)
+  {
+    lx = Derivedlx::Constant(
+      n,1,-numeric_limits<typename Derivedlx::Scalar>::max());
+  }else
+  {
+    lx = p_lx;
+  }
+  if(p_ux.size() == 0)
+  {
+    ux = Derivedux::Constant(
+      n,1,numeric_limits<typename Derivedux::Scalar>::max());
+  }else
+  {
+    ux = p_ux;
+  }
+  assert(lx.rows() == n && "lx must have n rows");
+  assert(ux.rows() == n && "ux must have n rows");
+  assert(ux.cols() == 1 && "lx must be a column vector");
+  assert(lx.cols() == 1 && "ux must be a column vector");
+  assert((ux.array()-lx.array()).minCoeff() > 0 && "ux(i) must be > lx(i)");
+  if(Z.size() != 0)
+  {
+    // Initial guess should have correct size
+    assert(Z.rows() == n && "Z must have n rows");
+    assert(Z.cols() == 1 && "Z must be a column vector");
+  }
+  assert(known.cols() == 1 && "known must be a column vector");
+  // Number of knowns
+  const int nk = known.size();
+
+  // Initialize active sets
+  typedef int BOOL;
+#define TRUE 1
+#define FALSE 0
+  Matrix<BOOL,Dynamic,1> as_lx = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
+  Matrix<BOOL,Dynamic,1> as_ux = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
+  Matrix<BOOL,Dynamic,1> as_ieq = Matrix<BOOL,Dynamic,1>::Constant(Aieq.rows(),1,FALSE);
+
+  // Keep track of previous Z for comparison
+  DerivedZ old_Z;
+  old_Z = DerivedZ::Constant(
+      n,1,numeric_limits<typename DerivedZ::Scalar>::max());
+
+  int iter = 0;
+  while(true)
+  {
+#ifdef ACTIVE_SET_CPP_DEBUG
+    cout<<"Iteration: "<<iter<<":"<<endl;
+    cout<<"  pre"<<endl;
+#endif
+    // FIND BREACHES OF CONSTRAINTS
+    int new_as_lx = 0;
+    int new_as_ux = 0;
+    int new_as_ieq = 0;
+    if(Z.size() > 0)
+    {
+      for(int z = 0;z < n;z++)
+      {
+        if(Z(z) < lx(z))
+        {
+          new_as_lx += (as_lx(z)?0:1);
+          //new_as_lx++;
+          as_lx(z) = TRUE;
+        }
+        if(Z(z) > ux(z))
+        {
+          new_as_ux += (as_ux(z)?0:1);
+          //new_as_ux++;
+          as_ux(z) = TRUE;
+        }
+      }
+      if(Aieq.rows() > 0)
+      {
+        DerivedZ AieqZ;
+        AieqZ = Aieq*Z;
+        for(int a = 0;a<Aieq.rows();a++)
+        {
+          if(AieqZ(a) > Bieq(a))
+          {
+            new_as_ieq += (as_ieq(a)?0:1);
+            as_ieq(a) = TRUE;
+          }
+        }
+      }
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"  new_as_lx: "<<new_as_lx<<endl;
+      cout<<"  new_as_ux: "<<new_as_ux<<endl;
+#endif
+      const double diff = (Z-old_Z).squaredNorm();
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"diff: "<<diff<<endl;
+#endif
+      if(diff < params.solution_diff_threshold)
+      {
+        ret = SOLVER_STATUS_CONVERGED;
+        break;
+      }
+      old_Z = Z;
+    }
+
+    const int as_lx_count = std::count(as_lx.data(),as_lx.data()+n,TRUE);
+    const int as_ux_count = std::count(as_ux.data(),as_ux.data()+n,TRUE);
+    const int as_ieq_count =
+      std::count(as_ieq.data(),as_ieq.data()+as_ieq.size(),TRUE);
+#ifndef NDEBUG
+    {
+      int count = 0;
+      for(int a = 0;a<as_ieq.size();a++)
+      {
+        if(as_ieq(a))
+        {
+          assert(as_ieq(a) == TRUE);
+          count++;
+        }
+      }
+      assert(as_ieq_count == count);
+    }
+#endif
+
+    // PREPARE FIXED VALUES
+    Derivedknown known_i;
+    known_i.resize(nk + as_lx_count + as_ux_count,1);
+    DerivedY Y_i;
+    Y_i.resize(nk + as_lx_count + as_ux_count,1);
+    {
+      known_i.block(0,0,known.rows(),known.cols()) = known;
+      Y_i.block(0,0,Y.rows(),Y.cols()) = Y;
+      int k = nk;
+      // Then all lx
+      for(int z = 0;z < n;z++)
+      {
+        if(as_lx(z))
+        {
+          known_i(k) = z;
+          Y_i(k) = lx(z);
+          k++;
+        }
+      }
+      // Finally all ux
+      for(int z = 0;z < n;z++)
+      {
+        if(as_ux(z))
+        {
+          known_i(k) = z;
+          Y_i(k) = ux(z);
+          k++;
+        }
+      }
+      assert(k==Y_i.size());
+      assert(k==known_i.size());
+    }
+    //cout<<matlab_format((known_i.array()+1).eval(),"known_i")<<endl;
+    // PREPARE EQUALITY CONSTRAINTS
+    VectorXi as_ieq_list(as_ieq_count,1);
+    // Gather active constraints and resp. rhss
+    DerivedBeq Beq_i;
+    Beq_i.resize(Beq.rows()+as_ieq_count,1);
+    Beq_i.head(Beq.rows()) = Beq;
+    {
+      int k =0;
+      for(int a=0;a<as_ieq.size();a++)
+      {
+        if(as_ieq(a))
+        {
+          assert(k<as_ieq_list.size());
+          as_ieq_list(k)=a;
+          Beq_i(Beq.rows()+k,0) = Bieq(k,0);
+          k++;
+        }
+      }
+      assert(k == as_ieq_count);
+    }
+    // extract active constraint rows
+    SparseMatrix<AeqT> Aeq_i,Aieq_i;
+    slice(Aieq,as_ieq_list,1,Aieq_i);
+    // Append to equality constraints
+    cat(1,Aeq,Aieq_i,Aeq_i);
+
+
+    min_quad_with_fixed_data<AT> data;
+#ifndef NDEBUG
+    {
+      // NO DUPES!
+      Matrix<BOOL,Dynamic,1> fixed = Matrix<BOOL,Dynamic,1>::Constant(n,1,FALSE);
+      for(int k = 0;k<known_i.size();k++)
+      {
+        assert(!fixed[known_i(k)]);
+        fixed[known_i(k)] = TRUE;
+      }
+    }
+#endif
+
+    DerivedZ sol;
+    if(known_i.size() == A.rows())
+    {
+      // Everything's fixed?
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"  everything's fixed."<<endl;
+#endif
+      Z.resize(A.rows(),Y_i.cols());
+      slice_into(Y_i,known_i,1,Z);
+      sol.resize(0,Y_i.cols());
+      assert(Aeq_i.rows() == 0 && "All fixed but linearly constrained");
+    }else
+    {
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"  min_quad_with_fixed_precompute"<<endl;
+#endif
+      if(!min_quad_with_fixed_precompute(A,known_i,Aeq_i,params.Auu_pd,data))
+      {
+        cerr<<"Error: min_quad_with_fixed precomputation failed."<<endl;
+        if(iter > 0 && Aeq_i.rows() > Aeq.rows())
+        {
+          cerr<<"  *Are you sure rows of [Aeq;Aieq] are linearly independent?*"<<
+            endl;
+        }
+        ret = SOLVER_STATUS_ERROR;
+        break;
+      }
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"  min_quad_with_fixed_solve"<<endl;
+#endif
+      if(!min_quad_with_fixed_solve(data,B,Y_i,Beq_i,Z,sol))
+      {
+        cerr<<"Error: min_quad_with_fixed solve failed."<<endl;
+        ret = SOLVER_STATUS_ERROR;
+        break;
+      }
+      //cout<<matlab_format((Aeq*Z-Beq).eval(),"cr")<<endl;
+      //cout<<matlab_format(Z,"Z")<<endl;
+#ifdef ACTIVE_SET_CPP_DEBUG
+      cout<<"  post"<<endl;
+#endif
+      // Computing Lagrange multipliers needs to be adjusted slightly if A is not symmetric
+      assert(data.Auu_sym);
+    }
+
+    // Compute Lagrange multiplier values for known_i
+    SparseMatrix<AT> Ak;
+    // Slow
+    slice(A,known_i,1,Ak);
+    DerivedB Bk;
+    slice(B,known_i,Bk);
+    MatrixXd Lambda_known_i = -(0.5*Ak*Z + 0.5*Bk);
+    // reverse the lambda values for lx
+    Lambda_known_i.block(nk,0,as_lx_count,1) =
+      (-1*Lambda_known_i.block(nk,0,as_lx_count,1)).eval();
+
+    // Extract Lagrange multipliers for Aieq_i (always at back of sol)
+    VectorXd Lambda_Aieq_i(Aieq_i.rows(),1);
+    for(int l = 0;l<Aieq_i.rows();l++)
+    {
+      Lambda_Aieq_i(Aieq_i.rows()-1-l) = sol(sol.rows()-1-l);
+    }
+
+    // Remove from active set
+    for(int l = 0;l<as_lx_count;l++)
+    {
+      if(Lambda_known_i(nk + l) < params.inactive_threshold)
+      {
+        as_lx(known_i(nk + l)) = FALSE;
+      }
+    }
+    for(int u = 0;u<as_ux_count;u++)
+    {
+      if(Lambda_known_i(nk + as_lx_count + u) <
+        params.inactive_threshold)
+      {
+        as_ux(known_i(nk + as_lx_count + u)) = FALSE;
+      }
+    }
+    for(int a = 0;a<as_ieq_count;a++)
+    {
+      if(Lambda_Aieq_i(a) < params.inactive_threshold)
+      {
+        as_ieq(as_ieq_list(a)) = FALSE;
+      }
+    }
+
+    iter++;
+    //cout<<iter<<endl;
+    if(params.max_iter>0 && iter>=params.max_iter)
+    {
+      ret = SOLVER_STATUS_MAX_ITER;
+      break;
+    }
+
+  }
+
+  return ret;
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template igl::SolverStatus igl::active_set<double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, igl::active_set_params const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
+template igl::SolverStatus igl::active_set<double, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, double, Eigen::Matrix<double, -1, 1, 0, -1, 1>, double, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> > const&, Eigen::SparseMatrix<double, 0, int> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, igl::active_set_params const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/active_set.h

@@ -0,0 +1,111 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ACTIVE_SET_H
+#define IGL_ACTIVE_SET_H
+
+#include "igl_inline.h"
+#include "SolverStatus.h"
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  struct active_set_params;
+  // Known Bugs: rows of [Aeq;Aieq] **must** be linearly independent. Should be
+  // using QR decomposition otherwise:
+  //   http://www.okstate.edu/sas/v8/sashtml/ormp/chap5/sect32.htm
+  //
+  // ACTIVE_SET Minimize quadratic energy 
+  //
+  // 0.5*Z'*A*Z + Z'*B + C with constraints
+  //
+  // that Z(known) = Y, optionally also subject to the constraints Aeq*Z = Beq,
+  // and further optionally subject to the linear inequality constraints that
+  // Aieq*Z <= Bieq and constant inequality constraints lx <= x <= ux
+  //
+  // Inputs:
+  //   A  n by n matrix of quadratic coefficients
+  //   B  n by 1 column of linear coefficients
+  //   known  list of indices to known rows in Z
+  //   Y  list of fixed values corresponding to known rows in Z
+  //   Aeq  meq by n list of linear equality constraint coefficients
+  //   Beq  meq by 1 list of linear equality constraint constant values
+  //   Aieq  mieq by n list of linear inequality constraint coefficients
+  //   Bieq  mieq by 1 list of linear inequality constraint constant values
+  //   lx  n by 1 list of lower bounds [] implies -Inf
+  //   ux  n by 1 list of upper bounds [] implies Inf
+  //   params  struct of additional parameters (see below)
+  //   Z  if not empty, is taken to be an n by 1 list of initial guess values
+  //     (see output)
+  // Outputs:
+  //   Z  n by 1 list of solution values
+  // Returns true on success, false on error
+  //
+  // Benchmark: For a harmonic solve on a mesh with 325K facets, matlab 2.2
+  // secs, igl/min_quad_with_fixed.h 7.1 secs
+  //
+  template <
+    typename AT, 
+    typename DerivedB,
+    typename Derivedknown, 
+    typename DerivedY,
+    typename AeqT,
+    typename DerivedBeq,
+    typename AieqT,
+    typename DerivedBieq,
+    typename Derivedlx,
+    typename Derivedux,
+    typename DerivedZ
+    >
+  IGL_INLINE igl::SolverStatus active_set(
+    const Eigen::SparseMatrix<AT>& A,
+    const Eigen::PlainObjectBase<DerivedB> & B,
+    const Eigen::PlainObjectBase<Derivedknown> & known,
+    const Eigen::PlainObjectBase<DerivedY> & Y,
+    const Eigen::SparseMatrix<AeqT>& Aeq,
+    const Eigen::PlainObjectBase<DerivedBeq> & Beq,
+    const Eigen::SparseMatrix<AieqT>& Aieq,
+    const Eigen::PlainObjectBase<DerivedBieq> & Bieq,
+    const Eigen::PlainObjectBase<Derivedlx> & lx,
+    const Eigen::PlainObjectBase<Derivedux> & ux,
+    const igl::active_set_params & params,
+    Eigen::PlainObjectBase<DerivedZ> & Z
+    );
+};
+
+#include "EPS.h"
+struct igl::active_set_params
+{
+  // Input parameters for active_set:
+  //   Auu_pd  whether Auu is positive definite {false}
+  //   max_iter  Maximum number of iterations (0 = Infinity, {100})
+  //   inactive_threshold  Threshold on Lagrange multiplier values to determine
+  //     whether to keep constraints active {EPS}
+  //   constraint_threshold  Threshold on whether constraints are violated (0
+  //     is perfect) {EPS}
+  //   solution_diff_threshold  Threshold on the squared norm of the difference
+  //     between two consecutive solutions {EPS}
+  bool Auu_pd;
+  int max_iter;
+  double inactive_threshold;
+  double constraint_threshold;
+  double solution_diff_threshold;
+  active_set_params():
+    Auu_pd(false),
+    max_iter(100),
+    inactive_threshold(igl::DOUBLE_EPS),
+    constraint_threshold(igl::DOUBLE_EPS),
+    solution_diff_threshold(igl::DOUBLE_EPS)
+    {};
+};
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "active_set.cpp"
+#endif
+
+#endif

src/igl/adjacency_list.cpp

@@ -0,0 +1,168 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "adjacency_list.h"
+
+#include "verbose.h"
+#include <algorithm>
+
+template <typename Index, typename IndexVector>
+IGL_INLINE void igl::adjacency_list(
+    const Eigen::PlainObjectBase<Index>  & F,
+    std::vector<std::vector<IndexVector> >& A,
+    bool sorted)
+{
+  A.clear(); 
+  A.resize(F.maxCoeff()+1);
+  
+  // Loop over faces
+  for(int i = 0;i<F.rows();i++)
+  {
+    // Loop over this face
+    for(int j = 0;j<F.cols();j++)
+    {
+      // Get indices of edge: s --> d
+      int s = F(i,j);
+      int d = F(i,(j+1)%F.cols());
+      A.at(s).push_back(d);
+      A.at(d).push_back(s);
+    }
+  }
+  
+  // Remove duplicates
+  for(int i=0; i<(int)A.size();++i)
+  {
+    std::sort(A[i].begin(), A[i].end());
+    A[i].erase(std::unique(A[i].begin(), A[i].end()), A[i].end());
+  }
+  
+  // If needed, sort every VV
+  if (sorted)
+  {
+    // Loop over faces
+    
+    // for every vertex v store a set of ordered edges not incident to v that belongs to triangle incident on v.
+    std::vector<std::vector<std::vector<int> > > SR; 
+    SR.resize(A.size());
+    
+    for(int i = 0;i<F.rows();i++)
+    {
+      // Loop over this face
+      for(int j = 0;j<F.cols();j++)
+      {
+        // Get indices of edge: s --> d
+        int s = F(i,j);
+        int d = F(i,(j+1)%F.cols());
+        // Get index of opposing vertex v
+        int v = F(i,(j+2)%F.cols());
+        
+        std::vector<int> e(2);
+        e[0] = d;
+        e[1] = v;
+        SR[s].push_back(e);
+      }
+    }
+    
+    for(int v=0; v<(int)SR.size();++v)
+    {
+      std::vector<IndexVector>& vv = A.at(v);
+      std::vector<std::vector<int> >& sr = SR[v];
+      
+      std::vector<std::vector<int> > pn = sr;
+      
+      // Compute previous/next for every element in sr
+      for(int i=0;i<(int)sr.size();++i)
+      {
+        int a = sr[i][0];
+        int b = sr[i][1];
+        
+        // search for previous
+        int p = -1;
+        for(int j=0;j<(int)sr.size();++j)
+          if(sr[j][1] == a)
+            p = j;
+        pn[i][0] = p;
+        
+        // search for next
+        int n = -1;
+        for(int j=0;j<(int)sr.size();++j)
+          if(sr[j][0] == b)
+            n = j;
+        pn[i][1] = n;
+        
+      }
+      
+      // assume manifoldness (look for beginning of a single chain)
+      int c = 0;
+      for(int j=0; j<=(int)sr.size();++j)
+        if (pn[c][0] != -1)
+          c = pn[c][0];
+      
+      if (pn[c][0] == -1) // border case
+      {
+        // finally produce the new vv relation
+        for(int j=0; j<(int)sr.size();++j)
+        {
+          vv[j] = sr[c][0];
+          if (pn[c][1] != -1)
+            c = pn[c][1];
+        }
+        vv.back() = sr[c][1];
+      }
+      else
+      {
+        // finally produce the new vv relation
+        for(int j=0; j<(int)sr.size();++j)
+        {
+          vv[j] = sr[c][0];
+          
+          c = pn[c][1];
+        }
+      }
+    }
+  }
+}
+
+template <typename Index>
+IGL_INLINE void igl::adjacency_list(
+  const std::vector<std::vector<Index> > & F,
+  std::vector<std::vector<Index> >& A)
+{
+  A.clear(); 
+  A.resize(F.maxCoeff()+1);
+  
+  // Loop over faces
+  for(int i = 0;i<F.size();i++)
+  {
+    // Loop over this face
+    for(int j = 0;j<F[i].size();j++)
+    {
+      // Get indices of edge: s --> d
+      int s = F(i,j);
+      int d = F(i,(j+1)%F[i].size());
+      A.at(s).push_back(d);
+      A.at(d).push_back(s);
+    }
+  }
+  
+  // Remove duplicates
+  for(int i=0; i<(int)A.size();++i)
+  {
+    std::sort(A[i].begin(), A[i].end());
+    A[i].erase(std::unique(A[i].begin(), A[i].end()), A[i].end());
+  }
+  
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::adjacency_list<Eigen::Matrix<int, -1, 2, 0, -1, 2>, int>(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&, bool);
+// generated by autoexplicit.sh
+template void igl::adjacency_list<Eigen::Matrix<int, -1, -1, 0, -1, -1>, int>(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&, bool);
+template void igl::adjacency_list<Eigen::Matrix<int, -1, 3, 0, -1, 3>, int>(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&, bool);
+#endif

src/igl/adjacency_list.h

@@ -0,0 +1,51 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ADJACENCY_LIST_H
+#define IGL_ADJACENCY_LIST_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+#include <vector>
+namespace igl 
+{
+  // Constructs the graph adjacency list of a given mesh (V,F)
+  // Templates:
+  //   T  should be a eigen sparse matrix primitive type like int or double
+  // Inputs:
+  //   F       #F by dim list of mesh faces (must be triangles)
+  //   sorted  flag that indicates if the list should be sorted counter-clockwise
+  // Outputs: 
+  //   A  vector<vector<T> > containing at row i the adjacent vertices of vertex i
+  //
+  // Example:
+  //   // Mesh in (V,F)
+  //   vector<vector<double> > A;
+  //   adjacency_list(F,A);
+  //
+  // See also: edges, cotmatrix, diag
+  template <typename Index, typename IndexVector>
+  IGL_INLINE void adjacency_list(
+    const Eigen::PlainObjectBase<Index> & F, 
+    std::vector<std::vector<IndexVector> >& A,
+    bool sorted = false);
+
+  // Variant that accepts polygonal faces. 
+  // Each element of F is a set of indices of a polygonal face.
+  template <typename Index>
+  IGL_INLINE void adjacency_list(
+    const std::vector<std::vector<Index> > & F,
+    std::vector<std::vector<Index> >& A);
+
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "adjacency_list.cpp"
+#endif
+
+#endif

src/igl/adjacency_matrix.cpp

@@ -0,0 +1,74 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "adjacency_matrix.h"
+
+#include "verbose.h"
+
+#include <vector>
+
+template <typename DerivedF, typename T>
+IGL_INLINE void igl::adjacency_matrix(
+  const Eigen::MatrixBase<DerivedF> & F, 
+  Eigen::SparseMatrix<T>& A)
+{
+  using namespace std;
+  using namespace Eigen;
+  typedef typename DerivedF::Scalar Index;
+
+  typedef Triplet<T> IJV;
+  vector<IJV > ijv;
+  ijv.reserve(F.size()*2);
+  // Loop over **simplex** (i.e., **not quad**)
+  for(int i = 0;i<F.rows();i++)
+  {
+    // Loop over this **simplex**
+    for(int j = 0;j<F.cols();j++)
+    for(int k = j+1;k<F.cols();k++)
+    {
+      // Get indices of edge: s --> d
+      Index s = F(i,j);
+      Index d = F(i,k);
+      ijv.push_back(IJV(s,d,1));
+      ijv.push_back(IJV(d,s,1));
+    }
+  }
+
+  const Index n = F.maxCoeff()+1;
+  A.resize(n,n);
+  switch(F.cols())
+  {
+    case 3:
+      A.reserve(6*(F.maxCoeff()+1));
+      break;
+    case 4:
+      A.reserve(26*(F.maxCoeff()+1));
+      break;
+  }
+  A.setFromTriplets(ijv.begin(),ijv.end());
+
+  // Force all non-zeros to be one
+
+  // Iterate over outside
+  for(int k=0; k<A.outerSize(); ++k)
+  {
+    // Iterate over inside
+    for(typename Eigen::SparseMatrix<T>::InnerIterator it (A,k); it; ++it)
+    {
+      assert(it.value() != 0);
+      A.coeffRef(it.row(),it.col()) = 1;
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::adjacency_matrix<Eigen::Matrix<int, -1, -1, 0, -1, -1>, bool>(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<bool, 0, int>&);
+template void igl::adjacency_matrix<Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<double, 0, int>&);
+template void igl::adjacency_matrix<Eigen::Matrix<int, -1, -1, 0, -1, -1>, int>(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::SparseMatrix<int, 0, int>&);
+#endif

src/igl/adjacency_matrix.h

@@ -0,0 +1,51 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ADJACENCY_MATRIX_H
+#define IGL_ADJACENCY_MATRIX_H
+#include "igl_inline.h"
+
+#define EIGEN_YES_I_KNOW_SPARSE_MODULE_IS_NOT_STABLE_YET
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+
+namespace igl 
+{
+  // Constructs the graph adjacency matrix  of a given mesh (V,F)
+  // Templates:
+  //   T  should be a eigen sparse matrix primitive type like int or double
+  // Inputs:
+  //   F  #F by dim list of mesh simplices
+  // Outputs: 
+  //   A  max(F) by max(F) cotangent matrix, each row i corresponding to V(i,:)
+  //
+  // Example:
+  //   // Mesh in (V,F)
+  //   Eigen::SparseMatrix<double> A;
+  //   adjacency_matrix(F,A);
+  //   // sum each row 
+  //   SparseVector<double> Asum;
+  //   sum(A,1,Asum);
+  //   // Convert row sums into diagonal of sparse matrix
+  //   SparseMatrix<double> Adiag;
+  //   diag(Asum,Adiag);
+  //   // Build uniform laplacian
+  //   SparseMatrix<double> U;
+  //   U = A-Adiag;
+  //
+  // See also: edges, cotmatrix, diag
+  template <typename DerivedF, typename T>
+  IGL_INLINE void adjacency_matrix(
+    const Eigen::MatrixBase<DerivedF> & F, 
+    Eigen::SparseMatrix<T>& A);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "adjacency_matrix.cpp"
+#endif
+
+#endif

src/igl/all.cpp

@@ -0,0 +1,26 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "all.h"
+#include "redux.h"
+
+
+template <typename AType, typename DerivedB>
+IGL_INLINE void igl::all(
+  const Eigen::SparseMatrix<AType> & A, 
+  const int dim,
+  Eigen::PlainObjectBase<DerivedB>& B)
+{
+  typedef typename DerivedB::Scalar Scalar;
+  igl::redux(A,dim,[](Scalar a, Scalar b){ return a && b!=0;},B);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#endif
+
+

src/igl/all.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ALL_H
+#define IGL_ALL_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+namespace igl
+{
+  // For Dense matrices use: A.rowwise().all() or A.colwise().all()
+  //
+  // Inputs:
+  //   A  m by n sparse matrix
+  //   dim  dimension along which to check for all (1 or 2)
+  // Output:
+  //   B  n-long vector (if dim == 1) 
+  //   or
+  //   B  m-long vector (if dim == 2)
+  //
+  template <typename AType, typename DerivedB>
+  IGL_INLINE void all(
+    const Eigen::SparseMatrix<AType> & A, 
+    const int dim,
+    Eigen::PlainObjectBase<DerivedB>& B);
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "all.cpp"
+#endif
+#endif
+
+

src/igl/all_edges.cpp

@@ -0,0 +1,26 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "all_edges.h"
+#include "oriented_facets.h"
+
+template <typename DerivedF, typename DerivedE>
+IGL_INLINE void igl::all_edges(
+  const Eigen::MatrixBase<DerivedF> & F,
+  Eigen::PlainObjectBase<DerivedE> & E)
+{
+  return oriented_facets(F,E);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::all_edges<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template void igl::all_edges<Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 2, 0, -1, 2> >(Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> >&);
+template void igl::all_edges<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 2, 0, -1, 2> >(Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 2, 0, -1, 2> >&);
+template void igl::all_edges<Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template void igl::all_edges<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 2, 0, -1, 2> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 2, 0, -1, 2> >&);
+#endif

src/igl/all_edges.h

@@ -0,0 +1,38 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ALL_EDGES_H
+#define IGL_ALL_EDGES_H
+#include "igl_inline.h"
+#include <Eigen/Dense>
+namespace igl
+{
+  // Deprecated: call oriented_facets instead.
+  //
+  // ALL_EDGES Determines all "directed edges" of a given set of simplices. For
+  // a manifold mesh, this computes all of the half-edges
+  //
+  // Inputs:
+  //   F  #F by simplex_size list of "faces"
+  // Outputs:
+  //   E  #E by simplex_size-1  list of edges
+  //
+  // Note: this is not the same as igl::edges because this includes every
+  // directed edge including repeats (meaning interior edges on a surface will
+  // show up once for each direction and non-manifold edges may appear more than
+  // once for each direction).
+  template <typename DerivedF, typename DerivedE>
+  IGL_INLINE void all_edges(
+    const Eigen::MatrixBase<DerivedF> & F,
+    Eigen::PlainObjectBase<DerivedE> & E);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "all_edges.cpp"
+#endif
+
+#endif

src/igl/all_pairs_distances.cpp

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "all_pairs_distances.h"
+#include <Eigen/Dense>
+
+template <typename Mat>
+IGL_INLINE void igl::all_pairs_distances(
+  const Mat & V,
+  const Mat & U,
+  const bool squared,
+  Mat & D)
+{
+  // dimension should be the same
+  assert(V.cols() == U.cols());
+  // resize output
+  D.resize(V.rows(),U.rows());
+  for(int i = 0;i<V.rows();i++)
+  {
+    for(int j=0;j<U.rows();j++)
+    {
+      D(i,j) = (V.row(i)-U.row(j)).squaredNorm();
+      if(!squared)
+      {
+        D(i,j) = sqrt(D(i,j));
+      }
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::all_pairs_distances<Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, bool, Eigen::Matrix<double, -1, -1, 0, -1, -1>&);
+#endif

src/igl/all_pairs_distances.h

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ALL_PAIRS_DISTANCES_H
+#define IGL_ALL_PAIRS_DISTANCES_H
+#include "igl_inline.h"
+
+namespace igl
+{
+  // ALL_PAIRS_DISTANCES compute distances between each point i in V and point j
+  // in U
+  // 
+  // D = all_pairs_distances(V,U)
+  // 
+  // Templates:
+  //   Mat  matrix class like MatrixXd
+  // Inputs:
+  //   V  #V by dim list of points
+  //   U  #U by dim list of points
+  //   squared  whether to return squared distances
+  // Outputs:
+  //   D  #V by #U matrix of distances, where D(i,j) gives the distance or
+  //     squareed distance between V(i,:) and U(j,:)
+  // 
+  template <typename Mat>
+  IGL_INLINE void all_pairs_distances(
+    const Mat & V,
+    const Mat & U,
+    const bool squared, 
+    Mat & D);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "all_pairs_distances.cpp"
+#endif
+
+#endif

src/igl/ambient_occlusion.cpp

@@ -0,0 +1,137 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "ambient_occlusion.h"
+#include "random_dir.h"
+#include "ray_mesh_intersect.h"
+#include "EPS.h"
+#include "Hit.h"
+#include "parallel_for.h"
+#include <functional>
+#include <vector>
+#include <algorithm>
+
+template <
+  typename DerivedP,
+  typename DerivedN,
+  typename DerivedS >
+IGL_INLINE void igl::ambient_occlusion(
+  const std::function<
+    bool(
+      const Eigen::Vector3f&,
+      const Eigen::Vector3f&)
+      > & shoot_ray,
+  const Eigen::PlainObjectBase<DerivedP> & P,
+  const Eigen::PlainObjectBase<DerivedN> & N,
+  const int num_samples,
+  Eigen::PlainObjectBase<DerivedS> & S)
+{
+  using namespace Eigen;
+  const int n = P.rows();
+  // Resize output
+  S.resize(n,1);
+  // Embree seems to be parallel when constructing but not when tracing rays
+  const MatrixXf D = random_dir_stratified(num_samples).cast<float>();
+
+  const auto & inner = [&P,&N,&num_samples,&D,&S,&shoot_ray](const int p)
+  {
+    const Vector3f origin = P.row(p).template cast<float>();
+    const Vector3f normal = N.row(p).template cast<float>();
+    int num_hits = 0;
+    for(int s = 0;s<num_samples;s++)
+    {
+      Vector3f d = D.row(s);
+      if(d.dot(normal) < 0)
+      {
+        // reverse ray
+        d *= -1;
+      }
+      if(shoot_ray(origin,d))
+      {
+        num_hits++;
+      }
+    }
+    S(p) = (double)num_hits/(double)num_samples;
+  };
+  parallel_for(n,inner,1000);
+}
+
+template <
+  typename DerivedV,
+  int DIM,
+  typename DerivedF,
+  typename DerivedP,
+  typename DerivedN,
+  typename DerivedS >
+IGL_INLINE void igl::ambient_occlusion(
+  const igl::AABB<DerivedV,DIM> & aabb,
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  const Eigen::PlainObjectBase<DerivedP> & P,
+  const Eigen::PlainObjectBase<DerivedN> & N,
+  const int num_samples,
+  Eigen::PlainObjectBase<DerivedS> & S)
+{
+  const auto & shoot_ray = [&aabb,&V,&F](
+    const Eigen::Vector3f& _s,
+    const Eigen::Vector3f& dir)->bool
+  {
+    Eigen::Vector3f s = _s+1e-4*dir;
+    igl::Hit hit;
+    return aabb.intersect_ray(
+      V,
+      F,
+      s  .cast<typename DerivedV::Scalar>().eval(),
+      dir.cast<typename DerivedV::Scalar>().eval(),
+      hit);
+  };
+  return ambient_occlusion(shoot_ray,P,N,num_samples,S);
+
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedP,
+  typename DerivedN,
+  typename DerivedS >
+IGL_INLINE void igl::ambient_occlusion(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  const Eigen::PlainObjectBase<DerivedP> & P,
+  const Eigen::PlainObjectBase<DerivedN> & N,
+  const int num_samples,
+  Eigen::PlainObjectBase<DerivedS> & S)
+{
+  if(F.rows() < 100)
+  {
+    // Super naive
+    const auto & shoot_ray = [&V,&F](
+      const Eigen::Vector3f& _s,
+      const Eigen::Vector3f& dir)->bool
+    {
+      Eigen::Vector3f s = _s+1e-4*dir;
+      igl::Hit hit;
+      return ray_mesh_intersect(s,dir,V,F,hit);
+    };
+    return ambient_occlusion(shoot_ray,P,N,num_samples,S);
+  }
+  AABB<DerivedV,3> aabb;
+  aabb.init(V,F);
+  return ambient_occlusion(aabb,V,F,P,N,num_samples,S);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::ambient_occlusion<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(std::function<bool (Eigen::Matrix<float, 3, 1, 0, 3, 1> const&, Eigen::Matrix<float, 3, 1, 0, 3, 1> const&)> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::ambient_occlusion<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(std::function<bool (Eigen::Matrix<float, 3, 1, 0, 3, 1> const&, Eigen::Matrix<float, 3, 1, 0, 3, 1> const&)> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
+// generated by autoexplicit.sh
+template void igl::ambient_occlusion<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, -1, 1, 0, -1, 1> >(std::function<bool (Eigen::Matrix<float, 3, 1, 0, 3, 1> const&, Eigen::Matrix<float, 3, 1, 0, 3, 1> const&)> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 1, 0, -1, 1> >&);
+template void igl::ambient_occlusion<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(std::function<bool (Eigen::Matrix<float, 3, 1, 0, 3, 1> const&, Eigen::Matrix<float, 3, 1, 0, 3, 1> const&)> const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/ambient_occlusion.h

@@ -0,0 +1,80 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AMBIENT_OCCLUSION_H
+#define IGL_AMBIENT_OCCLUSION_H
+#include "igl_inline.h"
+#include "AABB.h"
+#include <Eigen/Core>
+#include <functional>
+namespace igl
+{
+  // Compute ambient occlusion per given point
+  //
+  // Inputs:
+  //    shoot_ray  function handle that outputs hits of a given ray against a
+  //      mesh (embedded in function handles as captured variable/data)
+  //    P  #P by 3 list of origin points
+  //    N  #P by 3 list of origin normals
+  // Outputs:
+  //    S  #P list of ambient occlusion values between 1 (fully occluded) and
+  //      0 (not occluded)
+  //
+  template <
+    typename DerivedP,
+    typename DerivedN,
+    typename DerivedS >
+  IGL_INLINE void ambient_occlusion(
+    const std::function<
+      bool(
+        const Eigen::Vector3f&,
+        const Eigen::Vector3f&)
+        > & shoot_ray,
+    const Eigen::PlainObjectBase<DerivedP> & P,
+    const Eigen::PlainObjectBase<DerivedN> & N,
+    const int num_samples,
+    Eigen::PlainObjectBase<DerivedS> & S);
+  // Inputs:
+  //   AABB  axis-aligned bounding box hierarchy around (V,F)
+  template <
+    typename DerivedV,
+    int DIM,
+    typename DerivedF,
+    typename DerivedP,
+    typename DerivedN,
+    typename DerivedS >
+  IGL_INLINE void ambient_occlusion(
+    const igl::AABB<DerivedV,DIM> & aabb,
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedF> & F,
+    const Eigen::PlainObjectBase<DerivedP> & P,
+    const Eigen::PlainObjectBase<DerivedN> & N,
+    const int num_samples,
+    Eigen::PlainObjectBase<DerivedS> & S);
+  // Inputs:
+  //    V  #V by 3 list of mesh vertex positions
+  //    F  #F by 3 list of mesh face indices into V
+  template <
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedP,
+    typename DerivedN,
+    typename DerivedS >
+  IGL_INLINE void ambient_occlusion(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedF> & F,
+    const Eigen::PlainObjectBase<DerivedP> & P,
+    const Eigen::PlainObjectBase<DerivedN> & N,
+    const int num_samples,
+    Eigen::PlainObjectBase<DerivedS> & S);
+
+};
+#ifndef IGL_STATIC_LIBRARY
+#  include "ambient_occlusion.cpp"
+#endif
+
+#endif

src/igl/angular_distance.cpp

@@ -0,0 +1,20 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "angular_distance.h"
+#include <igl/EPS.h>
+#include <igl/PI.h>
+IGL_INLINE double igl::angular_distance(
+  const Eigen::Quaterniond & A,
+  const Eigen::Quaterniond & B)
+{
+  assert(fabs(A.norm()-1)<FLOAT_EPS && "A should be unit norm");
+  assert(fabs(B.norm()-1)<FLOAT_EPS && "B should be unit norm");
+  //// acos is always in [0,2*pi)
+  //return acos(fabs(A.dot(B)));
+  return fmod(2.*acos(A.dot(B)),2.*PI);
+}

src/igl/angular_distance.h

@@ -0,0 +1,30 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ANGULAR_DISTANCE_H
+#define IGL_ANGULAR_DISTANCE_H
+#include "igl_inline.h"
+#include <Eigen/Geometry>
+namespace igl
+{
+  // The "angular distance" between two unit quaternions is the angle of the
+  // smallest rotation (treated as an Axis and Angle) that takes A to B.
+  //
+  // Inputs:
+  //   A  unit quaternion
+  //   B  unit quaternion
+  // Returns angular distance
+  IGL_INLINE double angular_distance(
+    const Eigen::Quaterniond & A,
+    const Eigen::Quaterniond & B);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#include "angular_distance.cpp"
+#endif
+
+#endif

src/igl/anttweakbar/ReAntTweakBar.cpp

@@ -0,0 +1,934 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "ReAntTweakBar.h"
+
+#include <cstdio>
+#include <cstring>
+#include <sstream>
+#include <iostream>
+#include <iomanip>
+#include <map>
+
+// GLOBAL WRAPPERS
+namespace 
+{
+  std::map<
+    TwType,std::pair<const char *,std::vector<TwEnumVal> > 
+    > ReTw_custom_types;
+}
+
+IGL_INLINE TwType igl::anttweakbar::ReTwDefineEnum(
+  const char *name, 
+  const TwEnumVal *enumValues, 
+  unsigned int nbValues)
+{
+  using namespace std;
+  // copy enum valus into vector
+  std::vector<TwEnumVal> enum_vals;
+  enum_vals.resize(nbValues);
+  for(unsigned int j = 0; j<nbValues;j++)
+  {
+    enum_vals[j] = enumValues[j];
+  }
+  TwType type = TwDefineEnum(name,enumValues,nbValues);
+
+  ReTw_custom_types[type] = 
+    std::pair<const char *,std::vector<TwEnumVal> >(name,enum_vals);
+
+  return type;
+}
+
+IGL_INLINE TwType igl::anttweakbar::ReTwDefineEnumFromString(
+  const char * _Name,
+  const char * _EnumString)
+{
+  // Taken directly from TwMgr.cpp, just replace TwDefineEnum with
+  // ReTwDefineEnum
+  using namespace std;
+  {
+    if (_EnumString == NULL) 
+        return ReTwDefineEnum(_Name, NULL, 0);
+
+    // split enumString
+    stringstream EnumStream(_EnumString);
+    string Label;
+    vector<string> Labels;
+    while( getline(EnumStream, Label, ',') ) {
+        // trim Label
+        size_t Start = Label.find_first_not_of(" \n\r\t");
+        size_t End = Label.find_last_not_of(" \n\r\t");
+        if( Start==string::npos || End==string::npos )
+            Label = "";
+        else
+            Label = Label.substr(Start, (End-Start)+1);
+        // store Label
+        Labels.push_back(Label);
+    }
+    // create TwEnumVal array
+    vector<TwEnumVal> Vals(Labels.size());
+    for( int i=0; i<(int)Labels.size(); i++ )
+    {
+        Vals[i].Value = i;
+        // Wrong:
+        //Vals[i].Label = Labels[i].c_str();
+        // Allocate char on heap
+        // http://stackoverflow.com/a/10050258/148668
+        char * c_label = new char[Labels[i].length()+1];
+        std::strcpy(c_label, Labels[i].c_str());
+        Vals[i].Label = c_label;
+    }
+
+    const TwType type = 
+      ReTwDefineEnum(_Name, Vals.empty() ? 
+        NULL : 
+        &(Vals[0]), (unsigned int)Vals.size());
+    return type;
+  }
+}
+
+namespace
+{
+  struct ReTwTypeString
+  {
+    TwType type;
+    const char * type_str;
+  };
+
+  #define RETW_NUM_DEFAULT_TYPE_STRINGS 23
+  ReTwTypeString ReTwDefaultTypeStrings[RETW_NUM_DEFAULT_TYPE_STRINGS] = 
+  {
+    {TW_TYPE_UNDEF,"TW_TYPE_UNDEF"},
+    {TW_TYPE_BOOLCPP,"TW_TYPE_BOOLCPP"},
+    {TW_TYPE_BOOL8,"TW_TYPE_BOOL8"},
+    {TW_TYPE_BOOL16,"TW_TYPE_BOOL16"},
+    {TW_TYPE_BOOL32,"TW_TYPE_BOOL32"},
+    {TW_TYPE_CHAR,"TW_TYPE_CHAR"},
+    {TW_TYPE_INT8,"TW_TYPE_INT8"},
+    {TW_TYPE_UINT8,"TW_TYPE_UINT8"},
+    {TW_TYPE_INT16,"TW_TYPE_INT16"},
+    {TW_TYPE_UINT16,"TW_TYPE_UINT16"},
+    {TW_TYPE_INT32,"TW_TYPE_INT32"},
+    {TW_TYPE_UINT32,"TW_TYPE_UINT32"},
+    {TW_TYPE_FLOAT,"TW_TYPE_FLOAT"},
+    {TW_TYPE_DOUBLE,"TW_TYPE_DOUBLE"},
+    {TW_TYPE_COLOR32,"TW_TYPE_COLOR32"},
+    {TW_TYPE_COLOR3F,"TW_TYPE_COLOR3F"},
+    {TW_TYPE_COLOR4F,"TW_TYPE_COLOR4F"},
+    {TW_TYPE_CDSTRING,"TW_TYPE_CDSTRING"},
+    {TW_TYPE_STDSTRING,"TW_TYPE_STDSTRING"},
+    {TW_TYPE_QUAT4F,"TW_TYPE_QUAT4F"},
+    {TW_TYPE_QUAT4D,"TW_TYPE_QUAT4D"},
+    {TW_TYPE_DIR3F,"TW_TYPE_DIR3F"},
+    {TW_TYPE_DIR3D,"TW_TYPE_DIR3D"}
+  };
+}
+
+IGL_INLINE igl::anttweakbar::ReTwBar::ReTwBar():
+ bar(NULL),
+  name(),
+  rw_items(),cb_items()
+{
+}
+
+IGL_INLINE igl::anttweakbar::ReTwBar::ReTwBar(
+    const igl::anttweakbar::ReTwBar & that):
+  bar(that.bar),
+  name(that.name),
+  rw_items(that.rw_items),
+  cb_items(that.cb_items)
+{
+}
+
+IGL_INLINE igl::anttweakbar::ReTwBar & 
+igl::anttweakbar::ReTwBar::operator=(const igl::anttweakbar::ReTwBar & that)
+{
+  // check for self assignment
+  if(this != &that)
+  {
+    bar = that.bar;
+    rw_items = that.rw_items;
+    cb_items = that.cb_items;
+  }
+  return *this;
+}
+
+
+// BAR WRAPPERS
+IGL_INLINE void igl::anttweakbar::ReTwBar::TwNewBar(const char * _name)
+{
+  this->bar = ::TwNewBar(_name);
+  // Alec: This causes trouble (not sure why) in multiple applications
+  // (medit, puppet) Probably there is some sort of memory corrpution.
+  // this->name = _name;
+  // Suspiciously this also fails:
+  //this->name = "foobar";
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwAddVarRW(
+  const char *name, 
+  TwType type, 
+  void *var, 
+  const char *def,
+  const bool record)
+{
+  int ret = ::TwAddVarRW(this->bar,name,type,var,def);
+  if(ret && record)
+  {
+    rw_items.push_back(ReTwRWItem(name,type,var));
+  }
+  return ret;
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwAddVarCB(
+  const char *name, 
+  TwType type, 
+  TwSetVarCallback setCallback, 
+  TwGetVarCallback getCallback, 
+  void *clientData, 
+  const char *def,
+  const bool record)
+{
+  int ret = 
+    ::TwAddVarCB(this->bar,name,type,setCallback,getCallback,clientData,def);
+  if(ret && record)
+  {
+    cb_items.push_back(ReTwCBItem(name,type,setCallback,getCallback,clientData));
+  }
+  return ret;
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwAddVarRO(
+  const char *name, 
+  TwType type, 
+  void *var, 
+  const char *def)
+{
+  int ret = ::TwAddVarRO(this->bar,name,type,var,def);
+  // Read only variables are not recorded
+  //if(ret)
+  //{
+  //  rw_items.push_back(ReTwRWItem(name,type,var));
+  //}
+  return ret;
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwAddButton(
+  const char *name, 
+  TwButtonCallback buttonCallback, 
+  void *clientData, 
+  const char *def)
+{
+  int ret = 
+    ::TwAddButton(this->bar,name,buttonCallback,clientData,def);
+  // buttons are not recorded
+  //if(ret)
+  //{
+  //  cb_items.push_back(ReTwCBItem(name,type,setCallback,getCallback,clientData));
+  //}
+  return ret;
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwSetParam(
+  const char *varName, 
+  const char *paramName, 
+  TwParamValueType paramValueType, 
+  unsigned int inValueCount, 
+  const void *inValues)
+{
+  // For now just pass these along
+  return 
+    ::TwSetParam(
+      this->bar,
+      varName,
+      paramName,
+      paramValueType,
+      inValueCount,
+      inValues);
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwGetParam(
+  const char *varName, 
+  const char *paramName, 
+  TwParamValueType paramValueType, 
+  unsigned int outValueMaxCount,
+  void *outValues)
+{
+  return 
+    ::TwGetParam(
+      this->bar,
+      varName,
+      paramName,
+      paramValueType,
+      outValueMaxCount,
+      outValues);
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwRefreshBar()
+{
+  return ::TwRefreshBar(this->bar);
+}
+
+IGL_INLINE int igl::anttweakbar::ReTwBar::TwTerminate()
+{
+  //std::cout<<"TwTerminate"<<std::endl;
+  int r = ::TwTerminate();
+  //std::cout<<"  "<<r<<std::endl;
+  return r;
+}
+
+IGL_INLINE bool igl::anttweakbar::ReTwBar::save(const char *file_name)
+{
+  FILE * fp;
+  if(file_name == NULL)
+  {
+    fp = stdout;
+  }else
+  {
+    fp = fopen(file_name,"w");
+  }
+
+  if(fp == NULL)
+  {
+    printf("ERROR: not able to open %s for writing...\n",file_name);
+    return false;
+  }
+
+  // Print all RW variables
+  for(
+    std::vector<ReTwRWItem>::iterator it = rw_items.begin(); 
+    it != rw_items.end(); 
+    it++)
+  {
+    std::string s = (*it).name;
+    const char * name = s.c_str();
+    TwType type = (*it).type;
+    void * var = (*it).var;
+    fprintf(fp,"%s: %s\n",
+      name,
+      get_value_as_string(var,type).c_str());
+  }
+
+  char var[REANTTWEAKBAR_MAX_CB_VAR_SIZE];
+  // Print all CB variables
+  for(
+    std::vector<ReTwCBItem>::iterator it = cb_items.begin(); 
+    it != cb_items.end(); 
+    it++)
+  {
+    const char * name = it->name.c_str();
+    TwType type = it->type;
+    //TwSetVarCallback setCallback = it->setCallback;
+    TwGetVarCallback getCallback = it->getCallback;
+    void * clientData = it->clientData;
+    // I'm not sure how to do what I want to do. getCallback needs to be sure
+    // that it can write to var. So var needs to point to a valid and big
+    // enough chunk of memory
+    getCallback(var,clientData);
+    fprintf(fp,"%s: %s\n",
+      name,
+      get_value_as_string(var,type).c_str());
+  }
+
+  fprintf(fp,"\n");
+
+  if(file_name != NULL)
+  {
+    fclose(fp);
+  }
+  // everything succeeded
+  return true;
+}
+
+IGL_INLINE std::string igl::anttweakbar::ReTwBar::get_value_as_string(
+  void * var, 
+  TwType type)
+{
+  std::stringstream sstr;
+  switch(type)
+  {
+    case TW_TYPE_BOOLCPP:
+      {
+        sstr << "TW_TYPE_BOOLCPP" << " ";
+        sstr << *(static_cast<bool*>(var));
+        break;
+      }
+    case TW_TYPE_QUAT4D:
+      {
+        sstr << "TW_TYPE_QUAT4D" << " ";
+        // Q: Why does casting to double* work? shouldn't I have to cast to
+        // double**?
+        double * q = static_cast<double*>(var);
+        sstr << std::setprecision(15) << q[0] << " " << q[1] << " " << q[2] << " " << q[3];
+        break;
+      }
+    case TW_TYPE_QUAT4F:
+      {
+        sstr << "TW_TYPE_QUAT4F" << " ";
+        // Q: Why does casting to float* work? shouldn't I have to cast to
+        // float**?
+        float * q = static_cast<float*>(var);
+        sstr << q[0] << " " << q[1] << " " << q[2] << " " << q[3];
+        break;
+      }
+    case TW_TYPE_COLOR4F:
+      {
+        sstr << "TW_TYPE_COLOR4F" << " ";
+        float * c = static_cast<float*>(var);
+        sstr << c[0] << " " << c[1] << " " << c[2] << " " << c[3];
+        break;
+      }
+    case TW_TYPE_COLOR3F:
+      {
+        sstr << "TW_TYPE_COLOR3F" << " ";
+        float * c = static_cast<float*>(var);
+        sstr << c[0] << " " << c[1] << " " << c[2];
+        break;
+      }
+    case TW_TYPE_DIR3D:
+      {
+        sstr << "TW_TYPE_DIR3D" << " ";
+        double * d = static_cast<double*>(var);
+        sstr << std::setprecision(15) << d[0] << " " << d[1] << " " << d[2];
+        break;
+      }
+    case TW_TYPE_DIR3F:
+      {
+        sstr << "TW_TYPE_DIR3F" << " ";
+        float * d = static_cast<float*>(var);
+        sstr << d[0] << " " << d[1] << " " << d[2];
+        break;
+      }
+    case TW_TYPE_BOOL32:
+      {
+        sstr << "TW_TYPE_BOOL32" << " ";
+        sstr << *(static_cast<int*>(var));
+        break;
+      }
+    case TW_TYPE_UINT8:
+      {
+        sstr << "TW_TYPE_UINT8" << " ";
+        // Cast to int so that it's human readable
+        sstr << (int)*(static_cast<unsigned char*>(var));
+        break;
+      }
+    case TW_TYPE_INT32:
+      {
+        sstr << "TW_TYPE_INT32" << " ";
+        sstr << *(static_cast<int*>(var));
+        break;
+      }
+    case TW_TYPE_UINT32:
+      {
+        sstr << "TW_TYPE_UINT32" << " ";
+        sstr << *(static_cast<unsigned int*>(var));
+        break;
+      }
+    case TW_TYPE_FLOAT:
+      {
+        sstr << "TW_TYPE_FLOAT" << " ";
+        sstr << *(static_cast<float*>(var));
+        break;
+      }
+    case TW_TYPE_DOUBLE:
+      {
+        sstr << "TW_TYPE_DOUBLE" << " ";
+        sstr << std::setprecision(15) << *(static_cast<double*>(var));
+        break;
+      }
+    case TW_TYPE_STDSTRING:
+      {
+        sstr << "TW_TYPE_STDSTRING" << " ";
+        std::string *destPtr = static_cast<std::string *>(var);
+        sstr << destPtr->c_str();
+        break;
+      }
+    default:
+      {
+        using namespace std;
+        std::map<TwType,std::pair<const char *,std::vector<TwEnumVal> > >::const_iterator iter = 
+          ReTw_custom_types.find(type);
+        if(iter != ReTw_custom_types.end())
+        {
+          sstr << (*iter).second.first << " ";
+          int enum_val = *(static_cast<int*>(var));
+          // try find display name for enum value
+          std::vector<TwEnumVal>::const_iterator eit = (*iter).second.second.begin();
+          bool found = false;
+          for(;eit<(*iter).second.second.end();eit++)
+          {
+            if(enum_val == eit->Value)
+            {
+              sstr << eit->Label;
+              found = true;
+              break;
+            }
+          }
+          if(!found)
+          {
+            sstr << "ERROR_ENUM_VALUE_NOT_DEFINED";
+          }
+        }else
+        {
+          sstr << "ERROR_TYPE_NOT_SUPPORTED";
+        }
+        break;
+      }
+  }
+  return sstr.str();
+}
+
+IGL_INLINE bool igl::anttweakbar::ReTwBar::load(const char *file_name)
+{
+  FILE * fp;
+  fp = fopen(file_name,"r");
+
+  if(fp == NULL)
+  {
+    printf("ERROR: not able to open %s for reading...\n",file_name);
+    return false;
+  }
+
+  // go through file line by line
+  char line[REANTTWEAKBAR_MAX_LINE];
+  bool still_comments;
+  char name[REANTTWEAKBAR_MAX_WORD];
+  char type_str[REANTTWEAKBAR_MAX_WORD];
+  char value_str[REANTTWEAKBAR_MAX_WORD];
+
+
+  // line number
+  int j = 0;
+  bool finished = false;
+  while(true)
+  {
+    // Eat comments
+    still_comments = true;
+    while(still_comments)
+    {
+      if(fgets(line,REANTTWEAKBAR_MAX_LINE,fp) == NULL)
+      {
+        finished = true;
+        break;
+      }
+      // Blank lines and lines that begin with # are comments
+      still_comments = (line[0] == '#' || line[0] == '\n');
+      j++;
+    }
+    if(finished)
+    {
+      break;
+    }
+
+    sscanf(line,"%[^:]: %s %[^\n]",name,type_str,value_str);
+    //printf("%s: %s %s\n",name, type_str,value_str);
+
+    TwType type;
+    if(!type_from_string(type_str,type))
+    {
+      printf("ERROR: %s type not found... Skipping...\n",type_str);
+      continue;
+    }
+    set_value_from_string(name,type,value_str);
+
+  }
+
+  fclose(fp);
+  
+  // everything succeeded
+  return true;
+}
+
+IGL_INLINE bool igl::anttweakbar::ReTwBar::type_from_string(
+  const char *type_str, TwType & type)
+{
+  // first check default types
+  for(int j = 0; j < RETW_NUM_DEFAULT_TYPE_STRINGS; j++)
+  {
+    if(strcmp(type_str,ReTwDefaultTypeStrings[j].type_str) == 0)
+    {
+      type = ReTwDefaultTypeStrings[j].type;
+      return true;
+      break;
+    }
+  }
+
+  // then check custom types
+  std::map<
+    TwType,std::pair<const char *,std::vector<TwEnumVal> > 
+    >::const_iterator iter = 
+    ReTw_custom_types.begin();
+  for(;iter != ReTw_custom_types.end(); iter++)
+  {
+    if(strcmp((*iter).second.first,type_str)==0)
+    {
+      type = (*iter).first;
+      return true;
+    }
+  }
+  return false;
+}
+
+bool igl::anttweakbar::ReTwBar::set_value_from_string(
+  const char * name, 
+  TwType type, 
+  const char * value_str)
+{
+  void * value = NULL;
+  // possible value slots
+  int i;
+  float v;
+  double dv;
+  float f[4];
+  double d[4];
+  bool b;
+  unsigned int u;
+  unsigned char uc;
+  std::string s;
+
+  // First try to get value from default types
+  switch(type)
+  {
+    case TW_TYPE_BOOLCPP:
+      {
+        int ib;
+        if(sscanf(value_str," %d",&ib) == 1)
+        {
+          b = ib!=0;
+          value = &b;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_QUAT4D:
+    //case TW_TYPE_COLOR4D:
+      {
+        if(sscanf(value_str," %lf %lf %lf %lf",&d[0],&d[1],&d[2],&d[3]) == 4)
+        {
+          value = &d;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_QUAT4F:
+    case TW_TYPE_COLOR4F:
+      {
+        if(sscanf(value_str," %f %f %f %f",&f[0],&f[1],&f[2],&f[3]) == 4)
+        {
+          value = &f;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    //case TW_TYPE_COLOR3D:
+    case TW_TYPE_DIR3D:
+      {
+        if(sscanf(value_str," %lf %lf %lf",&d[0],&d[1],&d[2]) == 3)
+        {
+          value = &d;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_COLOR3F:
+    case TW_TYPE_DIR3F:
+      {
+        if(sscanf(value_str," %f %f %f",&f[0],&f[1],&f[2]) == 3)
+        {
+          value = &f;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_UINT8:
+      {
+        if(sscanf(value_str," %d",&i) == 1)
+        {
+          // Cast to unsigned char
+          uc = (unsigned char) i;
+          value = &uc;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_BOOL32:
+    case TW_TYPE_INT32:
+      {
+        if(sscanf(value_str," %d",&i) == 1)
+        {
+          value = &i;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_UINT32:
+      {
+        if(sscanf(value_str," %u",&u) == 1)
+        {
+          value = &u;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_FLOAT:
+      {
+        if(sscanf(value_str," %f",&v) == 1)
+        {
+          value = &v;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_DOUBLE:
+      {
+        if(sscanf(value_str," %lf",&dv) == 1)
+        {
+          value = &dv;
+        }else
+        {
+          printf("ERROR: Bad value format...\n");
+          return false;
+        }
+        break;
+      }
+    case TW_TYPE_STDSTRING:
+      {
+        s  = value_str;
+        value = &s;
+        break;
+      }
+    default:
+      // Try to find type in custom enum types
+      std::map<TwType,std::pair<const char *,std::vector<TwEnumVal> > >::const_iterator iter = 
+        ReTw_custom_types.find(type);
+      if(iter != ReTw_custom_types.end())
+      {
+        std::vector<TwEnumVal>::const_iterator eit = (*iter).second.second.begin();
+        bool found = false;
+        for(;eit<(*iter).second.second.end();eit++)
+        {
+          if(strcmp(value_str,eit->Label) == 0)
+          {
+            i = eit->Value;
+            value = &i;
+            found = true;
+            break;
+          }
+        }
+        if(!found)
+        {
+          printf("ERROR_ENUM_VALUE_NOT_DEFINED");
+        }
+      }else
+      {
+        printf("ERROR_TYPE_NOT_SUPPORTED\n");
+      }
+
+      break;
+  }
+
+
+  // Find variable based on name
+  // First look in RW items
+  bool item_found = false;
+  for(
+    std::vector<ReTwRWItem>::iterator it = rw_items.begin(); 
+    it != rw_items.end(); 
+    it++)
+  {
+    if(it->name == name)
+    {
+      void * var = it->var;
+      switch(type)
+      {
+        case TW_TYPE_BOOLCPP:
+          {
+            bool * bvar = static_cast<bool*>(var);
+            bool * bvalue = static_cast<bool*>(value);
+            *bvar = *bvalue;
+            break;
+          }
+        case TW_TYPE_QUAT4D:
+        //case TW_TYPE_COLOR4D:
+          {
+            double * dvar = static_cast<double*>(var);
+            double * dvalue = static_cast<double*>(value);
+            dvar[0] = dvalue[0];
+            dvar[1] = dvalue[1];
+            dvar[2] = dvalue[2];
+            dvar[3] = dvalue[3];
+            break;
+          }
+        case TW_TYPE_QUAT4F:
+        case TW_TYPE_COLOR4F:
+          {
+            float * fvar = static_cast<float*>(var);
+            float * fvalue = static_cast<float*>(value);
+            fvar[0] = fvalue[0];
+            fvar[1] = fvalue[1];
+            fvar[2] = fvalue[2];
+            fvar[3] = fvalue[3];
+            break;
+          }
+        //case TW_TYPE_COLOR3D:
+        case TW_TYPE_DIR3D:
+          {
+            double * dvar = static_cast<double*>(var);
+            double * dvalue = static_cast<double*>(value);
+            dvar[0] = dvalue[0];
+            dvar[1] = dvalue[1];
+            dvar[2] = dvalue[2];
+            break;
+          }
+        case TW_TYPE_COLOR3F:
+        case TW_TYPE_DIR3F:
+          {
+            float * fvar = static_cast<float*>(var);
+            float * fvalue = static_cast<float*>(value);
+            fvar[0] = fvalue[0];
+            fvar[1] = fvalue[1];
+            fvar[2] = fvalue[2];
+            break;
+          }
+        case TW_TYPE_UINT8:
+          {
+            unsigned char * ucvar = static_cast<unsigned char*>(var);
+            unsigned char * ucvalue = static_cast<unsigned char*>(value);
+            *ucvar = *ucvalue;
+            break;
+          }
+        case TW_TYPE_BOOL32:
+        case TW_TYPE_INT32:
+          {
+            int * ivar = static_cast<int*>(var);
+            int * ivalue = static_cast<int*>(value);
+            *ivar = *ivalue;
+            break;
+          }
+        case TW_TYPE_UINT32:
+          {
+            unsigned int * uvar =   static_cast<unsigned int*>(var);
+            unsigned int * uvalue = static_cast<unsigned int*>(value);
+            *uvar = *uvalue;
+            break;
+          }
+        case TW_TYPE_FLOAT:
+          {
+            float * fvar = static_cast<float*>(var);
+            float * fvalue = static_cast<float*>(value);
+            *fvar = *fvalue;
+            break;
+          }
+        case TW_TYPE_DOUBLE:
+          {
+            double * dvar =   static_cast<double*>(var);
+            double * fvalue = static_cast<double*>(value);
+            *dvar = *fvalue;
+            break;
+          }
+        case TW_TYPE_STDSTRING:
+          {
+            std::string * svar =   static_cast<std::string*>(var);
+            std::string * svalue = static_cast<std::string*>(value);
+            *svar = *svalue;
+            break;
+          }
+        default:
+          // Try to find type in custom enum types
+          std::map<TwType,std::pair<const char *,std::vector<TwEnumVal> > >::iterator iter = 
+            ReTw_custom_types.find(type);
+          if(iter != ReTw_custom_types.end())
+          {
+            int * ivar = static_cast<int*>(var);
+            std::vector<TwEnumVal>::iterator eit = (*iter).second.second.begin();
+            bool found = false;
+            for(;eit<(*iter).second.second.end();eit++)
+            {
+              if(strcmp(value_str,eit->Label) == 0)
+              {
+                *ivar = eit->Value;
+                found = true;
+                break;
+              }
+            }
+            if(!found)
+            {
+              printf("ERROR_ENUM_VALUE_NOT_DEFINED");
+            }
+          }else
+          {
+            printf("ERROR_TYPE_NOT_SUPPORTED\n");
+          }
+          break;
+      }
+      item_found = true;
+      break;
+    }
+  }
+
+  // Try looking in CB items
+  if(!item_found)
+  {
+    for(
+      std::vector<ReTwCBItem>::iterator it = cb_items.begin(); 
+      it != cb_items.end(); 
+      it++)
+    {
+      if(it->name==name)
+      {
+        it->setCallback(value,it->clientData);
+        item_found = true;
+        break;
+      }
+    }
+  }
+
+  if(!item_found)
+  {
+    printf("ERROR: item '%s' not found\n",name);
+  }
+  return true;
+}
+
+IGL_INLINE const std::vector<igl::anttweakbar::ReTwRWItem> & 
+  igl::anttweakbar::ReTwBar::get_rw_items()
+{
+  return rw_items;
+}
+
+IGL_INLINE const std::vector<igl::anttweakbar::ReTwCBItem> & 
+  igl::anttweakbar::ReTwBar::get_cb_items()
+{
+  return cb_items;
+}

src/igl/anttweakbar/ReAntTweakBar.h

@@ -0,0 +1,286 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ANTTWEAKBAR_REANTTWEAKBAR_H
+#define IGL_ANTTWEAKBAR_REANTTWEAKBAR_H
+#include "../igl_inline.h"
+// ReAntTweakBar is a minimal wrapper for the AntTweakBar library that allows
+// "bars" to be saved and load from disk. Changing your existing app that uses
+// AntTweakBar to use ReAntTweakBar is trivial.
+// 
+// Many (but not all) variable types are supported. I'll try to keep track them
+// here:
+//   TW_TYPE_BOOLCPP
+//   TW_TYPE_QUAT4F
+//   TW_TYPE_QUAT4D
+//   TW_TYPE_COLOR4F
+//   TW_TYPE_COLOR4D
+//   TW_TYPE_COLOR3F
+//   TW_TYPE_DIR3F
+//   TW_TYPE_DIR3D
+//   TW_TYPE_BOOL32
+//   TW_TYPE_INT32
+//   TW_TYPE_UINT32
+//   TW_TYPE_FLOAT
+//   TW_TYPE_DOUBLE
+//   TW_TYPE_UINT8
+//   and
+//   custom TwTypes made with TwDefineEnum
+// 
+// I'm working on adding the rest on an as-needed basis. Adding a new type only
+// requires changes in a few places...
+// 
+//
+//
+
+// This allows the user to have a non-global, static installation of
+// AntTweakBar
+#include <AntTweakBar.h>
+// Instead of including AntTweakBar.h, just define the necessary types
+// Types used:
+//   - TwType
+//   - TwEnumVal
+//   - TwSetVarCallback
+//   - TwGetVarCallback
+//   - TwBar
+//   - TwButtonCallback
+
+
+#include <vector>
+#include <string>
+
+#define REANTTWEAKBAR_MAX_CB_VAR_SIZE 1000
+// Max line size for reading files
+#define REANTTWEAKBAR_MAX_LINE 1000
+#define REANTTWEAKBAR_MAX_WORD 100
+
+namespace igl
+{
+  namespace anttweakbar
+  {
+    TwType ReTwDefineEnum(
+      const char *name, 
+      const TwEnumVal *enumValues, 
+      unsigned int nbValues);
+    TwType ReTwDefineEnumFromString(const char * name,const char * enumString);
+    
+    struct ReTwRWItem
+    {
+      //const char * name;
+      std::string name;
+      TwType type;
+      void * var;
+      // Default constructor
+      IGL_INLINE ReTwRWItem(
+        const std::string _name,
+        TwType _type, 
+        void *_var):
+        name(_name),
+        type(_type),
+        var(_var)
+      {
+      }
+      // Shallow copy constructor
+      // I solemnly swear it's OK to copy var this way
+      // Q: Is it really?
+      IGL_INLINE ReTwRWItem(const ReTwRWItem & that):
+        name(that.name),
+        type(that.type),
+        var(that.var)
+      {
+      }
+      // Shallow assignment 
+      // I solemnly swear it's OK to copy var this way
+      IGL_INLINE ReTwRWItem & operator=(const ReTwRWItem & that)
+      {
+        if(this != &that)
+        {
+          this->name = that.name;
+          this->type = that.type;
+          this->var = that.var;
+        }
+        return *this;
+      }
+    };
+    
+    struct ReTwCBItem
+    {
+      //const char * name;
+      std::string name;
+      TwType type;
+      TwSetVarCallback setCallback;
+      TwGetVarCallback getCallback;
+      void * clientData;
+      // Default constructor
+      IGL_INLINE ReTwCBItem(
+        const std::string _name,
+        TwType _type, 
+        TwSetVarCallback _setCallback,
+        TwGetVarCallback _getCallback,
+        void * _clientData):
+        name(_name),
+        type(_type),
+        setCallback(_setCallback),
+        getCallback(_getCallback),
+        clientData(_clientData)
+      {
+      }
+      // Shallow copy
+      // I solemnly swear it's OK to copy clientData this way
+      IGL_INLINE ReTwCBItem(const ReTwCBItem & that):
+        name(that.name),
+        type(that.type),
+        setCallback(that.setCallback),
+        getCallback(that.getCallback),
+        clientData(that.clientData)
+      {
+      }
+      // Shallow assignment
+      // I solemnly swear it's OK to copy clientData this way
+      IGL_INLINE ReTwCBItem & operator=(const ReTwCBItem & that)
+      {
+        if(this != &that)
+        {
+          name = that.name;
+          type = that.type;
+          setCallback = that.setCallback;
+          getCallback = that.getCallback;
+          clientData = that.clientData;
+        }
+        return *this;
+      }
+  
+    };
+    
+    class ReTwBar
+    {
+      // VARIABLES
+      // Should be private, but seeing as I'm not going to implement all of the
+      // AntTweakBar public functions right away, I'll expose this so that at
+      // anytime AntTweakBar functions can be called directly on the bar
+      public:
+        TwBar * bar;
+        std::string name;
+      protected:
+        std::vector<ReTwRWItem> rw_items;
+        std::vector<ReTwCBItem> cb_items;
+      public:
+        // Default constructor with explicit initialization
+        IGL_INLINE ReTwBar();
+      private:
+        // Copy constructor does shallow copy
+        IGL_INLINE ReTwBar(const ReTwBar & that);
+        // Assignment operator does shallow assignment
+        IGL_INLINE ReTwBar &operator=(const ReTwBar & that);
+    
+      // WRAPPERS FOR ANTTWEAKBAR FUNCTIONS 
+      public:
+        IGL_INLINE void TwNewBar(const char *_name);
+        IGL_INLINE int TwAddVarRW(
+          const char *name, 
+          TwType type, 
+          void *var, 
+          const char *def,
+          const bool record=true);
+        IGL_INLINE int TwAddVarCB(
+          const char *name, 
+          TwType type, 
+          TwSetVarCallback setCallback, 
+          TwGetVarCallback getCallback, 
+          void *clientData, 
+          const char *def,
+          const bool record=true);
+        // Wrappers for convenience (not recorded, just passed on)
+        IGL_INLINE int TwAddVarRO(const char *name, TwType type, void *var, const char *def);
+        IGL_INLINE int TwAddButton(
+          const char *name, 
+          TwButtonCallback buttonCallback, 
+          void *clientData, 
+          const char *def);
+        IGL_INLINE int TwSetParam(
+          const char *varName, 
+          const char *paramName, 
+          TwParamValueType paramValueType, 
+          unsigned int inValueCount, 
+          const void *inValues);
+        IGL_INLINE int TwGetParam(
+          const char *varName, 
+          const char *paramName, 
+          TwParamValueType paramValueType, 
+          unsigned int outValueMaxCount, 
+          void *outValues);
+        IGL_INLINE int TwRefreshBar();
+        IGL_INLINE int TwTerminate();
+    
+    
+      // IO FUNCTIONS
+      public:
+        // Save current items to file
+        // Input:
+        //   file_name  name of file to save data to, can be null which means print
+        //   to stdout
+        // Return:
+        //   true only if there were no (fatal) errors
+        IGL_INLINE bool save(const char *file_name);
+        std::string get_value_as_string(
+          void * var, 
+          TwType type);
+        // Load into current items from file
+        // Input:
+        //   file_name  name of input file to load
+        // Return:
+        //   true only if there were no (fatal) errors
+        IGL_INLINE bool load(const char *file_name);
+        // Get TwType from string
+        // Input
+        //   type_str  string of type 
+        // Output
+        //   type  TwType converted from string
+        // Returns
+        //   true only if string matched a valid type
+        IGL_INLINE bool type_from_string(const char *type_str, TwType & type);
+        // I realize that I mix std::string and const char * all over the place.
+        // What can you do...
+        IGL_INLINE bool set_value_from_string(
+          const char * name, 
+          TwType type, 
+          const char * value_str);
+        IGL_INLINE const std::vector<ReTwRWItem> & get_rw_items();
+        IGL_INLINE const std::vector<ReTwCBItem> & get_cb_items();
+    };
+  }
+}
+
+// List of TwBar functions
+//TW_API TwBar *      TW_CALL TwNewBar(const char *barName);
+//TW_API int          TW_CALL TwDeleteBar(TwBar *bar);
+//TW_API int          TW_CALL TwDeleteAllBars();
+//TW_API int          TW_CALL TwSetTopBar(const TwBar *bar);
+//TW_API TwBar *      TW_CALL TwGetTopBar();
+//TW_API int          TW_CALL TwSetBottomBar(const TwBar *bar);
+//TW_API TwBar *      TW_CALL TwGetBottomBar();
+//TW_API const char * TW_CALL TwGetBarName(TwBar *bar);
+//TW_API int          TW_CALL TwGetBarCount();
+//TW_API TwBar *      TW_CALL TwGetBarByIndex(int barIndex);
+//TW_API TwBar *      TW_CALL TwGetBarByName(const char *barName);
+//TW_API int          TW_CALL TwRefreshBar(TwBar *bar);
+//TW_API int          TW_CALL TwTerminate();
+//
+//TW_API int      TW_CALL TwAddVarRW(TwBar *bar, const char *name, TwType type, void *var, const char *def);
+//TW_API int      TW_CALL TwAddVarRO(TwBar *bar, const char *name, TwType type, const void *var, const char *def);
+//TW_API int      TW_CALL TwAddVarCB(TwBar *bar, const char *name, TwType type, TwSetVarCallback setCallback, TwGetVarCallback getCallback, void *clientData, const char *def);
+//TW_API int      TW_CALL TwAddButton(TwBar *bar, const char *name, TwButtonCallback callback, void *clientData, const char *def);
+//TW_API int      TW_CALL TwAddSeparator(TwBar *bar, const char *name, const char *def);
+//TW_API int      TW_CALL TwRemoveVar(TwBar *bar, const char *name);
+//TW_API int      TW_CALL TwRemoveAllVars(TwBar *bar);
+
+// Until AntTweakBar dependency folder exists, this is header-only
+#ifndef IGL_STATIC_LIBRARY
+#  include "ReAntTweakBar.cpp"
+#endif
+
+#endif

src/igl/anttweakbar/cocoa_key_to_anttweakbar_key.cpp

@@ -0,0 +1,81 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "cocoa_key_to_anttweakbar_key.h"
+
+#include <AntTweakBar.h>
+
+IGL_INLINE int igl::anttweakbar::cocoa_key_to_anttweakbar_key(int key)
+{
+  // I've left commented the AntTweakBar key codes that correspond to keys I
+  // don't have on my keyboard. Please fill this in if you have those keys
+  switch(key)
+  {
+    case 127:
+      return TW_KEY_BACKSPACE;
+    case 9:
+      return TW_KEY_TAB;
+  //TW_KEY_CLEAR        = 0x0c,
+    case 3://ENTER
+    case 13:
+      return TW_KEY_RETURN;
+    case 27:
+      return TW_KEY_ESCAPE;
+    case 32:
+      return TW_KEY_SPACE;
+    // IN A GLUT APP 40 is (
+    //case 40:
+    case 63272:
+      return TW_KEY_DELETE;
+    case 63232:
+      return TW_KEY_UP;
+    case 63233:
+      return TW_KEY_DOWN;
+    case 63235:
+      return TW_KEY_RIGHT;
+    case 63234:
+      return TW_KEY_LEFT;
+  //TW_KEY_INSERT,
+  //TW_KEY_HOME,
+  //TW_KEY_END,
+  //TW_KEY_PAGE_UP,
+  //TW_KEY_PAGE_DOWN,
+    case 63236:
+      return TW_KEY_F1;
+    case 63237:
+      return TW_KEY_F2;
+    case 63238:
+      return TW_KEY_F3;
+    case 63239:
+      return TW_KEY_F4;
+    case 63240:
+      return TW_KEY_F5;
+    case 63241:
+      return TW_KEY_F6;
+    case 63242:
+      return TW_KEY_F7;
+    case 63243:
+      return TW_KEY_F8;
+    case 63244:
+      return TW_KEY_F9;
+    case 63245:
+      return TW_KEY_F10;
+    case 63246:
+      return TW_KEY_F11;
+    case 63247:
+      return TW_KEY_F12;
+    case 63248:
+      return TW_KEY_F13;
+    case 63249:
+      return TW_KEY_F14;
+    case 63250:
+      return TW_KEY_F15;
+    default:
+      break;
+  }
+  return key;
+}

src/igl/anttweakbar/cocoa_key_to_anttweakbar_key.h

@@ -0,0 +1,31 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ANTTWEAKBAR_COCOA_KEY_TO_ANTTWEAKBAR_KEY_H
+#define IGL_ANTTWEAKBAR_COCOA_KEY_TO_ANTTWEAKBAR_KEY_H
+#include "../igl_inline.h"
+
+
+namespace igl
+{
+  namespace anttweakbar
+  {
+    // Convert an unsigned char (like that from Cocoa apps) to AntTweakBar key
+    // code.
+    // See also: TranslateKey() in TwMgr.cpp in AntTweakBar source
+    // Inputs:
+    //   key  unsigned char key from keyboard
+    // Returns int of new key code 
+    IGL_INLINE int cocoa_key_to_anttweakbar_key(int key);
+  }
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "cocoa_key_to_anttweakbar_key.cpp"
+#endif
+
+#endif

src/igl/any.cpp

@@ -0,0 +1,26 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "any.h"
+#include "redux.h"
+
+
+template <typename AType, typename DerivedB>
+IGL_INLINE void igl::any(
+  const Eigen::SparseMatrix<AType> & A, 
+  const int dim,
+  Eigen::PlainObjectBase<DerivedB>& B)
+{
+  typedef typename DerivedB::Scalar Scalar;
+  igl::redux(A,dim,[](Scalar a, Scalar b){ return a || b!=0;},B);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::any<bool, Eigen::Array<bool, -1, 1, 0, -1, 1> >(Eigen::SparseMatrix<bool, 0, int> const&, int, Eigen::PlainObjectBase<Eigen::Array<bool, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/any.h

@@ -0,0 +1,35 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ANY_H
+#define IGL_ANY_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+namespace igl
+{
+  // For Dense matrices use: A.rowwise().any() or A.colwise().any()
+  //
+  // Inputs:
+  //   A  m by n sparse matrix
+  //   dim  dimension along which to check for any (1 or 2)
+  // Output:
+  //   B  n-long vector (if dim == 1) 
+  //   or
+  //   B  m-long vector (if dim == 2)
+  //
+  template <typename AType, typename DerivedB>
+  IGL_INLINE void any(
+    const Eigen::SparseMatrix<AType> & A, 
+    const int dim,
+    Eigen::PlainObjectBase<DerivedB>& B);
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "any.cpp"
+#endif
+#endif
+

src/igl/any_of.cpp

@@ -0,0 +1,20 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "any_of.h"
+#include <Eigen/Core>
+template <typename Mat>
+IGL_INLINE bool igl::any_of(const Mat & S)
+{
+  return std::any_of(S.data(),S.data()+S.size(),[](bool s){return s;});
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::any_of<Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::Matrix<int, -1, 1, 0, -1, 1> const&);
+#endif
+

src/igl/any_of.h

@@ -0,0 +1,26 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ANY_OF_H
+#define IGL_ANY_OF_H
+#include "igl_inline.h"
+namespace igl
+{
+  // Wrapper for STL `any_of` for matrix types
+  //
+  // Inputs:
+  //   S  matrix
+  // Returns whether any entries are true
+  //
+  // Seems that Eigen (now) implements this for `Eigen::Array` 
+  template <typename Mat>
+  IGL_INLINE bool any_of(const Mat & S);
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "any_of.cpp"
+#endif
+#endif

src/igl/arap.cpp

@@ -0,0 +1,312 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "arap.h"
+#include "colon.h"
+#include "cotmatrix.h"
+#include "massmatrix.h"
+#include "group_sum_matrix.h"
+#include "covariance_scatter_matrix.h"
+#include "speye.h"
+#include "mode.h"
+#include "project_isometrically_to_plane.h"
+#include "slice.h"
+#include "arap_rhs.h"
+#include "repdiag.h"
+#include "columnize.h"
+#include "fit_rotations.h"
+#include <cassert>
+#include <iostream>
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Derivedb>
+IGL_INLINE bool igl::arap_precomputation(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  const int dim,
+  const Eigen::PlainObjectBase<Derivedb> & b,
+  ARAPData & data)
+{
+  using namespace std;
+  using namespace Eigen;
+  typedef typename DerivedV::Scalar Scalar;
+  // number of vertices
+  const int n = V.rows();
+  data.n = n;
+  assert((b.size() == 0 || b.maxCoeff() < n) && "b out of bounds");
+  assert((b.size() == 0 || b.minCoeff() >=0) && "b out of bounds");
+  // remember b
+  data.b = b;
+  //assert(F.cols() == 3 && "For now only triangles");
+  // dimension
+  //const int dim = V.cols();
+  assert((dim == 3 || dim ==2) && "dim should be 2 or 3");
+  data.dim = dim;
+  //assert(dim == 3 && "Only 3d supported");
+  // Defaults
+  data.f_ext = MatrixXd::Zero(n,data.dim);
+
+  assert(data.dim <= V.cols() && "solve dim should be <= embedding");
+  bool flat = (V.cols() - data.dim)==1;
+
+  DerivedV plane_V;
+  DerivedF plane_F;
+  typedef SparseMatrix<Scalar> SparseMatrixS;
+  SparseMatrixS ref_map,ref_map_dim;
+  if(flat)
+  {
+    project_isometrically_to_plane(V,F,plane_V,plane_F,ref_map);
+    repdiag(ref_map,dim,ref_map_dim);
+  }
+  const PlainObjectBase<DerivedV>& ref_V = (flat?plane_V:V);
+  const PlainObjectBase<DerivedF>& ref_F = (flat?plane_F:F);
+  SparseMatrixS L;
+  cotmatrix(V,F,L);
+
+  ARAPEnergyType eff_energy = data.energy;
+  if(eff_energy == ARAP_ENERGY_TYPE_DEFAULT)
+  {
+    switch(F.cols())
+    {
+      case 3:
+        if(data.dim == 3)
+        {
+          eff_energy = ARAP_ENERGY_TYPE_SPOKES_AND_RIMS;
+        }else
+        {
+          eff_energy = ARAP_ENERGY_TYPE_ELEMENTS;
+        }
+        break;
+      case 4:
+        eff_energy = ARAP_ENERGY_TYPE_ELEMENTS;
+        break;
+      default:
+        assert(false);
+    }
+  }
+
+
+  // Get covariance scatter matrix, when applied collects the covariance
+  // matrices used to fit rotations to during optimization
+  covariance_scatter_matrix(ref_V,ref_F,eff_energy,data.CSM);
+  if(flat)
+  {
+    data.CSM = (data.CSM * ref_map_dim.transpose()).eval();
+  }
+  assert(data.CSM.cols() == V.rows()*data.dim);
+
+  // Get group sum scatter matrix, when applied sums all entries of the same
+  // group according to G
+  SparseMatrix<double> G_sum;
+  if(data.G.size() == 0)
+  {
+    if(eff_energy == ARAP_ENERGY_TYPE_ELEMENTS)
+    {
+      speye(F.rows(),G_sum);
+    }else
+    {
+      speye(n,G_sum);
+    }
+  }else
+  {
+    // groups are defined per vertex, convert to per face using mode
+    if(eff_energy == ARAP_ENERGY_TYPE_ELEMENTS)
+    {
+      Eigen::Matrix<int,Eigen::Dynamic,1> GG;
+      MatrixXi GF(F.rows(),F.cols());
+      for(int j = 0;j<F.cols();j++)
+      {
+        Matrix<int,Eigen::Dynamic,1> GFj;
+        slice(data.G,F.col(j),GFj);
+        GF.col(j) = GFj;
+      }
+      mode<int>(GF,2,GG);
+      data.G=GG;
+    }
+    //printf("group_sum_matrix()\n");
+    group_sum_matrix(data.G,G_sum);
+  }
+  SparseMatrix<double> G_sum_dim;
+  repdiag(G_sum,data.dim,G_sum_dim);
+  assert(G_sum_dim.cols() == data.CSM.rows());
+  data.CSM = (G_sum_dim * data.CSM).eval();
+
+
+  arap_rhs(ref_V,ref_F,data.dim,eff_energy,data.K);
+  if(flat)
+  {
+    data.K = (ref_map_dim * data.K).eval();
+  }
+  assert(data.K.rows() == data.n*data.dim);
+
+  SparseMatrix<double> Q = (-L).eval();
+
+  if(data.with_dynamics)
+  {
+    const double h = data.h;
+    assert(h != 0);
+    SparseMatrix<double> M;
+    massmatrix(V,F,MASSMATRIX_TYPE_DEFAULT,data.M);
+    const double dw = (1./data.ym)*(h*h);
+    SparseMatrix<double> DQ = dw * 1./(h*h)*data.M;
+    Q += DQ;
+    // Dummy external forces
+    data.f_ext = MatrixXd::Zero(n,data.dim);
+    data.vel = MatrixXd::Zero(n,data.dim);
+  }
+
+  return min_quad_with_fixed_precompute(
+    Q,b,SparseMatrix<double>(),true,data.solver_data);
+}
+
+template <
+  typename Derivedbc,
+  typename DerivedU>
+IGL_INLINE bool igl::arap_solve(
+  const Eigen::PlainObjectBase<Derivedbc> & bc,
+  ARAPData & data,
+  Eigen::PlainObjectBase<DerivedU> & U)
+{
+  using namespace Eigen;
+  using namespace std;
+  assert(data.b.size() == bc.rows());
+  if(bc.size() > 0)
+  {
+    assert(bc.cols() == data.dim && "bc.cols() match data.dim");
+  }
+  const int n = data.n;
+  int iter = 0;
+  if(U.size() == 0)
+  {
+    // terrible initial guess.. should at least copy input mesh
+#ifndef NDEBUG
+    cerr<<"arap_solve: Using terrible initial guess for U. Try U = V."<<endl;
+#endif
+    U = MatrixXd::Zero(data.n,data.dim);
+  }else
+  {
+    assert(U.cols() == data.dim && "U.cols() match data.dim");
+  }
+  // changes each arap iteration
+  MatrixXd U_prev = U;
+  // doesn't change for fixed with_dynamics timestep
+  MatrixXd U0;
+  if(data.with_dynamics)
+  {
+    U0 = U_prev;
+  }
+  while(iter < data.max_iter)
+  {
+    U_prev = U;
+    // enforce boundary conditions exactly
+    for(int bi = 0;bi<bc.rows();bi++)
+    {
+      U.row(data.b(bi)) = bc.row(bi);
+    }
+
+    const auto & Udim = U.replicate(data.dim,1);
+    assert(U.cols() == data.dim);
+    // As if U.col(2) was 0
+    MatrixXd S = data.CSM * Udim;
+    // THIS NORMALIZATION IS IMPORTANT TO GET SINGLE PRECISION SVD CODE TO WORK
+    // CORRECTLY.
+    S /= S.array().abs().maxCoeff();
+
+    const int Rdim = data.dim;
+    MatrixXd R(Rdim,data.CSM.rows());
+    if(R.rows() == 2)
+    {
+      fit_rotations_planar(S,R);
+    }else
+    {
+      fit_rotations(S,true,R);
+//#ifdef __SSE__ // fit_rotations_SSE will convert to float if necessary
+//      fit_rotations_SSE(S,R);
+//#else
+//      fit_rotations(S,true,R);
+//#endif
+    }
+    //for(int k = 0;k<(data.CSM.rows()/dim);k++)
+    //{
+    //  R.block(0,dim*k,dim,dim) = MatrixXd::Identity(dim,dim);
+    //}
+
+
+    // Number of rotations: #vertices or #elements
+    int num_rots = data.K.cols()/Rdim/Rdim;
+    // distribute group rotations to vertices in each group
+    MatrixXd eff_R;
+    if(data.G.size() == 0)
+    {
+      // copy...
+      eff_R = R;
+    }else
+    {
+      eff_R.resize(Rdim,num_rots*Rdim);
+      for(int r = 0;r<num_rots;r++)
+      {
+        eff_R.block(0,Rdim*r,Rdim,Rdim) =
+          R.block(0,Rdim*data.G(r),Rdim,Rdim);
+      }
+    }
+
+    MatrixXd Dl;
+    if(data.with_dynamics)
+    {
+      assert(data.M.rows() == n &&
+        "No mass matrix. Call arap_precomputation if changing with_dynamics");
+      const double h = data.h;
+      assert(h != 0);
+      //Dl = 1./(h*h*h)*M*(-2.*V0 + Vm1) - fext;
+      // data.vel = (V0-Vm1)/h
+      // h*data.vel = (V0-Vm1)
+      // -h*data.vel = -V0+Vm1)
+      // -V0-h*data.vel = -2V0+Vm1
+      const double dw = (1./data.ym)*(h*h);
+      Dl = dw * (1./(h*h)*data.M*(-U0 - h*data.vel) - data.f_ext);
+    }
+
+    VectorXd Rcol;
+    columnize(eff_R,num_rots,2,Rcol);
+    VectorXd Bcol = -data.K * Rcol;
+    assert(Bcol.size() == data.n*data.dim);
+    for(int c = 0;c<data.dim;c++)
+    {
+      VectorXd Uc,Bc,bcc,Beq;
+      Bc = Bcol.block(c*n,0,n,1);
+      if(data.with_dynamics)
+      {
+        Bc += Dl.col(c);
+      }
+      if(bc.size()>0)
+      {
+        bcc = bc.col(c);
+      }
+      min_quad_with_fixed_solve(
+        data.solver_data,
+        Bc,bcc,Beq,
+        Uc);
+      U.col(c) = Uc;
+    }
+
+    iter++;
+  }
+  if(data.with_dynamics)
+  {
+    // Keep track of velocity for next time
+    data.vel = (U-U0)/data.h;
+  }
+
+  return true;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+template bool igl::arap_solve<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, igl::ARAPData&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template bool igl::arap_precomputation<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, igl::ARAPData&);
+#endif

src/igl/arap.h

@@ -0,0 +1,104 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ARAP_H
+#define IGL_ARAP_H
+#include "igl_inline.h"
+#include "min_quad_with_fixed.h"
+#include "ARAPEnergyType.h"
+#include <Eigen/Core>
+#include <Eigen/Sparse>
+
+namespace igl
+{
+  struct ARAPData
+  {
+    // n  #V
+    // G  #V list of group indices (1 to k) for each vertex, such that vertex i
+    //    is assigned to group G(i)
+    // energy  type of energy to use
+    // with_dynamics  whether using dynamics (need to call arap_precomputation
+    //   after changing)
+    // f_ext  #V by dim list of external forces
+    // vel  #V by dim list of velocities
+    // h  dynamics time step
+    // ym  ~Young's modulus smaller is softer, larger is more rigid/stiff
+    // max_iter  maximum inner iterations
+    // K  rhs pre-multiplier
+    // M  mass matrix
+    // solver_data  quadratic solver data
+    // b  list of boundary indices into V
+    // dim  dimension being used for solving
+    int n;
+    Eigen::VectorXi G;
+    ARAPEnergyType energy;
+    bool with_dynamics;
+    Eigen::MatrixXd f_ext,vel;
+    double h;
+    double ym;
+    int max_iter;
+    Eigen::SparseMatrix<double> K,M;
+    Eigen::SparseMatrix<double> CSM;
+    min_quad_with_fixed_data<double> solver_data;
+    Eigen::VectorXi b;
+    int dim;
+      ARAPData():
+        n(0),
+        G(),
+        energy(ARAP_ENERGY_TYPE_DEFAULT),
+        with_dynamics(false),
+        f_ext(),
+        h(1),
+        ym(1),
+        max_iter(10),
+        K(),
+        CSM(),
+        solver_data(),
+        b(),
+        dim(-1) // force this to be set by _precomputation
+    {
+    };
+  };
+  
+  // Compute necessary information to start using an ARAP deformation
+  //
+  // Inputs:
+  //   V  #V by dim list of mesh positions
+  //   F  #F by simplex-size list of triangle|tet indices into V
+  //   dim  dimension being used at solve time. For deformation usually dim =
+  //     V.cols(), for surface parameterization V.cols() = 3 and dim = 2
+  //   b  #b list of "boundary" fixed vertex indices into V
+  // Outputs:
+  //   data  struct containing necessary precomputation
+  template <
+    typename DerivedV,
+    typename DerivedF,
+    typename Derivedb>
+  IGL_INLINE bool arap_precomputation(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedF> & F,
+    const int dim,
+    const Eigen::PlainObjectBase<Derivedb> & b,
+    ARAPData & data);
+  // Inputs:
+  //   bc  #b by dim list of boundary conditions
+  //   data  struct containing necessary precomputation and parameters
+  //   U  #V by dim initial guess
+  template <
+    typename Derivedbc,
+    typename DerivedU>
+  IGL_INLINE bool arap_solve(
+    const Eigen::PlainObjectBase<Derivedbc> & bc,
+    ARAPData & data,
+    Eigen::PlainObjectBase<DerivedU> & U);
+};
+
+#ifndef IGL_STATIC_LIBRARY
+#include "arap.cpp"
+#endif
+
+#endif

src/igl/arap_dof.cpp

@@ -0,0 +1,884 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "arap_dof.h"
+
+#include "cotmatrix.h"
+#include "massmatrix.h"
+#include "speye.h"
+#include "repdiag.h"
+#include "repmat.h"
+#include "slice.h"
+#include "colon.h"
+#include "is_sparse.h"
+#include "mode.h"
+#include "is_symmetric.h"
+#include "group_sum_matrix.h"
+#include "arap_rhs.h"
+#include "covariance_scatter_matrix.h"
+#include "fit_rotations.h"
+
+#include "verbose.h"
+#include "print_ijv.h"
+
+#include "get_seconds_hires.h"
+//#include "MKLEigenInterface.h"
+#include "min_quad_dense.h"
+#include "get_seconds.h"
+#include "columnize.h"
+
+// defined if no early exit is supported, i.e., always take a fixed number of iterations
+#define IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+
+// A careful derivation of this implementation is given in the corresponding
+// matlab function arap_dof.m
+template <typename LbsMatrixType, typename SSCALAR>
+IGL_INLINE bool igl::arap_dof_precomputation(
+  const Eigen::MatrixXd & V, 
+  const Eigen::MatrixXi & F,
+  const LbsMatrixType & M,
+  const Eigen::Matrix<int,Eigen::Dynamic,1> & G,
+  ArapDOFData<LbsMatrixType, SSCALAR> & data)
+{
+  using namespace Eigen;
+  typedef Matrix<SSCALAR, Dynamic, Dynamic> MatrixXS;
+  // number of mesh (domain) vertices
+  int n = V.rows();
+  // cache problem size
+  data.n = n;
+  // dimension of mesh
+  data.dim = V.cols();
+  assert(data.dim == M.rows()/n);
+  assert(data.dim*n == M.rows());
+  if(data.dim == 3)
+  {
+    // Check if z-coordinate is all zeros
+    if(V.col(2).minCoeff() == 0 && V.col(2).maxCoeff() == 0)
+    {
+      data.effective_dim = 2;
+    }
+  }else
+  {
+    data.effective_dim = data.dim;
+  }
+  // Number of handles
+  data.m = M.cols()/data.dim/(data.dim+1);
+  assert(data.m*data.dim*(data.dim+1) == M.cols());
+  //assert(m == C.rows());
+
+  //printf("n=%d; dim=%d; m=%d;\n",n,data.dim,data.m);
+
+  // Build cotangent laplacian
+  SparseMatrix<double> Lcot;
+  //printf("cotmatrix()\n");
+  cotmatrix(V,F,Lcot);
+  // Discrete laplacian (should be minus matlab version)
+  SparseMatrix<double> Lapl = -2.0*Lcot;
+#ifdef EXTREME_VERBOSE
+  cout<<"LaplIJV=["<<endl;print_ijv(Lapl,1);cout<<endl<<"];"<<
+    endl<<"Lapl=sparse(LaplIJV(:,1),LaplIJV(:,2),LaplIJV(:,3),"<<
+    Lapl.rows()<<","<<Lapl.cols()<<");"<<endl;
+#endif
+
+  // Get group sum scatter matrix, when applied sums all entries of the same
+  // group according to G
+  SparseMatrix<double> G_sum;
+  if(G.size() == 0)
+  {
+    speye(n,G_sum);
+  }else
+  {
+    // groups are defined per vertex, convert to per face using mode
+    Eigen::Matrix<int,Eigen::Dynamic,1> GG;
+    if(data.energy == ARAP_ENERGY_TYPE_ELEMENTS)
+    {
+      MatrixXi GF(F.rows(),F.cols());
+      for(int j = 0;j<F.cols();j++)
+      {
+        Matrix<int,Eigen::Dynamic,1> GFj;
+        slice(G,F.col(j),GFj);
+        GF.col(j) = GFj;
+      }
+      mode<int>(GF,2,GG);
+    }else
+    {
+      GG=G;
+    }
+    //printf("group_sum_matrix()\n");
+    group_sum_matrix(GG,G_sum);
+  }
+
+#ifdef EXTREME_VERBOSE
+  cout<<"G_sumIJV=["<<endl;print_ijv(G_sum,1);cout<<endl<<"];"<<
+    endl<<"G_sum=sparse(G_sumIJV(:,1),G_sumIJV(:,2),G_sumIJV(:,3),"<<
+    G_sum.rows()<<","<<G_sum.cols()<<");"<<endl;
+#endif
+
+  // Get covariance scatter matrix, when applied collects the covariance matrices
+  // used to fit rotations to during optimization
+  SparseMatrix<double> CSM;
+  //printf("covariance_scatter_matrix()\n");
+  covariance_scatter_matrix(V,F,data.energy,CSM);
+#ifdef EXTREME_VERBOSE
+  cout<<"CSMIJV=["<<endl;print_ijv(CSM,1);cout<<endl<<"];"<<
+    endl<<"CSM=sparse(CSMIJV(:,1),CSMIJV(:,2),CSMIJV(:,3),"<<
+    CSM.rows()<<","<<CSM.cols()<<");"<<endl;
+#endif
+  
+
+  // Build the covariance matrix "constructor". This is a set of *scatter*
+  // matrices that when multiplied on the right by column of the transformation
+  // matrix entries (the degrees of freedom) L, we get a stack of dim by 1
+  // covariance matrix column, with a column in the stack for each rotation
+  // *group*. The output is a list of matrices because we construct each column
+  // in the stack of covariance matrices with an independent matrix-vector
+  // multiplication.
+  //
+  // We want to build S which is a stack of dim by dim covariance matrices.
+  // Thus S is dim*g by dim, where dim is the number of dimensions and g is the
+  // number of groups. We can precompute dim matrices CSM_M such that column i
+  // in S is computed as S(:,i) = CSM_M{i} * L, where L is a column of the
+  // skinning transformation matrix values. To be clear, the covariance matrix
+  // for group k is then given as the dim by dim matrix pulled from the stack:
+  // S((k-1)*dim + 1:dim,:)
+
+  // Apply group sum to each dimension's block of covariance scatter matrix
+  SparseMatrix<double> G_sum_dim;
+  repdiag(G_sum,data.dim,G_sum_dim);
+  CSM = (G_sum_dim * CSM).eval();
+#ifdef EXTREME_VERBOSE
+  cout<<"CSMIJV=["<<endl;print_ijv(CSM,1);cout<<endl<<"];"<<
+    endl<<"CSM=sparse(CSMIJV(:,1),CSMIJV(:,2),CSMIJV(:,3),"<<
+    CSM.rows()<<","<<CSM.cols()<<");"<<endl;
+#endif
+
+  //printf("CSM_M()\n");
+  // Precompute CSM times M for each dimension
+  data.CSM_M.resize(data.dim);
+#ifdef EXTREME_VERBOSE
+  cout<<"data.CSM_M = cell("<<data.dim<<",1);"<<endl;
+#endif
+  // span of integers from 0 to n-1
+  Eigen::Matrix<int,Eigen::Dynamic,1> span_n(n);
+  for(int i = 0;i<n;i++)
+  {
+    span_n(i) = i;
+  }
+
+  // span of integers from 0 to M.cols()-1
+  Eigen::Matrix<int,Eigen::Dynamic,1> span_mlbs_cols(M.cols());
+  for(int i = 0;i<M.cols();i++)
+  {
+    span_mlbs_cols(i) = i;
+  }
+
+  // number of groups
+  int k = CSM.rows()/data.dim;
+  for(int i = 0;i<data.dim;i++)
+  {
+    //printf("CSM_M(): Mi\n");
+    LbsMatrixType M_i;
+    //printf("CSM_M(): slice\n");
+    slice(M,(span_n.array()+i*n).matrix().eval(),span_mlbs_cols,M_i);
+    LbsMatrixType M_i_dim;
+    data.CSM_M[i].resize(k*data.dim,data.m*data.dim*(data.dim+1));
+    assert(data.CSM_M[i].cols() == M.cols());
+    for(int j = 0;j<data.dim;j++)
+    {
+      SparseMatrix<double> CSMj;
+      //printf("CSM_M(): slice\n");
+      slice(
+        CSM,
+        colon<int>(j*k,(j+1)*k-1),
+        colon<int>(j*n,(j+1)*n-1),
+        CSMj);
+      assert(CSMj.rows() == k);
+      assert(CSMj.cols() == n);
+      LbsMatrixType CSMjM_i = CSMj * M_i;
+      if(is_sparse(CSMjM_i))
+      {
+        // Convert to full
+        //printf("CSM_M(): full\n");
+        MatrixXd CSMjM_ifull(CSMjM_i);
+//        printf("CSM_M[%d]: %d %d\n",i,data.CSM_M[i].rows(),data.CSM_M[i].cols());
+//        printf("CSM_M[%d].block(%d*%d=%d,0,%d,%d): %d %d\n",i,j,k,CSMjM_i.rows(),CSMjM_i.cols(),
+//            data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()).rows(),
+//            data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()).cols());
+//        printf("CSM_MjMi: %d %d\n",i,CSMjM_i.rows(),CSMjM_i.cols());
+//        printf("CSM_MjM_ifull: %d %d\n",i,CSMjM_ifull.rows(),CSMjM_ifull.cols());
+        data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()) = CSMjM_ifull;
+      }else
+      {
+        data.CSM_M[i].block(j*k,0,CSMjM_i.rows(),CSMjM_i.cols()) = CSMjM_i;
+      }
+    }
+#ifdef EXTREME_VERBOSE
+    cout<<"CSM_Mi=["<<endl<<data.CSM_M[i]<<endl<<"];"<<endl;
+#endif
+  }
+
+  // precompute arap_rhs matrix
+  //printf("arap_rhs()\n");
+  SparseMatrix<double> K;
+  arap_rhs(V,F,V.cols(),data.energy,K);
+//#ifdef EXTREME_VERBOSE
+//  cout<<"KIJV=["<<endl;print_ijv(K,1);cout<<endl<<"];"<<
+//    endl<<"K=sparse(KIJV(:,1),KIJV(:,2),KIJV(:,3),"<<
+//    K.rows()<<","<<K.cols()<<");"<<endl;
+//#endif
+  // Precompute left muliplication by M and right multiplication by G_sum
+  SparseMatrix<double> G_sumT = G_sum.transpose();
+  SparseMatrix<double> G_sumT_dim_dim;
+  repdiag(G_sumT,data.dim*data.dim,G_sumT_dim_dim);
+  LbsMatrixType MT = M.transpose();
+  // If this is a bottle neck then consider reordering matrix multiplication
+  data.M_KG = -4.0 * (MT * (K * G_sumT_dim_dim));
+//#ifdef EXTREME_VERBOSE
+//  cout<<"data.M_KGIJV=["<<endl;print_ijv(data.M_KG,1);cout<<endl<<"];"<<
+//    endl<<"data.M_KG=sparse(data.M_KGIJV(:,1),data.M_KGIJV(:,2),data.M_KGIJV(:,3),"<<
+//    data.M_KG.rows()<<","<<data.M_KG.cols()<<");"<<endl;
+//#endif
+
+  // Precompute system matrix
+  //printf("A()\n");
+  SparseMatrix<double> A;
+  repdiag(Lapl,data.dim,A);
+  data.Q = MT * (A * M);
+//#ifdef EXTREME_VERBOSE
+//  cout<<"QIJV=["<<endl;print_ijv(data.Q,1);cout<<endl<<"];"<<
+//    endl<<"Q=sparse(QIJV(:,1),QIJV(:,2),QIJV(:,3),"<<
+//    data.Q.rows()<<","<<data.Q.cols()<<");"<<endl;
+//#endif
+
+  // Always do dynamics precomputation so we can hot-switch
+  //if(data.with_dynamics)
+  //{
+    // Build cotangent laplacian
+    SparseMatrix<double> Mass;
+    //printf("massmatrix()\n");
+    massmatrix(V,F,(F.cols()>3?MASSMATRIX_TYPE_BARYCENTRIC:MASSMATRIX_TYPE_VORONOI),Mass);
+    //cout<<"MIJV=["<<endl;print_ijv(Mass,1);cout<<endl<<"];"<<
+    //  endl<<"M=sparse(MIJV(:,1),MIJV(:,2),MIJV(:,3),"<<
+    //  Mass.rows()<<","<<Mass.cols()<<");"<<endl;
+    //speye(data.n,Mass);
+    SparseMatrix<double> Mass_rep;
+    repdiag(Mass,data.dim,Mass_rep);
+
+    // Multiply either side by weights matrix (should be dense)
+    data.Mass_tilde = MT * Mass_rep * M;
+    MatrixXd ones(data.dim*data.n,data.dim);
+    for(int i = 0;i<data.n;i++)
+    {
+      for(int d = 0;d<data.dim;d++)
+      {
+        ones(i+d*data.n,d) = 1;
+      }
+    }
+    data.fgrav = MT * (Mass_rep * ones);
+    data.fext = MatrixXS::Zero(MT.rows(),1);
+    //data.fgrav = MT * (ones);
+  //}
+
+
+  // This may/should be superfluous
+  //printf("is_symmetric()\n");
+  if(!is_symmetric(data.Q))
+  {
+    //printf("Fixing symmetry...\n");
+    // "Fix" symmetry
+    LbsMatrixType QT = data.Q.transpose();
+    LbsMatrixType Q_copy = data.Q;
+    data.Q = 0.5*(Q_copy+QT);
+    // Check that ^^^ this really worked. It doesn't always
+    //assert(is_symmetric(*Q));
+  }
+
+  //printf("arap_dof_precomputation() succeeded... so far...\n");
+  verbose("Number of handles: %i\n", data.m);
+  return true;
+}
+
+/////////////////////////////////////////////////////////////////////////
+//
+// STATIC FUNCTIONS (These should be removed or properly defined)
+//
+/////////////////////////////////////////////////////////////////////////
+namespace igl
+{
+  // returns maximal difference of 'blok' from scalar times 3x3 identity:
+  template <typename SSCALAR>
+  inline static SSCALAR maxBlokErr(const Eigen::Matrix3f &blok)
+  {
+    SSCALAR mD;
+    SSCALAR value = blok(0,0);
+    SSCALAR diff1 = fabs(blok(1,1) - value);
+    SSCALAR diff2 = fabs(blok(2,2) - value);
+    if (diff1 > diff2) mD = diff1;
+    else mD = diff2;
+    
+    for (int v=0; v<3; v++)
+    {
+      for (int w=0; w<3; w++)
+      {
+        if (v == w)
+        {
+          continue;
+        }
+        if (mD < fabs(blok(v, w)))
+        {
+          mD = fabs(blok(v, w));
+        }
+      }
+    }
+    
+    return mD;
+  }
+  
+  // converts CSM_M_SSCALAR[0], CSM_M_SSCALAR[1], CSM_M_SSCALAR[2] into one
+  // "condensed" matrix CSM while checking we're not losing any information by
+  // this process; specifically, returns maximal difference from scaled 3x3
+  // identity blocks, which should be pretty small number
+  template <typename MatrixXS>
+  static typename MatrixXS::Scalar condense_CSM(
+    const std::vector<MatrixXS> &CSM_M_SSCALAR, 
+    int numBones, 
+    int dim, 
+    MatrixXS &CSM)
+  {
+    const int numRows = CSM_M_SSCALAR[0].rows();
+    assert(CSM_M_SSCALAR[0].cols() == dim*(dim+1)*numBones);
+    assert(CSM_M_SSCALAR[1].cols() == dim*(dim+1)*numBones);
+    assert(CSM_M_SSCALAR[2].cols() == dim*(dim+1)*numBones);
+    assert(CSM_M_SSCALAR[1].rows() == numRows);
+    assert(CSM_M_SSCALAR[2].rows() == numRows);
+  
+    const int numCols = (dim + 1)*numBones;
+    CSM.resize(numRows, numCols);
+  
+    typedef typename MatrixXS::Scalar SSCALAR;
+    SSCALAR maxDiff = 0.0f;
+  
+    for (int r=0; r<numRows; r++)
+    {
+      for (int coord=0; coord<dim+1; coord++)
+      {
+        for (int b=0; b<numBones; b++)
+        {
+          // this is just a test if we really have a multiple of 3x3 identity
+          Eigen::Matrix3f blok;
+          for (int v=0; v<3; v++)
+          {
+            for (int w=0; w<3; w++)
+            {
+              blok(v,w) = CSM_M_SSCALAR[v](r, coord*(numBones*dim) + b + w*numBones);
+            }          
+          }
+  
+          //SSCALAR value[3];
+          //for (int v=0; v<3; v++)
+          //  CSM_M_SSCALAR[v](r, coord*(numBones*dim) + b + v*numBones);
+  
+          SSCALAR mD = maxBlokErr<SSCALAR>(blok);
+          if (mD > maxDiff) maxDiff = mD;
+  
+          // use the first value:
+          CSM(r, coord*numBones + b) = blok(0,0);
+        }
+      }
+    }
+  
+    return maxDiff;
+  }
+  
+  // splits x_0, ... , x_dim coordinates in column vector 'L' into a numBones*(dimp1) x dim matrix 'Lsep';
+  // assumes 'Lsep' has already been preallocated
+  //
+  // is this the same as uncolumnize? no.
+  template <typename MatL, typename MatLsep>
+  static void splitColumns(
+   const MatL &L, 
+   int numBones, 
+   int dim, 
+   int dimp1, 
+   MatLsep &Lsep)
+  {
+    assert(L.cols() == 1);
+    assert(L.rows() == dim*(dimp1)*numBones);
+  
+    assert(Lsep.rows() == (dimp1)*numBones && Lsep.cols() == dim);
+  
+    for (int b=0; b<numBones; b++)
+    {
+      for (int coord=0; coord<dimp1; coord++)
+      {
+        for (int c=0; c<dim; c++)
+        {
+          Lsep(coord*numBones + b, c) = L(coord*numBones*dim + c*numBones + b, 0);
+        }
+      }
+    }
+  }
+  
+  
+  // the inverse of splitColumns, i.e., takes numBones*(dimp1) x dim matrix 'Lsep' and merges the dimensions
+  // into columns vector 'L' (which is assumed to be already allocated):
+  //
+  // is this the same as columnize? no.
+  template <typename MatrixXS>
+  static void mergeColumns(const MatrixXS &Lsep, int numBones, int dim, int dimp1, MatrixXS &L)
+  {
+    assert(L.cols() == 1);
+    assert(L.rows() == dim*(dimp1)*numBones);
+  
+    assert(Lsep.rows() == (dimp1)*numBones && Lsep.cols() == dim);
+  
+    for (int b=0; b<numBones; b++)
+    {
+      for (int coord=0; coord<dimp1; coord++)
+      {
+        for (int c=0; c<dim; c++)
+        {
+          L(coord*numBones*dim + c*numBones + b, 0) = Lsep(coord*numBones + b, c);
+        }
+      }
+    }
+  }
+  
+  // converts "Solve1" the "rotations" part of FullSolve matrix (the first part)
+  // into one "condensed" matrix CSolve1 while checking we're not losing any
+  // information by this process; specifically, returns maximal difference from
+  // scaled 3x3 identity blocks, which should be pretty small number
+  template <typename MatrixXS>
+  static typename MatrixXS::Scalar condense_Solve1(MatrixXS &Solve1, int numBones, int numGroups, int dim, MatrixXS &CSolve1)
+  {
+    assert(Solve1.rows() == dim*(dim + 1)*numBones);
+    assert(Solve1.cols() == dim*dim*numGroups);
+  
+    typedef typename MatrixXS::Scalar SSCALAR;
+    SSCALAR maxDiff = 0.0f;
+  
+    CSolve1.resize((dim + 1)*numBones, dim*numGroups);  
+    for (int rowCoord=0; rowCoord<dim+1; rowCoord++)
+    {
+      for (int b=0; b<numBones; b++)
+      {
+        for (int colCoord=0; colCoord<dim; colCoord++)
+        {
+          for (int g=0; g<numGroups; g++)
+          {
+            Eigen::Matrix3f blok;
+            for (int r=0; r<3; r++)
+            {
+              for (int c=0; c<3; c++)
+              {
+                blok(r, c) = Solve1(rowCoord*numBones*dim + r*numBones + b, colCoord*numGroups*dim + c*numGroups + g);
+              }
+            }
+  
+            SSCALAR mD = maxBlokErr<SSCALAR>(blok);
+            if (mD > maxDiff) maxDiff = mD;
+  
+            CSolve1(rowCoord*numBones + b, colCoord*numGroups + g) = blok(0,0);
+          }
+        }
+      }
+    }  
+    
+    return maxDiff;
+  }
+}
+
+template <typename LbsMatrixType, typename SSCALAR>
+IGL_INLINE bool igl::arap_dof_recomputation(
+  const Eigen::Matrix<int,Eigen::Dynamic,1> & fixed_dim,
+  const Eigen::SparseMatrix<double> & A_eq,
+  ArapDOFData<LbsMatrixType, SSCALAR> & data)
+{
+  using namespace Eigen;
+  typedef Matrix<SSCALAR, Dynamic, Dynamic> MatrixXS;
+
+  LbsMatrixType * Q;
+  LbsMatrixType Qdyn;
+  if(data.with_dynamics)
+  {
+    // multiply by 1/timestep and to quadratic coefficients matrix
+    // Might be missing a 0.5 here
+    LbsMatrixType Q_copy = data.Q;
+    Qdyn = Q_copy + (1.0/(data.h*data.h))*data.Mass_tilde;
+    Q = &Qdyn;
+
+    // This may/should be superfluous
+    //printf("is_symmetric()\n");
+    if(!is_symmetric(*Q))
+    {
+      //printf("Fixing symmetry...\n");
+      // "Fix" symmetry
+      LbsMatrixType QT = (*Q).transpose();
+      LbsMatrixType Q_copy = *Q;
+      *Q = 0.5*(Q_copy+QT);
+      // Check that ^^^ this really worked. It doesn't always
+      //assert(is_symmetric(*Q));
+    }
+  }else
+  {
+    Q = &data.Q;
+  }
+
+  assert((int)data.CSM_M.size() == data.dim);
+  assert(A_eq.cols() == data.m*data.dim*(data.dim+1));
+  data.fixed_dim = fixed_dim;
+
+  if(fixed_dim.size() > 0)
+  {
+    assert(fixed_dim.maxCoeff() < data.m*data.dim*(data.dim+1));
+    assert(fixed_dim.minCoeff() >= 0);
+  }
+
+#ifdef EXTREME_VERBOSE
+  cout<<"data.fixed_dim=["<<endl<<data.fixed_dim<<endl<<"]+1;"<<endl;
+#endif
+
+  // Compute dense solve matrix (alternative of matrix factorization)
+  //printf("min_quad_dense_precompute()\n");
+  MatrixXd Qfull(*Q);
+  MatrixXd A_eqfull(A_eq);
+  MatrixXd M_Solve;
+
+  double timer0_start = get_seconds_hires();
+  bool use_lu = data.effective_dim != 2;
+  //use_lu = false;
+  //printf("use_lu: %s\n",(use_lu?"TRUE":"FALSE"));
+  min_quad_dense_precompute(Qfull, A_eqfull, use_lu,M_Solve);
+  double timer0_end = get_seconds_hires();
+  verbose("Bob timing: %.20f\n", (timer0_end - timer0_start)*1000.0);
+
+  // Precompute full solve matrix:
+  const int fsRows = data.m * data.dim * (data.dim + 1); // 12 * number_of_bones
+  const int fsCols1 = data.M_KG.cols(); // 9 * number_of_posConstraints
+  const int fsCols2 = A_eq.rows(); // number_of_posConstraints
+  data.M_FullSolve.resize(fsRows, fsCols1 + fsCols2);
+  // note the magical multiplicative constant "-0.5", I've no idea why it has
+  // to be there :)
+  data.M_FullSolve << 
+    (-0.5 * M_Solve.block(0, 0, fsRows, fsRows) * data.M_KG).template cast<SSCALAR>(), 
+    M_Solve.block(0, fsRows, fsRows, fsCols2).template cast<SSCALAR>();
+
+  if(data.with_dynamics)
+  {
+    printf(
+      "---------------------------------------------------------------------\n"
+      "\n\n\nWITH DYNAMICS recomputation\n\n\n"
+      "---------------------------------------------------------------------\n"
+      );
+    // Also need to save Π1 before it gets multiplied by Ktilde (aka M_KG)
+    data.Pi_1 = M_Solve.block(0, 0, fsRows, fsRows).template cast<SSCALAR>();
+  }
+
+  // Precompute condensed matrices,
+  // first CSM:
+  std::vector<MatrixXS> CSM_M_SSCALAR;
+  CSM_M_SSCALAR.resize(data.dim);
+  for (int i=0; i<data.dim; i++) CSM_M_SSCALAR[i] = data.CSM_M[i].template cast<SSCALAR>();
+  SSCALAR maxErr1 = condense_CSM(CSM_M_SSCALAR, data.m, data.dim, data.CSM);  
+  verbose("condense_CSM maxErr = %.15f (this should be close to zero)\n", maxErr1);
+  assert(fabs(maxErr1) < 1e-5);
+  
+  // and then solveBlock1:
+  // number of groups
+  const int k = data.CSM_M[0].rows()/data.dim;
+  MatrixXS SolveBlock1 = data.M_FullSolve.block(0, 0, data.M_FullSolve.rows(), data.dim * data.dim * k);
+  SSCALAR maxErr2 = condense_Solve1(SolveBlock1, data.m, k, data.dim, data.CSolveBlock1);  
+  verbose("condense_Solve1 maxErr = %.15f (this should be close to zero)\n", maxErr2);
+  assert(fabs(maxErr2) < 1e-5);
+
+  return true;
+}
+
+template <typename LbsMatrixType, typename SSCALAR>
+IGL_INLINE bool igl::arap_dof_update(
+  const ArapDOFData<LbsMatrixType, SSCALAR> & data,
+  const Eigen::Matrix<double,Eigen::Dynamic,1> & B_eq,
+  const Eigen::MatrixXd & L0,
+  const int max_iters,
+  const double 
+#ifdef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+  tol,
+#else
+  /*tol*/,
+#endif
+  Eigen::MatrixXd & L
+  )
+{
+  using namespace Eigen;
+  typedef Matrix<SSCALAR, Dynamic, Dynamic> MatrixXS;
+#ifdef ARAP_GLOBAL_TIMING
+  double timer_start = get_seconds_hires();
+#endif
+
+  // number of dimensions
+  assert((int)data.CSM_M.size() == data.dim);
+  assert((int)L0.size() == (data.m)*data.dim*(data.dim+1));
+  assert(max_iters >= 0);
+  assert(tol >= 0);
+
+  // timing variables
+  double 
+    sec_start, 
+    sec_covGather, 
+    sec_fitRotations, 
+    //sec_rhs, 
+    sec_prepMult, 
+    sec_solve, sec_end;
+
+  assert(L0.cols() == 1);
+#ifdef EXTREME_VERBOSE
+  cout<<"dim="<<data.dim<<";"<<endl;
+  cout<<"m="<<data.m<<";"<<endl;
+#endif
+
+  // number of groups
+  const int k = data.CSM_M[0].rows()/data.dim;
+  for(int i = 0;i<data.dim;i++)
+  {
+    assert(data.CSM_M[i].rows()/data.dim == k);
+  }
+#ifdef EXTREME_VERBOSE
+  cout<<"k="<<k<<";"<<endl;
+#endif
+
+  // resize output and initialize with initial guess
+  L = L0;
+#ifndef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+  // Keep track of last solution
+  MatrixXS L_prev;
+#endif
+  // We will be iterating on L_SSCALAR, only at the end we convert back to double
+  MatrixXS L_SSCALAR = L.cast<SSCALAR>();
+
+  int iters = 0;
+#ifndef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+  double max_diff = tol+1;  
+#endif
+
+  MatrixXS S(k*data.dim,data.dim);
+  MatrixXS R(data.dim,data.dim*k);
+  Eigen::Matrix<SSCALAR,Eigen::Dynamic,1> Rcol(data.dim * data.dim * k);
+  Matrix<SSCALAR,Dynamic,1> B_eq_SSCALAR = B_eq.cast<SSCALAR>();
+  Matrix<SSCALAR,Dynamic,1> B_eq_fix_SSCALAR;
+  Matrix<SSCALAR,Dynamic,1> L0SSCALAR = L0.cast<SSCALAR>();
+  slice(L0SSCALAR, data.fixed_dim, B_eq_fix_SSCALAR);    
+  //MatrixXS rhsFull(Rcol.rows() + B_eq.rows() + B_eq_fix_SSCALAR.rows(), 1); 
+
+  MatrixXS Lsep(data.m*(data.dim + 1), 3);  
+  const MatrixXS L_part2 = 
+    data.M_FullSolve.block(0, Rcol.rows(), data.M_FullSolve.rows(), B_eq_SSCALAR.rows()) * B_eq_SSCALAR;
+  const MatrixXS L_part3 = 
+    data.M_FullSolve.block(0, Rcol.rows() + B_eq_SSCALAR.rows(), data.M_FullSolve.rows(), B_eq_fix_SSCALAR.rows()) * B_eq_fix_SSCALAR;
+  MatrixXS L_part2and3 = L_part2 + L_part3;
+
+  // preallocate workspace variables:
+  MatrixXS Rxyz(k*data.dim, data.dim);  
+  MatrixXS L_part1xyz((data.dim + 1) * data.m, data.dim);
+  MatrixXS L_part1(data.dim * (data.dim + 1) * data.m, 1);
+
+#ifdef ARAP_GLOBAL_TIMING
+    double timer_prepFinished = get_seconds_hires();
+#endif
+
+#ifdef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+  while(iters < max_iters)
+#else
+  while(iters < max_iters && max_diff > tol)
+#endif
+  {  
+    if(data.print_timings)
+    {
+      sec_start = get_seconds_hires();
+    }
+
+#ifndef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+    L_prev = L_SSCALAR;
+#endif
+    ///////////////////////////////////////////////////////////////////////////
+    // Local step: Fix positions, fit rotations
+    ///////////////////////////////////////////////////////////////////////////    
+  
+    // Gather covariance matrices    
+
+    splitColumns(L_SSCALAR, data.m, data.dim, data.dim + 1, Lsep);
+
+    S = data.CSM * Lsep; 
+    // interestingly, this doesn't seem to be so slow, but
+    //MKL is still 2x faster (probably due to AVX)
+    //#ifdef IGL_ARAP_DOF_DOUBLE_PRECISION_SOLVE
+    //    MKL_matMatMult_double(S, data.CSM, Lsep);
+    //#else
+    //    MKL_matMatMult_single(S, data.CSM, Lsep);
+    //#endif
+    
+    if(data.print_timings)
+    {
+      sec_covGather = get_seconds_hires();
+    }
+
+#ifdef EXTREME_VERBOSE
+    cout<<"S=["<<endl<<S<<endl<<"];"<<endl;
+#endif
+    // Fit rotations to covariance matrices
+    if(data.effective_dim == 2)
+    {
+      fit_rotations_planar(S,R);
+    }else
+    {
+#ifdef __SSE__ // fit_rotations_SSE will convert to float if necessary
+      fit_rotations_SSE(S,R);
+#else
+      fit_rotations(S,false,R);
+#endif
+    }
+
+#ifdef EXTREME_VERBOSE
+    cout<<"R=["<<endl<<R<<endl<<"];"<<endl;
+#endif  
+
+    if(data.print_timings)
+    {
+      sec_fitRotations = get_seconds_hires();
+    }
+  
+    ///////////////////////////////////////////////////////////////////////////
+    // "Global" step: fix rotations per mesh vertex, solve for
+    // linear transformations at handles
+    ///////////////////////////////////////////////////////////////////////////
+
+    // all this shuffling is retarded and not completely negligible time-wise;
+    // TODO: change fit_rotations_XXX so it returns R in the format ready for
+    // CSolveBlock1 multiplication
+    columnize(R, k, 2, Rcol);
+#ifdef EXTREME_VERBOSE
+    cout<<"Rcol=["<<endl<<Rcol<<endl<<"];"<<endl;
+#endif  
+    splitColumns(Rcol, k, data.dim, data.dim, Rxyz);
+    
+    if(data.print_timings)
+    {
+      sec_prepMult = get_seconds_hires();
+    }  
+    
+    L_part1xyz = data.CSolveBlock1 * Rxyz;
+    //#ifdef IGL_ARAP_DOF_DOUBLE_PRECISION_SOLVE
+    //    MKL_matMatMult_double(L_part1xyz, data.CSolveBlock1, Rxyz);    
+    //#else
+    //    MKL_matMatMult_single(L_part1xyz, data.CSolveBlock1, Rxyz);    
+    //#endif
+    mergeColumns(L_part1xyz, data.m, data.dim, data.dim + 1, L_part1);
+
+    if(data.with_dynamics)
+    {
+      // Consider reordering or precomputing matrix multiplications
+      MatrixXS L_part1_dyn(data.dim * (data.dim + 1) * data.m, 1);
+      // Eigen can't parse this:
+      //L_part1_dyn = 
+      //  -(2.0/(data.h*data.h)) * data.Pi_1 * data.Mass_tilde * data.L0 +
+      //   (1.0/(data.h*data.h)) * data.Pi_1 * data.Mass_tilde * data.Lm1;
+      // -1.0 because we've moved these linear terms to the right hand side
+      //MatrixXS temp = -1.0 * 
+      //    ((-2.0/(data.h*data.h)) * data.L0.array() + 
+      //      (1.0/(data.h*data.h)) * data.Lm1.array()).matrix();
+      //MatrixXS temp = -1.0 * 
+      //    ( (-1.0/(data.h*data.h)) * data.L0.array() + 
+      //      (1.0/(data.h*data.h)) * data.Lm1.array()
+      //      (-1.0/(data.h*data.h)) * data.L0.array() + 
+      //      ).matrix();
+      //Lvel0 = (1.0/(data.h)) * data.Lm1.array() - data.L0.array();
+      MatrixXS temp = -1.0 * 
+          ( (-1.0/(data.h*data.h)) * data.L0.array() + 
+            (1.0/(data.h)) * data.Lvel0.array()
+            ).matrix();
+      MatrixXd temp_d = temp.template cast<double>();
+
+      MatrixXd temp_g = data.fgrav*(data.grav_mag*data.grav_dir);
+
+      assert(data.fext.rows() == temp_g.rows());
+      assert(data.fext.cols() == temp_g.cols());
+      MatrixXd temp2 = data.Mass_tilde * temp_d + temp_g + data.fext.template cast<double>();
+      MatrixXS temp2_f = temp2.template cast<SSCALAR>();
+      L_part1_dyn = data.Pi_1 * temp2_f;
+      L_part1.array() = L_part1.array() + L_part1_dyn.array();
+    }
+
+    //L_SSCALAR = L_part1 + L_part2and3;
+    assert(L_SSCALAR.rows() == L_part1.rows() && L_SSCALAR.rows() == L_part2and3.rows());
+    for (int i=0; i<L_SSCALAR.rows(); i++)
+    {
+      L_SSCALAR(i, 0) = L_part1(i, 0) + L_part2and3(i, 0);
+    }
+
+#ifdef EXTREME_VERBOSE
+    cout<<"L=["<<endl<<L<<endl<<"];"<<endl;
+#endif  
+
+    if(data.print_timings)
+    {
+      sec_solve = get_seconds_hires();
+    }
+
+#ifndef IGL_ARAP_DOF_FIXED_ITERATIONS_COUNT
+    // Compute maximum absolute difference with last iteration's solution
+    max_diff = (L_SSCALAR-L_prev).eval().array().abs().matrix().maxCoeff();
+#endif
+    iters++;  
+
+    if(data.print_timings)
+    {
+      sec_end = get_seconds_hires();
+#ifndef WIN32
+      // trick to get sec_* variables to compile without warning on mac
+      if(false)
+#endif
+      printf(
+        "\ntotal iteration time = %f "
+        "[local: covGather = %f, "
+        "fitRotations = %f, "
+        "global: prep = %f, "
+        "solve = %f, "
+        "error = %f [ms]]\n", 
+        (sec_end - sec_start)*1000.0, 
+        (sec_covGather - sec_start)*1000.0, 
+        (sec_fitRotations - sec_covGather)*1000.0, 
+        (sec_prepMult - sec_fitRotations)*1000.0, 
+        (sec_solve - sec_prepMult)*1000.0, 
+        (sec_end - sec_solve)*1000.0 );
+    }
+  }
+
+
+  L = L_SSCALAR.template cast<double>();
+  assert(L.cols() == 1);
+
+#ifdef ARAP_GLOBAL_TIMING
+  double timer_finito = get_seconds_hires();
+  printf(
+    "ARAP preparation = %f, "
+    "all %i iterations = %f [ms]\n", 
+    (timer_prepFinished - timer_start)*1000.0, 
+    max_iters, 
+    (timer_finito - timer_prepFinished)*1000.0);  
+#endif
+
+  return true;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::arap_dof_update<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double>(ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double> const&, Eigen::Matrix<double, -1, 1, 0, -1, 1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, int, double, Eigen::Matrix<double, -1, -1, 0, -1, -1>&);
+template bool igl::arap_dof_recomputation<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double>(Eigen::Matrix<int, -1, 1, 0, -1, 1> const&, Eigen::SparseMatrix<double, 0, int> const&, ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double>&);
+template bool igl::arap_dof_precomputation<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, 1, 0, -1, 1> const&, ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, double>&);
+template bool igl::arap_dof_update<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float>(igl::ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float> const&, Eigen::Matrix<double, -1, 1, 0, -1, 1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, int, double, Eigen::Matrix<double, -1, -1, 0, -1, -1>&);
+template bool igl::arap_dof_recomputation<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float>(Eigen::Matrix<int, -1, 1, 0, -1, 1> const&, Eigen::SparseMatrix<double, 0, int> const&, igl::ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float>&);
+template bool igl::arap_dof_precomputation<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, 1, 0, -1, 1> const&, igl::ArapDOFData<Eigen::Matrix<double, -1, -1, 0, -1, -1>, float>&);
+#endif

src/igl/arap_dof.h

@@ -0,0 +1,244 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ARAP_ENERGY_TYPE_DOF_H
+#define IGL_ARAP_ENERGY_TYPE_DOF_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+#include "ARAPEnergyType.h"
+#include <vector>
+
+namespace igl
+{
+  // Caller example:
+  //
+  // Once:
+  // arap_dof_precomputation(...)
+  //
+  // Each frame:
+  // while(not satisfied)
+  //   arap_dof_update(...)
+  // end
+  
+  template <typename LbsMatrixType, typename SSCALAR>
+  struct ArapDOFData;
+  
+  ///////////////////////////////////////////////////////////////////////////
+  //
+  // Arap DOF precomputation consists of two parts the computation. The first is
+  // that which depends solely on the mesh (V,F), the linear blend skinning
+  // weights (M) and the groups G. Then there's the part that depends on the
+  // previous precomputation and the list of free and fixed vertices. 
+  //
+  ///////////////////////////////////////////////////////////////////////////
+  
+  
+  // The code and variables differ from the description in Section 3 of "Fast
+  // Automatic Skinning Transformations" by [Jacobson et al. 2012]
+  // 
+  // Here is a useful conversion table:
+  //
+  // [article]                             [code]
+  // S = \tilde{K} T                       S = CSM * Lsep
+  // S --> R                               S --> R --shuffled--> Rxyz
+  // Gamma_solve RT = Pi_1 \tilde{K} RT    L_part1xyz = CSolveBlock1 * Rxyz 
+  // Pi_1 \tilde{K}                        CSolveBlock1
+  // Peq = [T_full; P_pos]                 
+  // T_full                                B_eq_fix <--- L0
+  // P_pos                                 B_eq
+  // Pi_2 * P_eq =                         Lpart2and3 = Lpart2 + Lpart3
+  //   Pi_2_left T_full +                  Lpart3 = M_fullsolve(right) * B_eq_fix
+  //   Pi_2_right P_pos                    Lpart2 = M_fullsolve(left) * B_eq
+  // T = [Pi_1 Pi_2] [\tilde{K}TRT P_eq]   L = Lpart1 + Lpart2and3
+  //
+  
+  // Precomputes the system we are going to optimize. This consists of building
+  // constructor matrices (to compute covariance matrices from transformations
+  // and to build the poisson solve right hand side from rotation matrix entries)
+  // and also prefactoring the poisson system.
+  //
+  // Inputs:
+  //   V  #V by dim list of vertex positions
+  //   F  #F by {3|4} list of face indices
+  //   M  #V * dim by #handles * dim * (dim+1) matrix such that
+  //     new_V(:) = LBS(V,W,A) = reshape(M * A,size(V)), where A is a column
+  //     vectors formed by the entries in each handle's dim by dim+1 
+  //     transformation matrix. Specifcally, A =
+  //       reshape(permute(Astack,[3 1 2]),n*dim*(dim+1),1)
+  //     or A = [Lxx;Lyx;Lxy;Lyy;tx;ty], and likewise for other dim
+  //     if Astack(:,:,i) is the dim by (dim+1) transformation at handle i
+  //     handles are ordered according to P then BE (point handles before bone
+  //     handles)
+  //   G  #V list of group indices (1 to k) for each vertex, such that vertex i 
+  //     is assigned to group G(i)
+  // Outputs:
+  //   data  structure containing all necessary precomputation for calling
+  //     arap_dof_update
+  // Returns true on success, false on error
+  //
+  // See also: lbs_matrix_column
+  template <typename LbsMatrixType, typename SSCALAR>
+  IGL_INLINE bool arap_dof_precomputation(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXi & F,
+    const LbsMatrixType & M,
+    const Eigen::Matrix<int,Eigen::Dynamic,1> & G,
+    ArapDOFData<LbsMatrixType, SSCALAR> & data);
+  
+  // Should always be called after arap_dof_precomputation, but may be called in
+  // between successive calls to arap_dof_update, recomputes precomputation
+  // given that there are only changes in free and fixed
+  //
+  // Inputs:
+  //   fixed_dim  list of transformation element indices for fixed (or partailly
+  //   fixed) handles: not necessarily the complement of 'free'
+  //    NOTE: the constraints for fixed transformations still need to be
+  //    present in A_eq
+  //   A_eq  dim*#constraint_points by m*dim*(dim+1)  matrix of linear equality
+  //     constraint coefficients. Each row corresponds to a linear constraint,
+  //     so that A_eq * L = Beq says that the linear transformation entries in
+  //     the column L should produce the user supplied positional constraints
+  //     for each handle in Beq. The row A_eq(i*dim+d) corresponds to the
+  //     constrain on coordinate d of position i
+  // Outputs:
+  //   data  structure containing all necessary precomputation for calling
+  //     arap_dof_update
+  // Returns true on success, false on error
+  //
+  // See also: lbs_matrix_column
+  template <typename LbsMatrixType, typename SSCALAR>
+  IGL_INLINE bool arap_dof_recomputation(
+    const Eigen::Matrix<int,Eigen::Dynamic,1> & fixed_dim,
+    const Eigen::SparseMatrix<double> & A_eq,
+    ArapDOFData<LbsMatrixType, SSCALAR> & data);
+  
+  // Optimizes the transformations attached to each weight function based on
+  // precomputed system.
+  //
+  // Inputs:
+  //   data  precomputation data struct output from arap_dof_precomputation
+  //   Beq  dim*#constraint_points constraint values.
+  //   L0  #handles * dim * dim+1 list of initial guess transformation entries,
+  //     also holds fixed transformation entries for fixed handles
+  //   max_iters  maximum number of iterations
+  //   tol  stopping criteria parameter. If variables (linear transformation
+  //     matrix entries) change by less than 'tol' the optimization terminates,
+  //       0.75 (weak tolerance)
+  //       0.0 (extreme tolerance)
+  // Outputs:
+  //   L  #handles * dim * dim+1 list of final optimized transformation entries,
+  //     allowed to be the same as L
+  template <typename LbsMatrixType, typename SSCALAR>
+  IGL_INLINE bool arap_dof_update(
+    const ArapDOFData<LbsMatrixType,SSCALAR> & data,
+    const Eigen::Matrix<double,Eigen::Dynamic,1> & B_eq,
+    const Eigen::MatrixXd & L0,
+    const int max_iters,
+    const double tol,
+    Eigen::MatrixXd & L
+    );
+  
+  // Structure that contains fields for all precomputed data or data that needs
+  // to be remembered at update
+  template <typename LbsMatrixType, typename SSCALAR>
+  struct ArapDOFData
+  {
+    typedef Eigen::Matrix<SSCALAR, Eigen::Dynamic, Eigen::Dynamic> MatrixXS;
+    // Type of arap energy we're solving
+    igl::ARAPEnergyType energy;
+    //// LU decomposition precomptation data; note: not used by araf_dop_update
+    //// any more, replaced by M_FullSolve
+    //igl::min_quad_with_fixed_data<double> lu_data;
+    // List of indices of fixed transformation entries
+    Eigen::Matrix<int,Eigen::Dynamic,1> fixed_dim;
+    // List of precomputed covariance scatter matrices multiplied by lbs
+    // matrices
+    //std::vector<Eigen::SparseMatrix<double> > CSM_M;
+    std::vector<Eigen::MatrixXd> CSM_M;
+    LbsMatrixType M_KG;
+    // Number of mesh vertices
+    int n;
+    // Number of weight functions
+    int m;
+    // Number of dimensions
+    int dim;
+    // Effective dimensions
+    int effective_dim;
+    // List of indices into C of positional constraints
+    Eigen::Matrix<int,Eigen::Dynamic,1> interpolated;
+    std::vector<bool> free_mask;
+    // Full quadratic coefficients matrix before lagrangian (should be dense)
+    LbsMatrixType Q;
+  
+  
+    //// Solve matrix for the global step
+    //Eigen::MatrixXd M_Solve; // TODO: remove from here
+  
+    // Full solve matrix that contains also conversion from rotations to the right hand side, 
+    // i.e., solves Poisson transformations just from rotations and positional constraints
+    MatrixXS M_FullSolve;
+  
+    // Precomputed condensed matrices (3x3 commutators folded to 1x1):
+    MatrixXS CSM;
+    MatrixXS CSolveBlock1;
+  
+    // Print timings at each update
+    bool print_timings;
+  
+    // Dynamics
+    bool with_dynamics;
+    // I'm hiding the extra dynamics stuff in this struct, which sort of defeats
+    // the purpose of this function-based coding style...
+  
+    // Time step
+    double h;
+  
+    // L0  #handles * dim * dim+1 list of transformation entries from
+    // previous solve
+    MatrixXS L0;
+    //// Lm1  #handles * dim * dim+1 list of transformation entries from
+    //// previous-previous solve
+    //MatrixXS Lm1;
+    // "Velocity"
+    MatrixXS Lvel0;
+  
+    // #V by dim matrix of external forces
+    // fext
+    MatrixXS fext;
+  
+    // Mass_tilde: MT * Mass * M
+    LbsMatrixType Mass_tilde;
+  
+    // Force due to gravity (premultiplier)
+    Eigen::MatrixXd fgrav;
+    // Direction of gravity
+    Eigen::Vector3d grav_dir;
+    // Magnitude of gravity
+    double grav_mag;
+    
+    // Π1 from the paper
+    MatrixXS Pi_1;
+  
+    // Default values
+    ArapDOFData(): 
+      energy(igl::ARAP_ENERGY_TYPE_SPOKES), 
+      with_dynamics(false),
+      h(1),
+      grav_dir(0,-1,0),
+      grav_mag(0)
+    {
+    }
+  };
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "arap_dof.cpp"
+#endif
+
+#endif

src/igl/arap_linear_block.cpp

@@ -0,0 +1,253 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "arap_linear_block.h"
+#include "verbose.h"
+#include "cotmatrix_entries.h"
+#include <Eigen/Dense>
+
+template <typename MatV, typename MatF, typename Scalar>
+IGL_INLINE void igl::arap_linear_block(
+  const MatV & V,
+  const MatF & F,
+  const int d,
+  const igl::ARAPEnergyType energy,
+  Eigen::SparseMatrix<Scalar> & Kd)
+{
+  switch(energy)
+  {
+    case ARAP_ENERGY_TYPE_SPOKES:
+      return igl::arap_linear_block_spokes(V,F,d,Kd);
+      break;
+    case ARAP_ENERGY_TYPE_SPOKES_AND_RIMS:
+      return igl::arap_linear_block_spokes_and_rims(V,F,d,Kd);
+      break;
+    case ARAP_ENERGY_TYPE_ELEMENTS:
+      return igl::arap_linear_block_elements(V,F,d,Kd);
+      break;
+    default:
+      verbose("Unsupported energy type: %d\n",energy);
+      assert(false);
+  }
+}
+
+
+template <typename MatV, typename MatF, typename Scalar>
+IGL_INLINE void igl::arap_linear_block_spokes(
+  const MatV & V,
+  const MatF & F,
+  const int d,
+  Eigen::SparseMatrix<Scalar> & Kd)
+{
+  using namespace std;
+  using namespace Eigen;
+  // simplex size (3: triangles, 4: tetrahedra)
+  int simplex_size = F.cols();
+  // Number of elements
+  int m = F.rows();
+  // Temporary output
+  Matrix<int,Dynamic,2> edges;
+  Kd.resize(V.rows(), V.rows());
+  vector<Triplet<Scalar> > Kd_IJV;
+  if(simplex_size == 3)
+  {
+    // triangles
+    Kd.reserve(7*V.rows());
+    Kd_IJV.reserve(7*V.rows());
+    edges.resize(3,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1;
+  }else if(simplex_size == 4)
+  {
+    // tets
+    Kd.reserve(17*V.rows());
+    Kd_IJV.reserve(17*V.rows());
+    edges.resize(6,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1,
+      3,0,
+      3,1,
+      3,2;
+  }
+  // gather cotangent weights
+  Matrix<Scalar,Dynamic,Dynamic> C;
+  cotmatrix_entries(V,F,C);
+  // should have weights for each edge
+  assert(C.cols() == edges.rows());
+  // loop over elements
+  for(int i = 0;i<m;i++)
+  {
+    // loop over edges of element
+    for(int e = 0;e<edges.rows();e++)
+    {
+      int source = F(i,edges(e,0));
+      int dest = F(i,edges(e,1));
+      double v = 0.5*C(i,e)*(V(source,d)-V(dest,d));
+      Kd_IJV.push_back(Triplet<Scalar>(source,dest,v));
+      Kd_IJV.push_back(Triplet<Scalar>(dest,source,-v));
+      Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
+      Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
+    }
+  }
+  Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
+  Kd.makeCompressed();
+}
+
+template <typename MatV, typename MatF, typename Scalar>
+IGL_INLINE void igl::arap_linear_block_spokes_and_rims(
+  const MatV & V,
+  const MatF & F,
+  const int d,
+  Eigen::SparseMatrix<Scalar> & Kd)
+{
+  using namespace std;
+  using namespace Eigen;
+  // simplex size (3: triangles, 4: tetrahedra)
+  int simplex_size = F.cols();
+  // Number of elements
+  int m = F.rows();
+  // Temporary output
+  Kd.resize(V.rows(), V.rows());
+  vector<Triplet<Scalar> > Kd_IJV;
+  Matrix<int,Dynamic,2> edges;
+  if(simplex_size == 3)
+  {
+    // triangles
+    Kd.reserve(7*V.rows());
+    Kd_IJV.reserve(7*V.rows());
+    edges.resize(3,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1;
+  }else if(simplex_size == 4)
+  {
+    // tets
+    Kd.reserve(17*V.rows());
+    Kd_IJV.reserve(17*V.rows());
+    edges.resize(6,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1,
+      3,0,
+      3,1,
+      3,2;
+    // Not implemented yet for tets
+    assert(false);
+  }
+  // gather cotangent weights
+  Matrix<Scalar,Dynamic,Dynamic> C;
+  cotmatrix_entries(V,F,C);
+  // should have weights for each edge
+  assert(C.cols() == edges.rows());
+  // loop over elements
+  for(int i = 0;i<m;i++)
+  {
+    // loop over edges of element
+    for(int e = 0;e<edges.rows();e++)
+    {
+      int source = F(i,edges(e,0));
+      int dest = F(i,edges(e,1));
+      double v = C(i,e)*(V(source,d)-V(dest,d))/3.0;
+      // loop over edges again
+      for(int f = 0;f<edges.rows();f++)
+      {
+        int Rs = F(i,edges(f,0));
+        int Rd = F(i,edges(f,1));
+        if(Rs == source && Rd == dest)
+        {
+          Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,v));
+          Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,-v));
+        }else if(Rd == source)
+        {
+          Kd_IJV.push_back(Triplet<Scalar>(Rd,Rs,v));
+        }else if(Rs == dest)
+        {
+          Kd_IJV.push_back(Triplet<Scalar>(Rs,Rd,-v));
+        }
+      }
+      Kd_IJV.push_back(Triplet<Scalar>(source,source,v));
+      Kd_IJV.push_back(Triplet<Scalar>(dest,dest,-v));
+    }
+  }
+  Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
+  Kd.makeCompressed();
+}
+
+template <typename MatV, typename MatF, typename Scalar>
+IGL_INLINE void igl::arap_linear_block_elements(
+  const MatV & V,
+  const MatF & F,
+  const int d,
+  Eigen::SparseMatrix<Scalar> & Kd)
+{
+  using namespace std;
+  using namespace Eigen;
+  // simplex size (3: triangles, 4: tetrahedra)
+  int simplex_size = F.cols();
+  // Number of elements
+  int m = F.rows();
+  // Temporary output
+  Kd.resize(V.rows(), F.rows());
+  vector<Triplet<Scalar> > Kd_IJV;
+  Matrix<int,Dynamic,2> edges;
+  if(simplex_size == 3)
+  {
+    // triangles
+    Kd.reserve(7*V.rows());
+    Kd_IJV.reserve(7*V.rows());
+    edges.resize(3,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1;
+  }else if(simplex_size == 4)
+  {
+    // tets
+    Kd.reserve(17*V.rows());
+    Kd_IJV.reserve(17*V.rows());
+    edges.resize(6,2);
+    edges << 
+      1,2,
+      2,0,
+      0,1,
+      3,0,
+      3,1,
+      3,2;
+  }
+  // gather cotangent weights
+  Matrix<Scalar,Dynamic,Dynamic> C;
+  cotmatrix_entries(V,F,C);
+  // should have weights for each edge
+  assert(C.cols() == edges.rows());
+  // loop over elements
+  for(int i = 0;i<m;i++)
+  {
+    // loop over edges of element
+    for(int e = 0;e<edges.rows();e++)
+    {
+      int source = F(i,edges(e,0));
+      int dest = F(i,edges(e,1));
+      double v = C(i,e)*(V(source,d)-V(dest,d));
+      Kd_IJV.push_back(Triplet<Scalar>(source,i,v));
+      Kd_IJV.push_back(Triplet<Scalar>(dest,i,-v));
+    }
+  }
+  Kd.setFromTriplets(Kd_IJV.begin(),Kd_IJV.end());
+  Kd.makeCompressed();
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template IGL_INLINE void igl::arap_linear_block<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, double>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, int, igl::ARAPEnergyType, Eigen::SparseMatrix<double, 0, int>&);
+#endif

src/igl/arap_linear_block.h

@@ -0,0 +1,78 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ARAP_LINEAR_BLOCK_H
+#define IGL_ARAP_LINEAR_BLOCK_H
+#include "igl_inline.h"
+
+#include <Eigen/Sparse>
+#include <igl/ARAPEnergyType.h>
+
+namespace igl
+{
+  // ARAP_LINEAR_BLOCK constructs a block of the matrix which constructs the
+  // linear terms of a given arap energy. When treating rotations as knowns
+  // (arranged in a column) then this constructs Kd of K such that the linear
+  // portion of the energy is as a column:
+  //   K * R = [Kx Z  ... Ky Z  ... 
+  //            Z  Kx ... Z  Ky ... 
+  //            ... ]
+  // These blocks are also used to build the "covariance scatter matrices".
+  // Here we want to build a scatter matrix that multiplies against positions
+  // (treated as known) producing covariance matrices to fit each rotation.
+  // Notice that in the case of the RHS of the poisson solve the rotations are
+  // known and the positions unknown, and vice versa for rotation fitting.
+  // These linear block just relate the rotations to the positions, linearly in
+  // each.
+  //
+  // Templates:
+  //   MatV  vertex position matrix, e.g. Eigen::MatrixXd
+  //   MatF  face index matrix, e.g. Eigen::MatrixXd
+  //   Scalar  e.g. double
+  // Inputs:
+  //   V  #V by dim list of initial domain positions
+  //   F  #F by #simplex size list of triangle indices into V
+  //   d  coordinate of linear constructor to build
+  //   energy  ARAPEnergyType enum value defining which energy is being used.
+  //     See ARAPEnergyType.h for valid options and explanations.
+  // Outputs:
+  //   Kd  #V by #V/#F block of the linear constructor matrix corresponding to
+  //     coordinate d
+  //
+  template <typename MatV, typename MatF, typename Scalar>
+  IGL_INLINE void arap_linear_block(
+    const MatV & V,
+    const MatF & F,
+    const int d,
+    const igl::ARAPEnergyType energy,
+    Eigen::SparseMatrix<Scalar> & Kd);
+  // Helper functions for each energy type
+  template <typename MatV, typename MatF, typename Scalar>
+  IGL_INLINE void arap_linear_block_spokes(
+    const MatV & V,
+    const MatF & F,
+    const int d,
+    Eigen::SparseMatrix<Scalar> & Kd);
+  template <typename MatV, typename MatF, typename Scalar>
+  IGL_INLINE void arap_linear_block_spokes_and_rims(
+    const MatV & V,
+    const MatF & F,
+    const int d,
+    Eigen::SparseMatrix<Scalar> & Kd);
+  template <typename MatV, typename MatF, typename Scalar>
+  IGL_INLINE void arap_linear_block_elements(
+    const MatV & V,
+    const MatF & F,
+    const int d,
+    Eigen::SparseMatrix<Scalar> & Kd);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "arap_linear_block.cpp"
+#endif
+
+#endif

src/igl/arap_rhs.cpp

@@ -0,0 +1,89 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "arap_rhs.h"
+#include "arap_linear_block.h"
+#include "verbose.h"
+#include "repdiag.h"
+#include "cat.h"
+#include <iostream>
+
+IGL_INLINE void igl::arap_rhs(
+  const Eigen::MatrixXd & V, 
+  const Eigen::MatrixXi & F,
+  const int dim,
+  const igl::ARAPEnergyType energy,
+  Eigen::SparseMatrix<double>& K)
+{
+  using namespace std;
+  using namespace Eigen;
+  // Number of dimensions
+  int Vdim = V.cols();
+  //// Number of mesh vertices
+  //int n = V.rows();
+  //// Number of mesh elements
+  //int m = F.rows();
+  //// number of rotations
+  //int nr;
+  switch(energy)
+  {
+    case ARAP_ENERGY_TYPE_SPOKES:
+      //nr = n;
+      break;
+    case ARAP_ENERGY_TYPE_SPOKES_AND_RIMS:
+      //nr = n;
+      break;
+    case ARAP_ENERGY_TYPE_ELEMENTS:
+      //nr = m;
+      break;
+    default:
+      fprintf(
+        stderr,
+        "arap_rhs.h: Error: Unsupported arap energy %d\n",
+        energy);
+      return;
+  }
+
+  SparseMatrix<double> KX,KY,KZ;
+  arap_linear_block(V,F,0,energy,KX);
+  arap_linear_block(V,F,1,energy,KY);
+  if(Vdim == 2)
+  {
+    K = cat(2,repdiag(KX,dim),repdiag(KY,dim));
+  }else if(Vdim == 3)
+  {
+    arap_linear_block(V,F,2,energy,KZ);
+    if(dim == 3)
+    {
+      K = cat(2,cat(2,repdiag(KX,dim),repdiag(KY,dim)),repdiag(KZ,dim));
+    }else if(dim ==2)
+    {
+      SparseMatrix<double> ZZ(KX.rows()*2,KX.cols());
+      K = cat(2,cat(2,
+            cat(2,repdiag(KX,dim),ZZ),
+            cat(2,repdiag(KY,dim),ZZ)),
+            cat(2,repdiag(KZ,dim),ZZ));
+    }else
+    {
+      assert(false);
+      fprintf(
+      stderr,
+      "arap_rhs.h: Error: Unsupported dimension %d\n",
+      dim);
+    }
+  }else
+  {
+    assert(false);
+    fprintf(
+     stderr,
+     "arap_rhs.h: Error: Unsupported dimension %d\n",
+     Vdim);
+    return;
+  }
+  
+}
+

src/igl/arap_rhs.h

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_ARAP_RHS_H
+#define IGL_ARAP_RHS_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+#include <igl/ARAPEnergyType.h>
+
+namespace igl
+{
+  // ARAP_RHS build right-hand side constructor of global poisson solve for
+  // various Arap energies
+  // Inputs:
+  //   V  #V by Vdim list of initial domain positions
+  //   F  #F by 3 list of triangle indices into V
+  //   dim  dimension being used at solve time. For deformation usually dim =
+  //     V.cols(), for surface parameterization V.cols() = 3 and dim = 2
+  //   energy  igl::ARAPEnergyType enum value defining which energy is being
+  //     used. See igl::ARAPEnergyType.h for valid options and explanations.
+  // Outputs:
+  //   K  #V*dim by #(F|V)*dim*dim matrix such that: 
+  //     b = K * reshape(permute(R,[3 1 2]),size(V|F,1)*size(V,2)*size(V,2),1);
+  //   
+  // See also: arap_linear_block
+  IGL_INLINE void arap_rhs(
+    const Eigen::MatrixXd & V, 
+    const Eigen::MatrixXi & F,
+    const int dim,
+    const igl::ARAPEnergyType energy,
+    Eigen::SparseMatrix<double>& K);
+}
+#ifndef IGL_STATIC_LIBRARY
+#include "arap_rhs.cpp"
+#endif
+#endif

src/igl/average_onto_faces.cpp

@@ -0,0 +1,29 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "average_onto_faces.h"
+
+template <typename T, typename I>
+IGL_INLINE void igl::average_onto_faces(const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &V,
+            const Eigen::Matrix<I, Eigen::Dynamic, Eigen::Dynamic> &F,
+            const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &S,
+            Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &SF)
+{
+  
+  SF = Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic>::Zero(F.rows(),S.cols());
+
+  for (int i = 0; i <F.rows(); ++i)
+    for (int j = 0; j<F.cols(); ++j)
+      SF.row(i) += S.row(F(i,j));
+
+  SF.array() /= F.cols();
+  
+};
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#endif

src/igl/average_onto_faces.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AVERAGE_ONTO_FACES_H
+#define IGL_AVERAGE_ONTO_FACES_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+namespace igl 
+{
+  // average_onto_vertices 
+  // Move a scalar field defined on faces to vertices by averaging
+  //
+  // Input:
+  // V,F: mesh
+  // S: scalar field defined on vertices, Vx1
+  // 
+  // Output:
+  // SV: scalar field defined on faces
+  template <typename T, typename I>
+  IGL_INLINE void average_onto_faces(
+    const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &V,
+    const Eigen::Matrix<I, Eigen::Dynamic, Eigen::Dynamic> &F,
+    const Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &S,
+    Eigen::Matrix<T, Eigen::Dynamic, Eigen::Dynamic> &SF);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "average_onto_faces.cpp"
+#endif
+
+#endif

src/igl/average_onto_vertices.cpp

@@ -0,0 +1,33 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "average_onto_vertices.h"
+
+template<typename DerivedV,typename DerivedF,typename DerivedS>
+IGL_INLINE void igl::average_onto_vertices(const Eigen::MatrixBase<DerivedV> &V,
+  const Eigen::MatrixBase<DerivedF> &F,
+  const Eigen::MatrixBase<DerivedS> &S,
+  Eigen::MatrixBase<DerivedS> &SV)
+{
+  SV = DerivedS::Zero(V.rows(),S.cols());
+  Eigen::Matrix<typename DerivedF::Scalar,Eigen::Dynamic,1> COUNT(V.rows());
+  COUNT.setZero();
+  for (int i = 0; i <F.rows(); ++i)
+  {
+    for (int j = 0; j<F.cols(); ++j)
+    {
+      SV.row(F(i,j)) += S.row(i);
+      COUNT[F(i,j)] ++;
+    }
+  }
+  for (int i = 0; i <V.rows(); ++i)
+    SV.row(i) /= COUNT[i];
+};
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+#endif

src/igl/average_onto_vertices.h

@@ -0,0 +1,35 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AVERAGE_ONTO_VERTICES_H
+#define IGL_AVERAGE_ONTO_VERTICES_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+namespace igl 
+{
+  // average_onto_vertices 
+  // Move a scalar field defined on faces to vertices by averaging
+  //
+  // Input:
+  // V,F: mesh
+  // S: scalar field defined on faces, Fx1
+  // 
+  // Output:
+  // SV: scalar field defined on vertices
+  template<typename DerivedV,typename DerivedF,typename DerivedS>
+  IGL_INLINE void average_onto_vertices(const Eigen::MatrixBase<DerivedV> &V,
+    const Eigen::MatrixBase<DerivedF> &F,
+    const Eigen::MatrixBase<DerivedS> &S,
+    Eigen::MatrixBase<DerivedS> &SV);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "average_onto_vertices.cpp"
+#endif
+
+#endif

src/igl/avg_edge_length.cpp

@@ -0,0 +1,39 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "avg_edge_length.h"
+
+#include <vector>
+
+template <typename DerivedV, typename DerivedF>
+IGL_INLINE double igl::avg_edge_length(
+  const Eigen::MatrixBase<DerivedV>& V,
+  const Eigen::MatrixBase<DerivedF>& F)
+{
+  double avg = 0;
+  long int count = 0;
+
+  // Augh. Technically this is double counting interior edges...
+  for (unsigned i=0;i<F.rows();++i)
+  {
+    for (unsigned j=0;j<F.cols();++j)
+    {
+      ++count;
+      avg += (V.row(F(i,j)) - V.row(F(i,(j+1)%F.cols()))).norm();
+    }
+  }
+
+  return avg / (double) count;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template double igl::avg_edge_length<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&);
+template double igl::avg_edge_length<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&);
+// generated by autoexplicit.sh
+#endif

src/igl/avg_edge_length.h

@@ -0,0 +1,41 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AVERAGEEDGELENGTH_H
+#define IGL_AVERAGEEDGELENGTH_H
+
+#include "igl_inline.h"
+#include <Eigen/Core>
+#include <string>
+#include <vector>
+
+namespace igl 
+{
+  // Compute the average edge length for the given triangle mesh
+  // Templates:
+  //   DerivedV derived from vertex positions matrix type: i.e. MatrixXd
+  //   DerivedF derived from face indices matrix type: i.e. MatrixXi
+  //   DerivedL derived from edge lengths matrix type: i.e. MatrixXd
+  // Inputs:
+  //   V  eigen matrix #V by 3
+  //   F  #F by simplex-size list of mesh faces (must be simplex)
+  // Outputs:
+  //   l  average edge length
+  //
+  // See also: adjacency_matrix
+  template <typename DerivedV, typename DerivedF>
+  IGL_INLINE double avg_edge_length(
+    const Eigen::MatrixBase<DerivedV>& V,
+    const Eigen::MatrixBase<DerivedF>& F);
+
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "avg_edge_length.cpp"
+#endif
+
+#endif

src/igl/axis_angle_to_quat.cpp

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "axis_angle_to_quat.h"
+#include "EPS.h"
+#include <cmath>
+
+// http://www.antisphere.com/Wiki/tools:anttweakbar
+template <typename Q_type>
+IGL_INLINE void igl::axis_angle_to_quat(
+  const Q_type *axis, 
+  const Q_type angle,
+  Q_type *out)
+{
+    Q_type n = axis[0]*axis[0] + axis[1]*axis[1] + axis[2]*axis[2];
+    if( fabs(n)>igl::EPS<Q_type>())
+    {
+        Q_type f = 0.5*angle;
+        out[3] = cos(f);
+        f = sin(f)/sqrt(n);
+        out[0] = axis[0]*f;
+        out[1] = axis[1]*f;
+        out[2] = axis[2]*f;
+    }
+    else
+    {
+        out[3] = 1.0;
+        out[0] = out[1] = out[2] = 0.0;
+    }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::axis_angle_to_quat<double>(double const*, double, double*);
+// generated by autoexplicit.sh
+template void igl::axis_angle_to_quat<float>(float const*, float, float*);
+#endif

src/igl/axis_angle_to_quat.h

@@ -0,0 +1,33 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_AXIS_ANGLE_TO_QUAT_H
+#define IGL_AXIS_ANGLE_TO_QUAT_H
+#include "igl_inline.h"
+
+namespace igl
+{
+  // Convert axis angle representation of a rotation to a quaternion
+  // A Quaternion, q, is defined here as an arrays of four scalars (x,y,z,w),
+  // such that q = x*i + y*j + z*k + w
+  // Inputs:
+  //   axis  3d vector
+  //   angle  scalar
+  // Outputs:
+  //   quaternion
+  template <typename Q_type>
+  IGL_INLINE void axis_angle_to_quat(
+    const Q_type *axis, 
+    const Q_type angle,
+    Q_type *out);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "axis_angle_to_quat.cpp"
+#endif
+
+#endif

src/igl/barycenter.cpp

@@ -0,0 +1,57 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "barycenter.h"
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename DerivedBC>
+IGL_INLINE void igl::barycenter(
+    const Eigen::MatrixBase<DerivedV> & V,
+    const Eigen::MatrixBase<DerivedF> & F,
+    Eigen::PlainObjectBase<DerivedBC> & BC)
+{
+  BC.setZero(F.rows(),V.cols());
+  // Loop over faces
+  for(int i = 0;i<F.rows();i++)
+  {
+    // loop around face
+    for(int j = 0;j<F.cols();j++)
+    {
+      // Accumulate
+      BC.row(i) += V.row(F(i,j));
+    }
+    // average
+    BC.row(i) /= double(F.cols());
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<double, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<float, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<float, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<float, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, -1, 0, -1, -1> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, 3, 1, -1, 3>, Eigen::Matrix<float, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, 3, 0, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::barycenter<Eigen::Matrix<float, -1, 3, 1, -1, 3>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<float, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<float, -1, 3, 1, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, -1, -1, 0, -1, -1> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 4, 0, -1, 4> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 4, 0, -1, 4> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, 4, 0, -1, 4>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 4, 0, -1, 4> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 4, 0, -1, 4> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 4, 0, -1, 4> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, 3, 0, -1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, 3, 0, -1, 3>, Eigen::Matrix<int, -1, 3, 0, -1, 3>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, 3, 0, -1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::barycenter<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, 2, 0, -1, 2> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, 2, 0, -1, 2> >&);
+#endif

src/igl/barycenter.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BARYCENTER_H
+#define IGL_BARYCENTER_H
+#include "igl_inline.h"
+#include <Eigen/Dense>
+namespace igl
+{
+  // Computes the barycenter of every simplex
+  //
+  // Inputs:
+  //   V  #V x dim matrix of vertex coordinates
+  //   F  #F x simplex_size  matrix of indices of simplex corners into V
+  // Output:
+  //   BC  #F x dim matrix of 3d vertices
+  //
+  template <
+    typename DerivedV,
+    typename DerivedF,
+    typename DerivedBC>
+  IGL_INLINE void barycenter(
+      const Eigen::MatrixBase<DerivedV> & V,
+      const Eigen::MatrixBase<DerivedF> & F,
+      Eigen::PlainObjectBase<DerivedBC> & BC);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "barycenter.cpp"
+#endif
+
+#endif

src/igl/barycentric_coordinates.cpp

@@ -0,0 +1,113 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "barycentric_coordinates.h"
+#include "volume.h"
+
+template <
+  typename DerivedP,
+  typename DerivedA,
+  typename DerivedB,
+  typename DerivedC,
+  typename DerivedD,
+  typename DerivedL>
+IGL_INLINE void igl::barycentric_coordinates(
+  const Eigen::MatrixBase<DerivedP> & P,
+  const Eigen::MatrixBase<DerivedA> & A,
+  const Eigen::MatrixBase<DerivedB> & B,
+  const Eigen::MatrixBase<DerivedC> & C,
+  const Eigen::MatrixBase<DerivedD> & D,
+  Eigen::PlainObjectBase<DerivedL> & L)
+{
+  using namespace Eigen;
+  assert(P.cols() == 3 && "query must be in 3d");
+  assert(A.cols() == 3 && "corners must be in 3d");
+  assert(B.cols() == 3 && "corners must be in 3d");
+  assert(C.cols() == 3 && "corners must be in 3d");
+  assert(D.cols() == 3 && "corners must be in 3d");
+  assert(P.rows() == A.rows() && "Must have same number of queries as corners");
+  assert(A.rows() == B.rows() && "Corners must be same size");
+  assert(A.rows() == C.rows() && "Corners must be same size");
+  assert(A.rows() == D.rows() && "Corners must be same size");
+  typedef Matrix<typename DerivedL::Scalar,DerivedL::RowsAtCompileTime,1> 
+    VectorXS;
+  // Total volume
+  VectorXS vol,LA,LB,LC,LD;
+  volume(B,D,C,P,LA);
+  volume(A,C,D,P,LB);
+  volume(A,D,B,P,LC);
+  volume(A,B,C,P,LD);
+  volume(A,B,C,D,vol);
+  L.resize(P.rows(),4);
+  L<<LA,LB,LC,LD;
+  L.array().colwise() /= vol.array();
+}
+
+template <
+  typename DerivedP,
+  typename DerivedA,
+  typename DerivedB,
+  typename DerivedC,
+  typename DerivedL>
+IGL_INLINE void igl::barycentric_coordinates(
+  const Eigen::MatrixBase<DerivedP> & P,
+  const Eigen::MatrixBase<DerivedA> & A,
+  const Eigen::MatrixBase<DerivedB> & B,
+  const Eigen::MatrixBase<DerivedC> & C,
+  Eigen::PlainObjectBase<DerivedL> & L)
+{
+  using namespace Eigen;
+#ifndef NDEBUG
+  const int DIM = P.cols();
+  assert(A.cols() == DIM && "corners must be in same dimension as query");
+  assert(B.cols() == DIM && "corners must be in same dimension as query");
+  assert(C.cols() == DIM && "corners must be in same dimension as query");
+  assert(P.rows() == A.rows() && "Must have same number of queries as corners");
+  assert(A.rows() == B.rows() && "Corners must be same size");
+  assert(A.rows() == C.rows() && "Corners must be same size");
+#endif
+
+  // http://gamedev.stackexchange.com/a/23745
+  typedef 
+    Eigen::Array<
+      typename DerivedP::Scalar,
+               DerivedP::RowsAtCompileTime,
+               DerivedP::ColsAtCompileTime>
+    ArrayS;
+  typedef 
+    Eigen::Array<
+      typename DerivedP::Scalar,
+               DerivedP::RowsAtCompileTime,
+               1>
+    VectorS;
+
+  const ArrayS v0 = B.array() - A.array();
+  const ArrayS v1 = C.array() - A.array();
+  const ArrayS v2 = P.array() - A.array();
+  VectorS d00 = (v0*v0).rowwise().sum();
+  VectorS d01 = (v0*v1).rowwise().sum();
+  VectorS d11 = (v1*v1).rowwise().sum();
+  VectorS d20 = (v2*v0).rowwise().sum();
+  VectorS d21 = (v2*v1).rowwise().sum();
+  VectorS denom = d00 * d11 - d01 * d01;
+  L.resize(P.rows(),3);
+  L.col(1) = (d11 * d20 - d01 * d21) / denom;
+  L.col(2) = (d00 * d21 - d01 * d20) / denom;
+  L.col(0) = 1.0f -(L.col(1) + L.col(2)).array();
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::barycentric_coordinates<Eigen::Matrix<float, 1, -1, 1, 1, -1>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, 1, -1, 1, 1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, 1, -1, 1, 1, -1>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, -1, 1, 1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3>, Eigen::Matrix<float, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<float, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Matrix<double, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, 1, 2, 1, 1, 2>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Matrix<double, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, 2, 1, 1, 2> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, 1, 3, 1, 1, 3>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false>, Eigen::Matrix<double, 1, 3, 1, 1, 3> >(Eigen::MatrixBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::MatrixBase<Eigen::Block<Eigen::Matrix<double, -1, -1, 0, -1, -1> const, 1, -1, false> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, 1, 3, 1, 1, 3> >&);
+template void igl::barycentric_coordinates<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/barycentric_coordinates.h

@@ -0,0 +1,68 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BARYCENTRIC_COORDINATES_H
+#define IGL_BARYCENTRIC_COORDINATES_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  // Compute barycentric coordinates in a tet
+  //
+  // Inputs:
+  //   P  #P by 3 Query points in 3d
+  //   A  #P by 3 Tet corners in 3d
+  //   B  #P by 3 Tet corners in 3d
+  //   C  #P by 3 Tet corners in 3d
+  //   D  #P by 3 Tet corners in 3d
+  // Outputs:
+  //   L  #P by 4 list of barycentric coordinates
+  //   
+  template <
+    typename DerivedP,
+    typename DerivedA,
+    typename DerivedB,
+    typename DerivedC,
+    typename DerivedD,
+    typename DerivedL>
+  IGL_INLINE void barycentric_coordinates(
+    const Eigen::MatrixBase<DerivedP> & P,
+    const Eigen::MatrixBase<DerivedA> & A,
+    const Eigen::MatrixBase<DerivedB> & B,
+    const Eigen::MatrixBase<DerivedC> & C,
+    const Eigen::MatrixBase<DerivedD> & D,
+    Eigen::PlainObjectBase<DerivedL> & L);
+  // Compute barycentric coordinates in a triangle
+  //
+  // Inputs:
+  //   P  #P by dim Query points
+  //   A  #P by dim Triangle corners
+  //   B  #P by dim Triangle corners
+  //   C  #P by dim Triangle corners
+  // Outputs:
+  //   L  #P by 3 list of barycentric coordinates
+  //   
+  template <
+    typename DerivedP,
+    typename DerivedA,
+    typename DerivedB,
+    typename DerivedC,
+    typename DerivedL>
+  IGL_INLINE void barycentric_coordinates(
+    const Eigen::MatrixBase<DerivedP> & P,
+    const Eigen::MatrixBase<DerivedA> & A,
+    const Eigen::MatrixBase<DerivedB> & B,
+    const Eigen::MatrixBase<DerivedC> & C,
+    Eigen::PlainObjectBase<DerivedL> & L);
+
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "barycentric_coordinates.cpp"
+#endif
+
+#endif

src/igl/barycentric_to_global.cpp

@@ -0,0 +1,44 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Daniele Panozzo <daniele.panozzo@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "barycentric_to_global.h"
+
+// For error printing
+#include <cstdio>
+#include <vector>
+
+namespace igl
+{
+  template <typename Scalar, typename Index>
+  IGL_INLINE Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> barycentric_to_global(
+    const Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> & V,
+    const Eigen::Matrix<Index,Eigen::Dynamic,Eigen::Dynamic>  & F,
+    const Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> & bc)
+  {
+    Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> R;
+    R.resize(bc.rows(),3);
+
+    for (unsigned i=0; i<R.rows(); ++i)
+    {
+      unsigned id = round(bc(i,0));
+      double u   = bc(i,1);
+      double v   = bc(i,2);
+
+      if (id != -1)
+        R.row(i) = V.row(F(id,0)) +
+                  ((V.row(F(id,1)) - V.row(F(id,0))) * u +
+                   (V.row(F(id,2)) - V.row(F(id,0))) * v  );
+      else
+        R.row(i) << 0,0,0;
+    }
+    return R;
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+template Eigen::Matrix<double, -1, -1, 0, -1, -1> igl::barycentric_to_global<double, int>(Eigen::Matrix<double, -1, -1, 0, -1, -1> const&, Eigen::Matrix<int, -1, -1, 0, -1, -1> const&, Eigen::Matrix<double, -1, -1, 0, -1, -1> const&);
+#endif

src/igl/barycentric_to_global.h

@@ -0,0 +1,42 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Daniele Panozzo <daniele.panozzo@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BARYCENTRIC2GLOBAL_H
+#define IGL_BARYCENTRIC2GLOBAL_H
+#include <igl/igl_inline.h>
+
+#include <Eigen/Dense>
+#include <Eigen/Sparse>
+
+namespace igl 
+{
+  // Converts barycentric coordinates in the embree form to 3D coordinates
+  // Embree stores barycentric coordinates as triples: fid, bc1, bc2
+  // fid is the id of a face, bc1 is the displacement of the point wrt the 
+  // first vertex v0 and the edge v1-v0. Similarly, bc2 is the displacement
+  // wrt v2-v0.
+  // 
+  // Input:
+  // V:  #Vx3 Vertices of the mesh
+  // F:  #Fxe Faces of the mesh
+  // bc: #Xx3 Barycentric coordinates, one row per point
+  //
+  // Output:
+  // #X: #Xx3 3D coordinates of all points in bc
+  template <typename Scalar, typename Index>
+  IGL_INLINE Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> 
+    barycentric_to_global(
+      const Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic> & V, 
+      const Eigen::Matrix<Index,Eigen::Dynamic,Eigen::Dynamic>   & F, 
+      const Eigen::Matrix<Scalar,Eigen::Dynamic,Eigen::Dynamic>  & bc);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "barycentric_to_global.cpp"
+#endif
+
+#endif

src/igl/basename.cpp

@@ -0,0 +1,38 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "basename.h"
+
+#include <algorithm>
+
+IGL_INLINE std::string igl::basename(const std::string & path)
+{
+  if(path == "")
+  {
+    return std::string("");
+  }
+  // http://stackoverflow.com/questions/5077693/dirnamephp-similar-function-in-c
+  std::string::const_reverse_iterator last_slash =
+    std::find(
+      path.rbegin(), 
+      path.rend(), '/');
+  if( last_slash == path.rend() )
+  {
+    // No slashes found
+    return path;
+  }else if(1 == (last_slash.base() - path.begin()))
+  {
+    // Slash is first char
+    return std::string(path.begin()+1,path.end());
+  }else if(path.end() == last_slash.base() )
+  {
+    // Slash is last char
+    std::string redo = std::string(path.begin(),path.end()-1);
+    return igl::basename(redo);
+  }
+  return std::string(last_slash.base(),path.end());
+}

src/igl/basename.h

@@ -0,0 +1,29 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BASENAME_H
+#define IGL_BASENAME_H
+#include "igl_inline.h"
+
+#include <string>
+
+namespace igl
+{
+  // Function like PHP's basename: /etc/sudoers.d --> sudoers.d
+  // Input:
+  //  path  string containing input path
+  // Returns string containing basename (see php's basename)
+  //
+  // See also: dirname, pathinfo
+  IGL_INLINE std::string basename(const std::string & path);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "basename.cpp"
+#endif
+
+#endif

src/igl/bbw.cpp

@@ -0,0 +1,143 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2016 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "bbw.h"
+#include "min_quad_with_fixed.h"
+#include "harmonic.h"
+#include "parallel_for.h"
+#include <Eigen/Sparse>
+#include <iostream>
+#include <mutex>
+#include <cstdio>
+
+igl::BBWData::BBWData():
+  partition_unity(false),
+  W0(),
+  active_set_params(),
+  verbosity(0)
+{
+  // We know that the Bilaplacian is positive semi-definite
+  active_set_params.Auu_pd = true;
+}
+
+void igl::BBWData::print()
+{
+  using namespace std;
+  cout<<"partition_unity: "<<partition_unity<<endl;
+  cout<<"W0=["<<endl<<W0<<endl<<"];"<<endl;
+}
+
+
+template <
+  typename DerivedV,
+  typename DerivedEle,
+  typename Derivedb,
+  typename Derivedbc,
+  typename DerivedW>
+IGL_INLINE bool igl::bbw(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedEle> & Ele,
+  const Eigen::PlainObjectBase<Derivedb> & b,
+  const Eigen::PlainObjectBase<Derivedbc> & bc,
+  igl::BBWData & data,
+  Eigen::PlainObjectBase<DerivedW> & W
+  )
+{
+  using namespace std;
+  using namespace Eigen;
+  assert(!data.partition_unity && "partition_unity not implemented yet");
+  // number of domain vertices
+  int n = V.rows();
+  // number of handles
+  int m = bc.cols();
+  // Build biharmonic operator
+  Eigen::SparseMatrix<typename DerivedV::Scalar> Q;
+  harmonic(V,Ele,2,Q);
+  W.derived().resize(n,m);
+  // No linear terms
+  VectorXd c = VectorXd::Zero(n);
+  // No linear constraints
+  SparseMatrix<typename DerivedW::Scalar> A(0,n),Aeq(0,n),Aieq(0,n);
+  VectorXd Beq(0,1),Bieq(0,1);
+  // Upper and lower box constraints (Constant bounds)
+  VectorXd ux = VectorXd::Ones(n);
+  VectorXd lx = VectorXd::Zero(n);
+  active_set_params eff_params = data.active_set_params;
+  if(data.verbosity >= 1)
+  {
+    cout<<"BBW: max_iter: "<<data.active_set_params.max_iter<<endl;
+    cout<<"BBW: eff_max_iter: "<<eff_params.max_iter<<endl;
+  }
+  if(data.verbosity >= 1)
+  {
+    cout<<"BBW: Computing initial weights for "<<m<<" handle"<<
+      (m!=1?"s":"")<<"."<<endl;
+  }
+  min_quad_with_fixed_data<typename DerivedW::Scalar > mqwf;
+  min_quad_with_fixed_precompute(Q,b,Aeq,true,mqwf);
+  min_quad_with_fixed_solve(mqwf,c,bc,Beq,W);
+  // decrement
+  eff_params.max_iter--;
+  bool error = false;
+  // Loop over handles
+  std::mutex critical;
+  const auto & optimize_weight = [&](const int i)
+  {
+    // Quicker exit for paralle_for
+    if(error)
+    {
+      return;
+    }
+    if(data.verbosity >= 1)
+    {
+      std::lock_guard<std::mutex> lock(critical);
+      cout<<"BBW: Computing weight for handle "<<i+1<<" out of "<<m<<
+        "."<<endl;
+    }
+    VectorXd bci = bc.col(i);
+    VectorXd Wi;
+    // use initial guess
+    Wi = W.col(i);
+    SolverStatus ret = active_set(
+        Q,c,b,bci,Aeq,Beq,Aieq,Bieq,lx,ux,eff_params,Wi);
+    switch(ret)
+    {
+      case SOLVER_STATUS_CONVERGED:
+        break;
+      case SOLVER_STATUS_MAX_ITER:
+        cerr<<"active_set: max iter without convergence."<<endl;
+        break;
+      case SOLVER_STATUS_ERROR:
+      default:
+        cerr<<"active_set error."<<endl;
+        error = true;
+    }
+    W.col(i) = Wi;
+  };
+  parallel_for(m,optimize_weight,2);
+  if(error)
+  {
+    return false;
+  }
+
+#ifndef NDEBUG
+  const double min_rowsum = W.rowwise().sum().array().abs().minCoeff();
+  if(min_rowsum < 0.1)
+  {
+    cerr<<"bbw.cpp: Warning, minimum row sum is very low. Consider more "
+      "active set iterations or enforcing partition of unity."<<endl;
+  }
+#endif
+
+  return true;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::bbw<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, igl::BBWData&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif
+

src/igl/bbw.h

@@ -0,0 +1,77 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BBW_H
+#define IGL_BBW_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+#include <igl/active_set.h>
+
+namespace igl
+{
+  // Container for BBW computation related data and flags
+  class BBWData
+  {
+    public:
+      // Enforce partition of unity during optimization (optimize all weight
+      // simultaneously)
+      bool partition_unity;
+      // Initial guess
+      Eigen::MatrixXd W0;
+      igl::active_set_params active_set_params;
+      // Verbosity level
+      // 0: quiet
+      // 1: loud
+      // 2: louder
+      int verbosity;
+    public:
+      IGL_INLINE BBWData();
+      // Print current state of object
+      IGL_INLINE void print();
+  };
+
+  // Compute Bounded Biharmonic Weights on a given domain (V,Ele) with a given
+  // set of boundary conditions
+  //
+  // Templates
+  //   DerivedV  derived type of eigen matrix for V (e.g. MatrixXd)
+  //   DerivedF  derived type of eigen matrix for F (e.g. MatrixXi)
+  //   Derivedb  derived type of eigen matrix for b (e.g. VectorXi)
+  //   Derivedbc  derived type of eigen matrix for bc (e.g. MatrixXd)
+  //   DerivedW  derived type of eigen matrix for W (e.g. MatrixXd)
+  // Inputs:
+  //   V  #V by dim vertex positions
+  //   Ele  #Elements by simplex-size list of element indices
+  //   b  #b boundary indices into V
+  //   bc #b by #W list of boundary values
+  //   data  object containing options, initial guess --> solution and results
+  // Outputs:
+  //   W  #V by #W list of *unnormalized* weights to normalize use
+  //    igl::normalize_row_sums(W,W);
+  // Returns true on success, false on failure
+  template <
+    typename DerivedV,
+    typename DerivedEle,
+    typename Derivedb,
+    typename Derivedbc,
+    typename DerivedW>
+  IGL_INLINE bool bbw(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedEle> & Ele,
+    const Eigen::PlainObjectBase<Derivedb> & b,
+    const Eigen::PlainObjectBase<Derivedbc> & bc,
+    BBWData & data,
+    Eigen::PlainObjectBase<DerivedW> & W);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "bbw.cpp"
+#endif
+
+#endif
+

src/igl/bfs.cpp

@@ -0,0 +1,93 @@
+#include "bfs.h"
+#include "list_to_matrix.h"
+#include <vector>
+#include <queue>
+
+template <
+  typename AType,
+  typename DerivedD,
+  typename DerivedP>
+IGL_INLINE void igl::bfs(
+  const AType & A,
+  const size_t s,
+  Eigen::PlainObjectBase<DerivedD> & D,
+  Eigen::PlainObjectBase<DerivedP> & P)
+{
+  std::vector<typename DerivedD::Scalar> vD;
+  std::vector<typename DerivedP::Scalar> vP;
+  bfs(A,s,vD,vP);
+  list_to_matrix(vD,D);
+  list_to_matrix(vP,P);
+}
+
+template <
+  typename AType,
+  typename DType,
+  typename PType>
+IGL_INLINE void igl::bfs(
+  const std::vector<std::vector<AType> > & A,
+  const size_t s,
+  std::vector<DType> & D,
+  std::vector<PType> & P)
+{
+  // number of nodes
+  int N = s+1;
+  for(const auto & Ai : A) for(const auto & a : Ai) N = std::max(N,a+1);
+  std::vector<bool> seen(N,false);
+  P.resize(N,-1);
+  std::queue<std::pair<int,int> > Q;
+  Q.push({s,-1});
+  while(!Q.empty())
+  {
+    const int f = Q.front().first;
+    const int p = Q.front().second;
+    Q.pop();
+    if(seen[f])
+    {
+      continue;
+    }
+    D.push_back(f);
+    P[f] = p;
+    seen[f] = true;
+    for(const auto & n : A[f]) Q.push({n,f});
+  }
+}
+
+
+template <
+  typename AType,
+  typename DType,
+  typename PType>
+IGL_INLINE void igl::bfs(
+  const Eigen::SparseMatrix<AType> & A,
+  const size_t s,
+  std::vector<DType> & D,
+  std::vector<PType> & P)
+{
+  // number of nodes
+  int N = A.rows();
+  assert(A.rows() == A.cols());
+  std::vector<bool> seen(N,false);
+  P.resize(N,-1);
+  std::queue<std::pair<int,int> > Q;
+  Q.push({s,-1});
+  while(!Q.empty())
+  {
+    const int f = Q.front().first;
+    const int p = Q.front().second;
+    Q.pop();
+    if(seen[f])
+    {
+      continue;
+    }
+    D.push_back(f);
+    P[f] = p;
+    seen[f] = true;
+    for(typename Eigen::SparseMatrix<AType>::InnerIterator it (A,f); it; ++it)
+    {
+      if(it.value()) Q.push({it.index(),f});
+    }
+  }
+
+}
+

src/igl/bfs.h

@@ -0,0 +1,54 @@
+#ifndef IGL_BFS_H
+#define IGL_BFS_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+#include <vector>
+#include <Eigen/Sparse>
+namespace igl
+{
+  // Traverse a **directed** graph represented by an adjacency list using
+  // breadth first search
+  //
+  // Inputs:
+  //   A  #V list of adjacency lists  or #V by #V adjacency matrix
+  //   s  starting node (index into A)
+  // Outputs:
+  //   D  #V list of indices into rows of A in the order in which graph nodes
+  //     are discovered.
+  //   P  #V list of indices into rows of A of predecessor in resulting
+  //     spanning tree {-1 indicates root/not discovered), order corresponds to
+  //     V **not** D.
+  template <
+    typename AType,
+    typename DerivedD,
+    typename DerivedP>
+  IGL_INLINE void bfs(
+    const AType & A,
+    const size_t s,
+    Eigen::PlainObjectBase<DerivedD> & D,
+    Eigen::PlainObjectBase<DerivedP> & P);
+
+  template <
+    typename AType,
+    typename DType,
+    typename PType>
+  IGL_INLINE void bfs(
+    const std::vector<std::vector<AType> > & A,
+    const size_t s,
+    std::vector<DType> & D,
+    std::vector<PType> & P);
+  template <
+    typename AType,
+    typename DType,
+    typename PType>
+  IGL_INLINE void bfs(
+    const Eigen::SparseMatrix<AType> & A,
+    const size_t s,
+    std::vector<DType> & D,
+    std::vector<PType> & P);
+}
+#ifndef IGL_STATIC_LIBRARY
+#  include "bfs.cpp"
+#endif
+#endif
+

src/igl/bfs_orient.cpp

@@ -0,0 +1,100 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "bfs_orient.h"
+#include "orientable_patches.h"
+#include <Eigen/Sparse>
+#include <queue>
+
+template <typename DerivedF, typename DerivedFF, typename DerivedC>
+IGL_INLINE void igl::bfs_orient(
+  const Eigen::PlainObjectBase<DerivedF> & F,
+  Eigen::PlainObjectBase<DerivedFF> & FF,
+  Eigen::PlainObjectBase<DerivedC> & C)
+{
+  using namespace Eigen;
+  using namespace std;
+  SparseMatrix<int> A;
+  orientable_patches(F,C,A);
+
+  // number of faces
+  const int m = F.rows();
+  // number of patches
+  const int num_cc = C.maxCoeff()+1;
+  VectorXi seen = VectorXi::Zero(m);
+
+  // Edge sets
+  const int ES[3][2] = {{1,2},{2,0},{0,1}};
+
+  if(&FF != &F)
+  {
+    FF = F;
+  }
+  // loop over patches
+#pragma omp parallel for
+  for(int c = 0;c<num_cc;c++)
+  {
+    queue<int> Q;
+    // find first member of patch c
+    for(int f = 0;f<FF.rows();f++)
+    {
+      if(C(f) == c)
+      {
+        Q.push(f);
+        break;
+      }
+    }
+    assert(!Q.empty());
+    while(!Q.empty())
+    {
+      const int f = Q.front();
+      Q.pop();
+      if(seen(f) > 0)
+      {
+        continue;
+      }
+      seen(f)++;
+      // loop over neighbors of f
+      for(typename SparseMatrix<int>::InnerIterator it (A,f); it; ++it)
+      {
+        // might be some lingering zeros, and skip self-adjacency
+        if(it.value() != 0 && it.row() != f)
+        {
+          const int n = it.row();
+          assert(n != f);
+          // loop over edges of f
+          for(int efi = 0;efi<3;efi++)
+          {
+            // efi'th edge of face f
+            Vector2i ef(FF(f,ES[efi][0]),FF(f,ES[efi][1]));
+            // loop over edges of n
+            for(int eni = 0;eni<3;eni++)
+            {
+              // eni'th edge of face n
+              Vector2i en(FF(n,ES[eni][0]),FF(n,ES[eni][1]));
+              // Match (half-edges go same direction)
+              if(ef(0) == en(0) && ef(1) == en(1))
+              {
+                // flip face n
+                FF.row(n) = FF.row(n).reverse().eval();
+              }
+            }
+          }
+          // add neighbor to queue
+          Q.push(n);
+        }
+      }
+    }
+  }
+
+  // make sure flip is OK if &FF = &F
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::bfs_orient<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/bfs_orient.h

@@ -0,0 +1,36 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BFS_ORIENT_H
+#define IGL_BFS_ORIENT_H
+#include <Eigen/Core>
+#include <igl/igl_inline.h>
+
+namespace igl
+{
+  // Consistently orient faces in orientable patches using BFS
+  //
+  // F = bfs_orient(F,V);
+  //
+  // Inputs:
+  //  F  #F by 3 list of faces
+  // Outputs:
+  //  FF  #F by 3 list of faces (OK if same as F)
+  //  C  #F list of component ids
+  //
+  //
+  template <typename DerivedF, typename DerivedFF, typename DerivedC>
+  IGL_INLINE void bfs_orient(
+    const Eigen::PlainObjectBase<DerivedF> & F,
+    Eigen::PlainObjectBase<DerivedFF> & FF,
+    Eigen::PlainObjectBase<DerivedC> & C);
+};
+#ifndef IGL_STATIC_LIBRARY
+#  include "bfs_orient.cpp"
+#endif
+
+#endif

src/igl/biharmonic_coordinates.cpp

@@ -0,0 +1,203 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "biharmonic_coordinates.h"
+#include "cotmatrix.h"
+#include "sum.h"
+#include "massmatrix.h"
+#include "min_quad_with_fixed.h"
+#include "crouzeix_raviart_massmatrix.h"
+#include "crouzeix_raviart_cotmatrix.h"
+#include "normal_derivative.h"
+#include "on_boundary.h"
+#include <Eigen/Sparse>
+
+template <
+  typename DerivedV,
+  typename DerivedT,
+  typename SType,
+  typename DerivedW>
+IGL_INLINE bool igl::biharmonic_coordinates(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedT> & T,
+  const std::vector<std::vector<SType> > & S,
+  Eigen::PlainObjectBase<DerivedW> & W)
+{
+  return biharmonic_coordinates(V,T,S,2,W);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedT,
+  typename SType,
+  typename DerivedW>
+IGL_INLINE bool igl::biharmonic_coordinates(
+  const Eigen::PlainObjectBase<DerivedV> & V,
+  const Eigen::PlainObjectBase<DerivedT> & T,
+  const std::vector<std::vector<SType> > & S,
+  const int k,
+  Eigen::PlainObjectBase<DerivedW> & W)
+{
+  using namespace Eigen;
+  using namespace std;
+  // This is not the most efficient way to build A, but follows "Linear
+  // Subspace Design for Real-Time Shape Deformation" [Wang et al. 2015].
+  SparseMatrix<double> A;
+  {
+    DiagonalMatrix<double,Dynamic> Minv;
+    SparseMatrix<double> L,K;
+    Array<bool,Dynamic,Dynamic> C;
+    {
+      Array<bool,Dynamic,1> I;
+      on_boundary(T,I,C);
+    }
+#ifdef false 
+    // Version described in paper is "wrong"
+    // http://www.cs.toronto.edu/~jacobson/images/error-in-linear-subspace-design-for-real-time-shape-deformation-2017-wang-et-al.pdf
+    SparseMatrix<double> N,Z,M;
+    normal_derivative(V,T,N);
+    {
+      std::vector<Triplet<double> >ZIJV;
+      for(int t =0;t<T.rows();t++)
+      {
+        for(int f =0;f<T.cols();f++)
+        {
+          if(C(t,f))
+          {
+            const int i = t+f*T.rows();
+            for(int c = 1;c<T.cols();c++)
+            {
+              ZIJV.emplace_back(T(t,(f+c)%T.cols()),i,1);
+            }
+          }
+        }
+      }
+      Z.resize(V.rows(),N.rows());
+      Z.setFromTriplets(ZIJV.begin(),ZIJV.end());
+      N = (Z*N).eval();
+    }
+    cotmatrix(V,T,L);
+    K = N+L;
+    massmatrix(V,T,MASSMATRIX_TYPE_DEFAULT,M);
+    // normalize
+    M /= ((VectorXd)M.diagonal()).array().abs().maxCoeff();
+    Minv =
+      ((VectorXd)M.diagonal().array().inverse()).asDiagonal();
+#else
+    Eigen::SparseMatrix<double> M;
+    Eigen::MatrixXi E;
+    Eigen::VectorXi EMAP;
+    crouzeix_raviart_massmatrix(V,T,M,E,EMAP);
+    crouzeix_raviart_cotmatrix(V,T,E,EMAP,L);
+    // Ad  #E by #V facet-vertex incidence matrix
+    Eigen::SparseMatrix<double> Ad(E.rows(),V.rows());
+    {
+      std::vector<Eigen::Triplet<double> > AIJV(E.size());
+      for(int e = 0;e<E.rows();e++)
+      {
+        for(int c = 0;c<E.cols();c++)
+        {
+          AIJV[e+c*E.rows()] = Eigen::Triplet<double>(e,E(e,c),1);
+        }
+      }
+      Ad.setFromTriplets(AIJV.begin(),AIJV.end());
+    }
+    // Degrees
+    Eigen::VectorXd De;
+    sum(Ad,2,De);
+    Eigen::DiagonalMatrix<double,Eigen::Dynamic> De_diag = 
+      De.array().inverse().matrix().asDiagonal();
+    K = L*(De_diag*Ad);
+    // normalize
+    M /= ((VectorXd)M.diagonal()).array().abs().maxCoeff();
+    Minv = ((VectorXd)M.diagonal().array().inverse()).asDiagonal();
+    // kill boundary edges
+    for(int f = 0;f<T.rows();f++)
+    {
+      for(int c = 0;c<T.cols();c++)
+      {
+        if(C(f,c))
+        {
+          const int e = EMAP(f+T.rows()*c);
+          Minv.diagonal()(e) = 0;
+        }
+      }
+    }
+
+#endif
+    switch(k)
+    {
+      default:
+        assert(false && "unsupported");
+      case 2:
+        // For C1 smoothness in 2D, one should use bi-harmonic
+        A = K.transpose() * (Minv * K);
+        break;
+      case 3:
+        // For C1 smoothness in 3D, one should use tri-harmonic
+        A = K.transpose() * (Minv * (-L * (Minv * K)));
+        break;
+    }
+  }
+  // Vertices in point handles
+  const size_t mp =
+    count_if(S.begin(),S.end(),[](const vector<int> & h){return h.size()==1;});
+  // number of region handles
+  const size_t r = S.size()-mp;
+  // Vertices in region handles
+  size_t mr = 0;
+  for(const auto & h : S)
+  {
+    if(h.size() > 1)
+    {
+      mr += h.size();
+    }
+  }
+  const size_t dim = T.cols()-1;
+  // Might as well be dense... I think...
+  MatrixXd J = MatrixXd::Zero(mp+mr,mp+r*(dim+1));
+  VectorXi b(mp+mr);
+  MatrixXd H(mp+r*(dim+1),dim);
+  {
+    int v = 0;
+    int c = 0;
+    for(int h = 0;h<S.size();h++)
+    {
+      if(S[h].size()==1)
+      {
+        H.row(c) = V.block(S[h][0],0,1,dim);
+        J(v,c++) = 1;
+        b(v) = S[h][0];
+        v++;
+      }else
+      {
+        assert(S[h].size() >= dim+1);
+        for(int p = 0;p<S[h].size();p++)
+        {
+          for(int d = 0;d<dim;d++)
+          {
+            J(v,c+d) = V(S[h][p],d);
+          }
+          J(v,c+dim) = 1;
+          b(v) = S[h][p];
+          v++;
+        }
+        H.block(c,0,dim+1,dim).setIdentity();
+        c+=dim+1;
+      }
+    }
+  }
+  // minimize    ½ W' A W'
+  // subject to  W(b,:) = J
+  return min_quad_with_fixed(
+    A,VectorXd::Zero(A.rows()).eval(),b,J,SparseMatrix<double>(),VectorXd(),true,W);
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template bool igl::biharmonic_coordinates<Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, int, Eigen::Matrix<double, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > const&, int, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> >&);
+#endif

src/igl/biharmonic_coordinates.h

@@ -0,0 +1,90 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BIHARMONIC_COORDINATES_H
+#define IGL_BIHARMONIC_COORDINATES_H
+#include "igl_inline.h"
+#include <Eigen/Dense>
+#include <vector>
+namespace igl
+{
+  // Compute "discrete biharmonic generalized barycentric coordinates" as
+  // described in "Linear Subspace Design for Real-Time Shape Deformation"
+  // [Wang et al. 2015]. Not to be confused with "Bounded Biharmonic Weights
+  // for Real-Time Deformation" [Jacobson et al. 2011] or "Biharmonic
+  // Coordinates" (2D complex barycentric coordinates) [Weber et al. 2012].
+  // These weights minimize a discrete version of the squared Laplacian energy
+  // subject to positional interpolation constraints at selected vertices
+  // (point handles) and transformation interpolation constraints at regions
+  // (region handles).
+  //
+  // Templates:
+  //   HType  should be a simple index type e.g. `int`,`size_t`
+  // Inputs:
+  //   V  #V by dim list of mesh vertex positions
+  //   T  #T by dim+1 list of / triangle indices into V      if dim=2
+  //                          \ tetrahedron indices into V   if dim=3
+  //   S  #point-handles+#region-handles list of lists of selected vertices for
+  //     each handle. Point handles should have singleton lists and region
+  //     handles should have lists of size at least dim+1 (and these points
+  //     should be in general position).
+  // Outputs:
+  //   W  #V by #points-handles+(#region-handles * dim+1) matrix of weights so
+  //     that columns correspond to each handles generalized barycentric
+  //     coordinates (for point-handles) or animation space weights (for region
+  //     handles).
+  // returns true only on success
+  //
+  // Example:
+  //
+  //     MatrixXd W;
+  //     igl::biharmonic_coordinates(V,F,S,W);
+  //     const size_t dim = T.cols()-1;
+  //     MatrixXd H(W.cols(),dim);
+  //     {
+  //       int c = 0;
+  //       for(int h = 0;h<S.size();h++)
+  //       {
+  //         if(S[h].size()==1)
+  //         {
+  //           H.row(c++) = V.block(S[h][0],0,1,dim);
+  //         }else
+  //         {
+  //           H.block(c,0,dim+1,dim).setIdentity();
+  //           c+=dim+1;
+  //         }
+  //       }
+  //     }
+  //     assert( (V-(W*H)).array().maxCoeff() < 1e-7 );
+  template <
+    typename DerivedV,
+    typename DerivedT,
+    typename SType,
+    typename DerivedW>
+  IGL_INLINE bool biharmonic_coordinates(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedT> & T,
+    const std::vector<std::vector<SType> > & S,
+    Eigen::PlainObjectBase<DerivedW> & W);
+  // k  2-->biharmonic, 3-->triharmonic
+  template <
+    typename DerivedV,
+    typename DerivedT,
+    typename SType,
+    typename DerivedW>
+  IGL_INLINE bool biharmonic_coordinates(
+    const Eigen::PlainObjectBase<DerivedV> & V,
+    const Eigen::PlainObjectBase<DerivedT> & T,
+    const std::vector<std::vector<SType> > & S,
+    const int k,
+    Eigen::PlainObjectBase<DerivedW> & W);
+
+};
+#  ifndef IGL_STATIC_LIBRARY
+#    include "biharmonic_coordinates.cpp"
+#  endif
+#endif

src/igl/bijective_composite_harmonic_mapping.cpp

@@ -0,0 +1,115 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "bijective_composite_harmonic_mapping.h"
+
+#include "slice.h"
+#include "doublearea.h"
+#include "harmonic.h"
+//#include "matlab/MatlabWorkspace.h"
+#include <iostream>
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Derivedb,
+  typename Derivedbc,
+  typename DerivedU>
+IGL_INLINE bool igl::bijective_composite_harmonic_mapping(
+  const Eigen::MatrixBase<DerivedV> & V,
+  const Eigen::MatrixBase<DerivedF> & F,
+  const Eigen::MatrixBase<Derivedb> & b,
+  const Eigen::MatrixBase<Derivedbc> & bc,
+  Eigen::PlainObjectBase<DerivedU> & U)
+{
+  return bijective_composite_harmonic_mapping(V,F,b,bc,1,200,20,true,U);
+}
+
+template <
+  typename DerivedV,
+  typename DerivedF,
+  typename Derivedb,
+  typename Derivedbc,
+  typename DerivedU>
+IGL_INLINE bool igl::bijective_composite_harmonic_mapping(
+  const Eigen::MatrixBase<DerivedV> & V,
+  const Eigen::MatrixBase<DerivedF> & F,
+  const Eigen::MatrixBase<Derivedb> & b,
+  const Eigen::MatrixBase<Derivedbc> & bc,
+  const int min_steps,
+  const int max_steps,
+  const int num_inner_iters,
+  const bool test_for_flips,
+  Eigen::PlainObjectBase<DerivedU> & U)
+{
+  typedef typename Derivedbc::Scalar Scalar;
+  assert(V.cols() == 2 && bc.cols() == 2 && "Input should be 2D");
+  assert(F.cols() == 3 && "F should contain triangles");
+  int tries = 0;
+  int nsteps = min_steps;
+  Derivedbc bc0;
+  slice(V,b,1,bc0);
+
+  // It's difficult to check for flips "robustly" in the sense that the input
+  // mesh might not have positive/consistent sign to begin with. 
+
+  while(nsteps<=max_steps)
+  {
+    U = V;
+    int flipped = 0;
+    int nans = 0;
+    int step = 0;
+    for(;step<=nsteps;step++)
+    {
+      const Scalar t = ((Scalar)step)/((Scalar)nsteps);
+      // linearly interpolate boundary conditions
+      // TODO: replace this with something that guarantees a homotopic "morph"
+      // of the boundary conditions. Something like "Homotopic Morphing of
+      // Planar Curves" [Dym et al. 2015] but also handling multiple connected
+      // components.
+      Derivedbc bct = bc0 + t*(bc - bc0);
+      // Compute dsicrete harmonic map using metric of previous step
+      for(int iter = 0;iter<num_inner_iters;iter++)
+      {
+        //std::cout<<nsteps<<" t: "<<t<<" iter: "<<iter;
+        //igl::matlab::MatlabWorkspace mw;
+        //mw.save(U,"U");
+        //mw.save_index(F,"F");
+        //mw.save_index(b,"b");
+        //mw.save(bct,"bct");
+        //mw.write("numerical.mat");
+        harmonic(DerivedU(U),F,b,bct,1,U);
+        igl::slice(U,b,1,bct);
+        nans = (U.array() != U.array()).count();
+        if(test_for_flips)
+        {
+          Eigen::Matrix<Scalar,Eigen::Dynamic,1> A;
+          doublearea(U,F,A);
+          flipped = (A.array() < 0 ).count();
+          //std::cout<<"  "<<flipped<<"  nan? "<<(U.array() != U.array()).any()<<std::endl;
+          if(flipped == 0 && nans == 0) break;
+        }
+      }
+      if(flipped > 0 || nans>0) break;
+    }
+    if(flipped == 0 && nans == 0)
+    {
+      return step == nsteps+1;
+    }
+    nsteps *= 2;
+  }
+  //std::cout<<"failed to finish in "<<nsteps<<"..."<<std::endl;
+  return false;
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template bool igl::bijective_composite_harmonic_mapping<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 1, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> >&);
+// generated by autoexplicit.sh
+template bool igl::bijective_composite_harmonic_mapping<Eigen::Matrix<double, -1, -1, 1, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1>, Eigen::Matrix<double, -1, -1, 0, -1, -1>, Eigen::Matrix<double, -1, -1, 1, -1, -1> >(Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::MatrixBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> > const&, Eigen::MatrixBase<Eigen::Matrix<double, -1, -1, 0, -1, -1> > const&, int, int, int, bool, Eigen::PlainObjectBase<Eigen::Matrix<double, -1, -1, 1, -1, -1> >&);
+#endif

src/igl/bijective_composite_harmonic_mapping.h

@@ -0,0 +1,79 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2017 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
+#define IGL_BIJECTIVE_COMPOSITE_HARMONIC_MAPPING_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+
+namespace igl 
+{
+  // Compute a planar mapping of a triangulated polygon (V,F) subjected to
+  // boundary conditions (b,bc). The mapping should be bijective in the sense
+  // that no triangles' areas become negative (this assumes they started
+  // positive). This mapping is computed by "composing" harmonic mappings
+  // between incremental morphs of the boundary conditions. This is a bit like
+  // a discrete version of "Bijective Composite Mean Value Mappings" [Schneider
+  // et al. 2013] but with a discrete harmonic map (cf. harmonic coordinates)
+  // instead of mean value coordinates. This is inspired by "Embedding a
+  // triangular graph within a given boundary" [Xu et al. 2011].
+  //
+  // Inputs:
+  //   V  #V by 2 list of triangle mesh vertex positions
+  //   F  #F by 3 list of triangle indices into V
+  //   b  #b list of boundary indices into V
+  //   bc  #b by 2 list of boundary conditions corresponding to b
+  // Outputs:
+  //   U  #V by 2 list of output mesh vertex locations
+  // Returns true if and only if U contains a successful bijectie mapping
+  //
+  // 
+  template <
+    typename DerivedV,
+    typename DerivedF,
+    typename Derivedb,
+    typename Derivedbc,
+    typename DerivedU>
+  IGL_INLINE bool bijective_composite_harmonic_mapping(
+    const Eigen::MatrixBase<DerivedV> & V,
+    const Eigen::MatrixBase<DerivedF> & F,
+    const Eigen::MatrixBase<Derivedb> & b,
+    const Eigen::MatrixBase<Derivedbc> & bc,
+    Eigen::PlainObjectBase<DerivedU> & U);
+  //
+  // Inputs:
+  //   min_steps  minimum number of steps to take from V(b,:) to bc
+  //   max_steps  minimum number of steps to take from V(b,:) to bc (if
+  //     max_steps == min_steps then no further number of steps will be tried)
+  //   num_inner_iters  number of iterations of harmonic solves to run after
+  //     for each morph step (to try to push flips back in)
+  //   test_for_flips  whether to check if flips occurred (and trigger more
+  //     steps). if test_for_flips = false then this function always returns
+  //     true
+  // 
+  template <
+    typename DerivedV,
+    typename DerivedF,
+    typename Derivedb,
+    typename Derivedbc,
+    typename DerivedU>
+  IGL_INLINE bool bijective_composite_harmonic_mapping(
+    const Eigen::MatrixBase<DerivedV> & V,
+    const Eigen::MatrixBase<DerivedF> & F,
+    const Eigen::MatrixBase<Derivedb> & b,
+    const Eigen::MatrixBase<Derivedbc> & bc,
+    const int min_steps,
+    const int max_steps,
+    const int num_inner_iters,
+    const bool test_for_flips,
+    Eigen::PlainObjectBase<DerivedU> & U);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "bijective_composite_harmonic_mapping.cpp"
+#endif
+#endif

src/igl/bone_parents.cpp

@@ -0,0 +1,32 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2015 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "bone_parents.h"
+
+template <typename DerivedBE, typename DerivedP>
+IGL_INLINE void igl::bone_parents(
+  const Eigen::PlainObjectBase<DerivedBE>& BE,
+  Eigen::PlainObjectBase<DerivedP>& P)
+{
+  P.resize(BE.rows(),1);
+  // Stupid O(n²) version
+  for(int e = 0;e<BE.rows();e++)
+  {
+    P(e) = -1;
+    for(int f = 0;f<BE.rows();f++)
+    {
+      if(BE(e,0) == BE(f,1))
+      {
+        P(e) = f;
+      }
+    }
+  }
+}
+
+#ifdef IGL_STATIC_LIBRARY
+template void igl::bone_parents<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif

src/igl/bone_parents.h

@@ -0,0 +1,32 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2014 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BONE_PARENTS_H
+#define IGL_BONE_PARENTS_H
+#include "igl_inline.h"
+#include <Eigen/Core>
+namespace igl
+{
+  // BONE_PARENTS Recover "parent" bones from directed graph representation.
+  // 
+  // Inputs:
+  //   BE  #BE by 2 list of directed bone edges
+  // Outputs:
+  //   P  #BE by 1 list of parent indices into BE, -1 means root.
+  //
+  template <typename DerivedBE, typename DerivedP>
+  IGL_INLINE void bone_parents(
+    const Eigen::PlainObjectBase<DerivedBE>& BE,
+    Eigen::PlainObjectBase<DerivedP>& P);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "bone_parents.cpp"
+#endif
+
+#endif
+

src/igl/boundary_conditions.cpp

@@ -0,0 +1,192 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "boundary_conditions.h"
+
+#include "verbose.h"
+#include "EPS.h"
+#include "project_to_line.h"
+
+#include <vector>
+#include <map>
+#include <iostream>
+
+IGL_INLINE bool igl::boundary_conditions(
+  const Eigen::MatrixXd & V  ,
+  const Eigen::MatrixXi & /*Ele*/,
+  const Eigen::MatrixXd & C  ,
+  const Eigen::VectorXi & P  ,
+  const Eigen::MatrixXi & BE ,
+  const Eigen::MatrixXi & CE ,
+  Eigen::VectorXi &       b  ,
+  Eigen::MatrixXd &       bc )
+{
+  using namespace Eigen;
+  using namespace std;
+
+  if(P.size()+BE.rows() == 0)
+  {
+    verbose("^%s: Error: no handles found\n",__FUNCTION__);
+    return false;
+  }
+
+  vector<int> bci;
+  vector<int> bcj;
+  vector<double> bcv;
+
+  // loop over points
+  for(int p = 0;p<P.size();p++)
+  {
+    VectorXd pos = C.row(P(p));
+    // loop over domain vertices
+    for(int i = 0;i<V.rows();i++)
+    {
+      // Find samples just on pos
+      //Vec3 vi(V(i,0),V(i,1),V(i,2));
+      // EIGEN GOTCHA:
+      // double sqrd = (V.row(i)-pos).array().pow(2).sum();
+      // Must first store in temporary
+      VectorXd vi = V.row(i);
+      double sqrd = (vi-pos).squaredNorm();
+      if(sqrd <= FLOAT_EPS)
+      {
+        //cout<<"sum((["<<
+        //  V(i,0)<<" "<<
+        //  V(i,1)<<" "<<
+        //  V(i,2)<<"] - ["<<
+        //  pos(0)<<" "<<
+        //  pos(1)<<" "<<
+        //  pos(2)<<"]).^2) = "<<sqrd<<endl;
+        bci.push_back(i);
+        bcj.push_back(p);
+        bcv.push_back(1.0);
+      }
+    }
+  }
+
+  // loop over bone edges
+  for(int e = 0;e<BE.rows();e++)
+  {
+    // loop over domain vertices
+    for(int i = 0;i<V.rows();i++)
+    {
+      // Find samples from tip up to tail
+      VectorXd tip = C.row(BE(e,0));
+      VectorXd tail = C.row(BE(e,1));
+      // Compute parameter along bone and squared distance
+      double t,sqrd;
+      project_to_line(
+          V(i,0),V(i,1),V(i,2),
+          tip(0),tip(1),tip(2),
+          tail(0),tail(1),tail(2),
+          t,sqrd);
+      if(t>=-FLOAT_EPS && t<=(1.0f+FLOAT_EPS) && sqrd<=FLOAT_EPS)
+      {
+        bci.push_back(i);
+        bcj.push_back(P.size()+e);
+        bcv.push_back(1.0);
+      }
+    }
+  }
+
+  // loop over cage edges
+  for(int e = 0;e<CE.rows();e++)
+  {
+    // loop over domain vertices
+    for(int i = 0;i<V.rows();i++)
+    {
+      // Find samples from tip up to tail
+      VectorXd tip = C.row(P(CE(e,0)));
+      VectorXd tail = C.row(P(CE(e,1)));
+      // Compute parameter along bone and squared distance
+      double t,sqrd;
+      project_to_line(
+          V(i,0),V(i,1),V(i,2),
+          tip(0),tip(1),tip(2),
+          tail(0),tail(1),tail(2),
+          t,sqrd);
+      if(t>=-FLOAT_EPS && t<=(1.0f+FLOAT_EPS) && sqrd<=FLOAT_EPS)
+      {
+        bci.push_back(i);
+        bcj.push_back(CE(e,0));
+        bcv.push_back(1.0-t);
+        bci.push_back(i);
+        bcj.push_back(CE(e,1));
+        bcv.push_back(t);
+      }
+    }
+  }
+
+  // find unique boundary indices
+  vector<int> vb = bci;
+  sort(vb.begin(),vb.end());
+  vb.erase(unique(vb.begin(), vb.end()), vb.end());
+
+  b.resize(vb.size());
+  bc = MatrixXd::Zero(vb.size(),P.size()+BE.rows());
+  // Map from boundary index to index in boundary
+  map<int,int> bim;
+  int i = 0;
+  // Also fill in b
+  for(vector<int>::iterator bit = vb.begin();bit != vb.end();bit++)
+  {
+    b(i) = *bit;
+    bim[*bit] = i;
+    i++;
+  }
+
+  // Build BC
+  for(i = 0;i < (int)bci.size();i++)
+  {
+    assert(bim.find(bci[i]) != bim.end());
+    bc(bim[bci[i]],bcj[i]) = bcv[i];
+  }
+
+  // Normalize across rows so that conditions sum to one
+  for(i = 0;i<bc.rows();i++)
+  {
+    double sum = bc.row(i).sum();
+    assert(sum != 0 && "Some boundary vertex getting all zero BCs");
+    bc.row(i).array() /= sum;
+  }
+
+  if(bc.size() == 0)
+  {
+    verbose("^%s: Error: boundary conditions are empty.\n",__FUNCTION__);
+    return false;
+  }
+
+  // If there's only a single boundary condition, the following tests
+  // are overzealous.
+  if(bc.cols() == 1)
+  {
+    // If there is only one weight function,
+    // then we expect that there is only one handle.
+    assert(P.rows() + BE.rows() == 1);
+    return true;
+  }
+
+  // Check that every Weight function has at least one boundary value of 1 and
+  // one value of 0
+  for(i = 0;i<bc.cols();i++)
+  {
+    double min_abs_c = bc.col(i).array().abs().minCoeff();
+    double max_c = bc.col(i).maxCoeff();
+    if(min_abs_c > FLOAT_EPS)
+    {
+      verbose("^%s: Error: handle %d does not receive 0 weight\n",__FUNCTION__,i);
+      return false;
+    }
+    if(max_c< (1-FLOAT_EPS))
+    {
+      verbose("^%s: Error: handle %d does not receive 1 weight\n",__FUNCTION__,i);
+      return false;
+    }
+  }
+
+  return true;
+}

src/igl/boundary_conditions.h

@@ -0,0 +1,55 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+// 
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+// 
+// This Source Code Form is subject to the terms of the Mozilla Public License 
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can 
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BOUNDARY_CONDITIONS_H
+#define IGL_BOUNDARY_CONDITIONS_H
+#include "igl_inline.h"
+#include <Eigen/Dense>
+
+namespace igl
+{
+
+  // Compute boundary conditions for automatic weights computation. This
+  // function expects that the given mesh (V,Ele) has sufficient samples
+  // (vertices) exactly at point handle locations and exactly along bone and
+  // cage edges.
+  //
+  // Inputs:
+  //   V  #V by dim list of domain vertices
+  //   Ele  #Ele by simplex-size list of simplex indices
+  //   C  #C by dim list of handle positions
+  //   P  #P by 1 list of point handle indices into C
+  //   BE  #BE by 2 list of bone edge indices into C
+  //   CE  #CE by 2 list of cage edge indices into *P*
+  // Outputs:
+  //   b  #b list of boundary indices (indices into V of vertices which have
+  //     known, fixed values)
+  //   bc #b by #weights list of known/fixed values for boundary vertices
+  //     (notice the #b != #weights in general because #b will include all the
+  //     intermediary samples along each bone, etc.. The ordering of the
+  //     weights corresponds to [P;BE]
+  // Returns false if boundary conditions are suspicious:
+  //   P and BE are empty
+  //   bc is empty
+  //   some column of bc doesn't have a 0 (assuming bc has >1 columns)
+  //   some column of bc doesn't have a 1 (assuming bc has >1 columns)
+  IGL_INLINE bool boundary_conditions(
+    const Eigen::MatrixXd & V,
+    const Eigen::MatrixXi & Ele,
+    const Eigen::MatrixXd & C,
+    const Eigen::VectorXi & P,
+    const Eigen::MatrixXi & BE,
+    const Eigen::MatrixXi & CE,
+    Eigen::VectorXi & b,
+    Eigen::MatrixXd & bc);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "boundary_conditions.cpp"
+#endif
+
+#endif

src/igl/boundary_facets.cpp

@@ -0,0 +1,141 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "boundary_facets.h"
+#include "face_occurrences.h"
+
+// IGL includes
+#include "sort.h"
+
+// STL includes
+#include <map>
+#include <iostream>
+
+template <typename IntegerT, typename IntegerF>
+IGL_INLINE void igl::boundary_facets(
+  const std::vector<std::vector<IntegerT> > & T,
+  std::vector<std::vector<IntegerF> > & F)
+{
+  using namespace std;
+
+  if(T.size() == 0)
+  {
+    F.clear();
+    return;
+  }
+
+  int simplex_size = T[0].size();
+  // Get a list of all faces
+  vector<vector<IntegerF> > allF(
+    T.size()*simplex_size,
+    vector<IntegerF>(simplex_size-1));
+
+  // Gather faces, loop over tets
+  for(int i = 0; i< (int)T.size();i++)
+  {
+    assert((int)T[i].size() == simplex_size);
+    switch(simplex_size)
+    {
+      case 4:
+        // get face in correct order
+        allF[i*simplex_size+0][0] = T[i][1];
+        allF[i*simplex_size+0][1] = T[i][3];
+        allF[i*simplex_size+0][2] = T[i][2];
+        // get face in correct order
+        allF[i*simplex_size+1][0] = T[i][0];
+        allF[i*simplex_size+1][1] = T[i][2];
+        allF[i*simplex_size+1][2] = T[i][3];
+        // get face in correct order
+        allF[i*simplex_size+2][0] = T[i][0];
+        allF[i*simplex_size+2][1] = T[i][3];
+        allF[i*simplex_size+2][2] = T[i][1];
+        // get face in correct order
+        allF[i*simplex_size+3][0] = T[i][0];
+        allF[i*simplex_size+3][1] = T[i][1];
+        allF[i*simplex_size+3][2] = T[i][2];
+        break;
+      case 3:
+        allF[i*simplex_size+0][0] = T[i][1];
+        allF[i*simplex_size+0][1] = T[i][2];
+        allF[i*simplex_size+1][0] = T[i][2];
+        allF[i*simplex_size+1][1] = T[i][0];
+        allF[i*simplex_size+2][0] = T[i][0];
+        allF[i*simplex_size+2][1] = T[i][1];
+        break;
+    }
+  }
+
+  // Counts
+  vector<int> C;
+  face_occurrences(allF,C);
+
+  // Q: Why not just count the number of ones?
+  // A: because we are including non-manifold edges as boundary edges
+  int twos = (int) count(C.begin(),C.end(),2);
+  //int ones = (int) count(C.begin(),C.end(),1);
+  // Resize output to fit number of ones
+  F.resize(allF.size() - twos);
+  //F.resize(ones);
+  int k = 0;
+  for(int i = 0;i< (int)allF.size();i++)
+  {
+    if(C[i] != 2)
+    {
+      assert(k<(int)F.size());
+      F[k] = allF[i];
+      k++;
+    }
+  }
+  assert(k==(int)F.size());
+  //if(k != F.size())
+  //{
+  //  printf("%d =? %d\n",k,F.size());
+  //}
+
+}
+
+#include "list_to_matrix.h"
+#include "matrix_to_list.h"
+
+template <typename DerivedT, typename DerivedF>
+IGL_INLINE void igl::boundary_facets(
+  const Eigen::PlainObjectBase<DerivedT>& T,
+  Eigen::PlainObjectBase<DerivedF>& F)
+{
+  assert(T.cols() == 0 || T.cols() == 4 || T.cols() == 3);
+  using namespace std;
+  using namespace Eigen;
+  // Cop out: use vector of vectors version
+  vector<vector<typename DerivedT::Scalar> > vT;
+  matrix_to_list(T,vT);
+  vector<vector<typename DerivedF::Scalar> > vF;
+  boundary_facets(vT,vF);
+  list_to_matrix(vF,F);
+}
+
+template <typename DerivedT, typename Ret>
+Ret igl::boundary_facets(
+  const Eigen::PlainObjectBase<DerivedT>& T)
+{
+  Ret F;
+  igl::boundary_facets(T,F);
+  return F;
+}
+
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+// generated by autoexplicit.sh
+template void igl::boundary_facets<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<unsigned int, -1, 3, 1, -1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<unsigned int, -1, 3, 1, -1, 3> >&);
+// generated by autoexplicit.sh
+template void igl::boundary_facets<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 3, 0, -1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 0, -1, 3> >&);
+template void igl::boundary_facets<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> >&);
+template void igl::boundary_facets<int, int>(std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > > const&, std::vector<std::vector<int, std::allocator<int> >, std::allocator<std::vector<int, std::allocator<int> > > >&);
+//template Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > igl::boundary_facets(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&);
+template Eigen::Matrix<int, -1, -1, 0, -1, -1> igl::boundary_facets<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, -1, 0, -1, -1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&);
+template void igl::boundary_facets<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 3, 1, -1, 3> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 3, 1, -1, 3> >&);
+#endif

src/igl/boundary_facets.h

@@ -0,0 +1,52 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2013 Alec Jacobson <alecjacobson@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#ifndef IGL_BOUNDARY_FACETS_H
+#define IGL_BOUNDARY_FACETS_H
+#include "igl_inline.h"
+
+#include <Eigen/Dense>
+
+#include <vector>
+
+namespace igl
+{
+  // BOUNDARY_FACETS Determine boundary faces (edges) of tetrahedra (triangles)
+  // stored in T (analogous to qptoolbox's `outline` and `boundary_faces`).
+  //
+  // Templates:
+  //   IntegerT  integer-value: e.g. int
+  //   IntegerF  integer-value: e.g. int
+  // Input:
+  //  T  tetrahedron (triangle) index list, m by 4 (3), where m is the number of tetrahedra
+  // Output:
+  //  F  list of boundary faces, n by 3 (2), where n is the number of boundary faces
+  //
+  //
+  template <typename IntegerT, typename IntegerF>
+  IGL_INLINE void boundary_facets(
+    const std::vector<std::vector<IntegerT> > & T,
+    std::vector<std::vector<IntegerF> > & F);
+
+  // Templates:
+  //   DerivedT  integer-value: i.e. from MatrixXi
+  //   DerivedF  integer-value: i.e. from MatrixXi
+  template <typename DerivedT, typename DerivedF>
+  IGL_INLINE void boundary_facets(
+    const Eigen::PlainObjectBase<DerivedT>& T,
+    Eigen::PlainObjectBase<DerivedF>& F);
+  // Same as above but returns F
+  template <typename DerivedT, typename Ret>
+  Ret boundary_facets(
+    const Eigen::PlainObjectBase<DerivedT>& T);
+}
+
+#ifndef IGL_STATIC_LIBRARY
+#  include "boundary_facets.cpp"
+#endif
+
+#endif

src/igl/boundary_loop.cpp

@@ -0,0 +1,153 @@
+// This file is part of libigl, a simple c++ geometry processing library.
+//
+// Copyright (C) 2014 Stefan Brugger <stefanbrugger@gmail.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla Public License
+// v. 2.0. If a copy of the MPL was not distributed with this file, You can
+// obtain one at http://mozilla.org/MPL/2.0/.
+#include "boundary_loop.h"
+#include "slice.h"
+#include "triangle_triangle_adjacency.h"
+#include "vertex_triangle_adjacency.h"
+#include "is_border_vertex.h"
+#include <set>
+
+template <typename DerivedF, typename Index>
+IGL_INLINE void igl::boundary_loop(
+    const Eigen::PlainObjectBase<DerivedF> & F,
+    std::vector<std::vector<Index> >& L)
+{
+  using namespace std;
+  using namespace Eigen;
+
+  if(F.rows() == 0)
+    return;
+
+  VectorXd Vdummy(F.maxCoeff()+1,1);
+  DerivedF TT,TTi;
+  vector<std::vector<int> > VF, VFi;
+  triangle_triangle_adjacency(F,TT,TTi);
+  vertex_triangle_adjacency(Vdummy,F,VF,VFi);
+
+  vector<bool> unvisited = is_border_vertex(Vdummy,F);
+  set<int> unseen;
+  for (size_t i = 0; i < unvisited.size(); ++i)
+  {
+    if (unvisited[i])
+      unseen.insert(unseen.end(),i);
+  }
+
+  while (!unseen.empty())
+  {
+    vector<Index> l;
+
+    // Get first vertex of loop
+    int start = *unseen.begin();
+    unseen.erase(unseen.begin());
+    unvisited[start] = false;
+    l.push_back(start);
+
+    bool done = false;
+    while (!done)
+    {
+      // Find next vertex
+      bool newBndEdge = false;
+      int v = l[l.size()-1];
+      int next;
+      for (int i = 0; i < (int)VF[v].size() && !newBndEdge; i++)
+      {
+        int fid = VF[v][i];
+
+        if (TT.row(fid).minCoeff() < 0.) // Face contains boundary edge
+        {
+          int vLoc = -1;
+          if (F(fid,0) == v) vLoc = 0;
+          if (F(fid,1) == v) vLoc = 1;
+          if (F(fid,2) == v) vLoc = 2;
+
+          int vNext = F(fid,(vLoc + 1) % F.cols());
+
+          newBndEdge = false;
+          if (unvisited[vNext] && TT(fid,vLoc) < 0)
+          {
+            next = vNext;
+            newBndEdge = true;
+          }
+        }
+      }
+
+      if (newBndEdge)
+      {
+        l.push_back(next);
+        unseen.erase(next);
+        unvisited[next] = false;
+      }
+      else
+        done = true;
+    }
+    L.push_back(l);
+  }
+}
+
+template <typename DerivedF, typename Index>
+IGL_INLINE void igl::boundary_loop(
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  std::vector<Index>& L)
+{
+  using namespace Eigen;
+  using namespace std;
+
+  if(F.rows() == 0)
+    return;
+
+  vector<vector<int> > Lall;
+  boundary_loop(F,Lall);
+
+  int idxMax = -1;
+  size_t maxLen = 0;
+  for (size_t i = 0; i < Lall.size(); ++i)
+  {
+    if (Lall[i].size() > maxLen)
+    {
+      maxLen = Lall[i].size();
+      idxMax = i;
+    }
+  }
+
+  //Check for meshes without boundary
+  if (idxMax == -1)
+  {
+      L.clear();
+      return;
+  }
+
+  L.resize(Lall[idxMax].size());
+  for (size_t i = 0; i < Lall[idxMax].size(); ++i)
+  {
+    L[i] = Lall[idxMax][i];
+  }
+}
+
+template <typename DerivedF, typename DerivedL>
+IGL_INLINE void igl::boundary_loop(
+  const Eigen::PlainObjectBase<DerivedF>& F,
+  Eigen::PlainObjectBase<DerivedL>& L)
+{
+  using namespace Eigen;
+  using namespace std;
+
+  if(F.rows() == 0)
+    return;
+
+  vector<int> Lvec;
+  boundary_loop(F,Lvec);
+
+  L.resize(Lvec.size());
+  for (size_t i = 0; i < Lvec.size(); ++i)
+    L(i) = Lvec[i];
+}
+
+#ifdef IGL_STATIC_LIBRARY
+// Explicit template instantiation
+template void igl::boundary_loop<Eigen::Matrix<int, -1, -1, 0, -1, -1>, Eigen::Matrix<int, -1, 1, 0, -1, 1> >(Eigen::PlainObjectBase<Eigen::Matrix<int, -1, -1, 0, -1, -1> > const&, Eigen::PlainObjectBase<Eigen::Matrix<int, -1, 1, 0, -1, 1> >&);
+#endif