WIP: own AABBTreeIndirect, builds up the tree 4x quicker than libigl.

This commit is contained in:
Vojtech Bubnik 2020-05-20 16:30:30 +02:00
parent abf279fc44
commit eeb9590d28
3 changed files with 618 additions and 0 deletions

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// AABB tree built upon external data set, referencing the external data by integer indices.
#ifndef slic3r_AABBTreeIndirect_hpp_
#define slic3r_AABBTreeIndirect_hpp_
#include <algorithm>
#include <limits>
#include <vector>
#include "Utils.hpp" // for next_highest_power_of_2()
extern "C"
{
#include <igl/raytri.c>
}
#include <igl/Hit.h>
#include <igl/ray_box_intersect.h>
namespace Slic3r {
namespace AABBTreeIndirect {
// AABB tree for raycasting and closest triangle search.
template<int ANumDimensions, typename ACoordType>
class Tree
{
public:
static constexpr int NumDimensions = ANumDimensions;
using CoordType = ACoordType;
using Vec3crd = Eigen::Matrix<CoordType, NumDimensions, 1, Eigen::DontAlign>;
using BoundingBox = Eigen::AlignedBox<CoordType, NumDimensions>;
// Following could be static constexpr size_t, but that would not link in C++11
enum : size_t {
// Node is not used.
npos = size_t(-1),
// Inner node (not leaf).
inner = size_t(-2)
};
struct Node {
// Index of the external source entity, for which this AABB tree was built, npos for internal nodes.
size_t idx = npos;
// Bounding box around this entity, possibly with epsilons applied.
BoundingBox bbox;
bool is_valid() const { return this->idx != npos; }
bool is_inner() const { return this->idx == inner; }
bool is_leaf() const { return ! this->is_inner(); }
template<typename SourceNode>
void set(const SourceNode &rhs) {
this->idx = rhs.idx();
this->bbox = rhs.bbox();
}
};
void clear() { m_nodes.clear(); }
// SourceNode shall implement
// size_t SourceNode::idx() const
// - index to the outside triangle.
// const Vec3crd& SourceNode::centroid() const
// - centroid of this node, for splitting the triangles into left / right bounding box.
// const BoundingBox& SourceNode::bbox() const
// - bounding box of this node, likely expanded with epsilon to account for numeric rounding during tree traversal.
template<typename SourceNode>
void build(std::vector<SourceNode> &&input)
{
if (input.empty())
clear();
else {
// Allocate enough memory for a full binary tree.
//FIXME fianlize the tree size formula.
m_nodes.assign(next_highest_power_of_2(input.size() * 2 + 1), Node());
build_recursive(input, 0, 0, input.size() - 1);
}
input.clear();
}
const std::vector<Node>& nodes() const { return m_nodes; }
const Node& node(size_t idx) const { return m_nodes[idx]; }
bool empty() const { return m_nodes.empty(); }
template<typename SourceNode>
void build(const std::vector<SourceNode> &input)
{
std::vector<SourceNode> copy(input);
this->build(std::move(copy));
}
private:
// Build a balanced tree by splitting the input sequence by an axis aligned plane at a dimension.
template<typename SourceNode>
void build_recursive(std::vector<SourceNode> &input, size_t node, const size_t left, const size_t right)
{
assert(node < m_nodes.size());
assert(left <= right);
if (left == right) {
// Insert a node into the balanced tree.
m_nodes[node].set(input[left]);
return;
}
// Calculate bounding box of the input.
BoundingBox bbox(input[left].bbox());
for (size_t i = left + 1; i <= right; ++ i)
bbox.extend(input[i].bbox());
int dimension = -1;
bbox.diagonal().maxCoeff(&dimension);
// Partition the input to left / right pieces of the same length to produce a balanced tree.
size_t center = (left + right) / 2;
partition_input(input, size_t(dimension), left, right, center);
// Insert a node into the tree.
m_nodes[node].idx = inner;
m_nodes[node].bbox = bbox;
build_recursive(input, node * 2 + 1, left, center);
build_recursive(input, node * 2 + 2, center + 1, right);
}
// Partition the input m_nodes <left, right> at "k" and "dimension" using the QuickSelect method:
// https://en.wikipedia.org/wiki/Quickselect
// Items left of the k'th item are lower than the k'th item in the "dimension",
// items right of the k'th item are higher than the k'th item in the "dimension",
template<typename SourceNode>
void partition_input(std::vector<SourceNode> &input, const size_t dimension, size_t left, size_t right, const size_t k) const
{
while (left < right) {
size_t center = (left + right) / 2;
CoordType pivot;
{
// Bubble sort the input[left], input[center], input[right], so that a median of the three values
// will end up in input[center].
CoordType left_value = input[left ].centroid()(dimension);
CoordType center_value = input[center].centroid()(dimension);
CoordType right_value = input[right ].centroid()(dimension);
if (left_value > center_value) {
std::swap(input[left], input[center]);
std::swap(left_value, center_value);
}
if (left_value > right_value) {
std::swap(input[left], input[right]);
right_value = left_value;
}
if (center_value > right_value) {
std::swap(input[center], input[right]);
center_value = right_value;
}
pivot = center_value;
}
if (right <= left + 2)
// The <left, right> interval is already sorted.
break;
size_t i = left;
size_t j = right - 1;
std::swap(input[center], input[j]);
// Partition the set based on the pivot.
for (;;) {
// Skip left points that are already at correct positions.
// Search will certainly stop at position (right - 1), which stores the pivot.
while (input[++ i].centroid()(dimension) < pivot) ;
// Skip right points that are already at correct positions.
while (input[-- j].centroid()(dimension) > pivot && i < j) ;
if (i >= j)
break;
std::swap(input[i], input[j]);
}
// Restore pivot to the center of the sequence.
std::swap(input[i], input[right - 1]);
// Which side the kth element is in?
if (k < i)
right = i - 1;
else if (k == i)
// Sequence is partitioned, kth element is at its place.
break;
else
left = i + 1;
}
}
std::vector<Node> m_nodes;
};
template<typename VertexType, typename IndexedFaceType>
inline Tree<3, typename VertexType::Scalar>
build_aabb_tree(const std::vector<VertexType> &vertices, const std::vector<IndexedFaceType> &faces)
{
using TreeType = Tree<3, typename VertexType::Scalar>;
using CoordType = typename TreeType::CoordType;
using Vec3crd = typename TreeType::Vec3crd;
using BoundingBox = typename TreeType::BoundingBox;
static constexpr CoordType eps = CoordType(1e-4);
struct InputType {
size_t idx() const { return m_idx; }
const BoundingBox& bbox() const { return m_bbox; }
const Vec3crd& centroid() const { return m_centroid; }
size_t m_idx;
BoundingBox m_bbox;
Vec3crd m_centroid;
};
std::vector<InputType> input;
input.reserve(faces.size());
Vec3crd veps(eps, eps, eps);
for (size_t i = 0; i < faces.size(); ++ i) {
const IndexedFaceType &face = faces[i];
const VertexType &v1 = vertices[face(0)];
const VertexType &v2 = vertices[face(1)];
const VertexType &v3 = vertices[face(2)];
InputType n;
n.m_idx = i;
n.m_centroid = (1./3.) * (v1 + v2 + v3);
n.m_bbox = BoundingBox(v1, v1);
n.m_bbox.extend(v2);
n.m_bbox.extend(v3);
n.m_bbox.min() -= veps;
n.m_bbox.max() += veps;
input.emplace_back(n);
}
TreeType out;
out.build(std::move(input));
return out;
}
namespace detail {
template<typename AVertexType, typename AIndexedFaceType, typename ATreeType, typename AVectorType>
struct RayIntersector {
using VertexType = AVertexType;
using IndexedFaceType = AIndexedFaceType;
using TreeType = ATreeType;
using VectorType = AVectorType;
const std::vector<VertexType> &vertices;
const std::vector<IndexedFaceType> &faces;
const TreeType &tree;
const VectorType origin;
const VectorType dir;
};
template<typename VertexType, typename IndexedFaceType, typename TreeType, typename VectorType>
struct RayIntersectorHits : RayIntersector<VertexType, IndexedFaceType, TreeType, VectorType> {
std::vector<igl::Hit> hits;
};
template<typename RayIntersectorType, typename Scalar>
static inline bool intersect_ray_recursive_first_hit(
RayIntersectorType &ray_intersector,
size_t node_idx,
Scalar min_t,
igl::Hit &hit)
{
const auto &nodes = ray_intersector.tree.nodes();
if (node_idx >= nodes.size())
return false;
const auto &node = nodes[node_idx];
if (! node.is_valid())
return false;
{
Scalar t_start, t_end;
if (! igl::ray_box_intersect(ray_intersector.origin, ray_intersector.dir, node.bbox.template cast<Scalar>(), Scalar(0), min_t, t_start, t_end))
return false;
}
if (node.is_leaf()) {
using Vector = Eigen::Matrix<Scalar, 3, 1>;
Vector origin_d = ray_intersector.origin.template cast<double>();
Vector dir_d = ray_intersector.dir .template cast<double>();
auto face = ray_intersector.faces[node.idx];
Vector v0 = ray_intersector.vertices[face(0)].template cast<double>();
Vector v1 = ray_intersector.vertices[face(1)].template cast<double>();
Vector v2 = ray_intersector.vertices[face(2)].template cast<double>();
// shoot ray, record hit
double t, u, v;
if (intersect_triangle1(origin_d.data(), dir_d.data(), v0.data(), v1.data(), v2.data(), &t, &u, &v) && t > 0.) {
hit = igl::Hit { int(node.idx), -1, float(u), float(v), float(t) };
return true;
}
return false;
}
// Left / right child node index.
size_t left = node_idx * 2 + 1;
size_t right = left + 1;
igl::Hit left_hit;
igl::Hit right_hit;
bool left_ret = intersect_ray_recursive_first_hit(ray_intersector, left, min_t, left_hit);
if (left_ret && left_hit.t < min_t) {
min_t = left_hit.t;
hit = left_hit;
} else
left_ret = false;
bool right_ret = intersect_ray_recursive_first_hit(ray_intersector, right, min_t, right_hit);
if (right_ret && right_hit.t < min_t)
hit = right_hit;
else
right_ret = false;
return left_ret || right_ret;
}
template<typename RayIntersectorType>
static inline void intersect_ray_recursive_all_hits(RayIntersectorType &ray_intersector, size_t node_idx)
{
using Vector = typename RayIntersectorType::VectorType;
using Scalar = typename Vector::Scalar;
const auto &node = ray_intersector.tree.node(node_idx);
if (! node.is_valid())
return;
{
Scalar t_start, t_end;
if (! igl::ray_box_intersect(ray_intersector.origin, ray_intersector.dir, node.bbox.template cast<Scalar>(),
Scalar(0), std::numeric_limits<Scalar>::infinity(), t_start, t_end))
return;
}
if (node.is_leaf()) {
using Vector = Eigen::Matrix<Scalar, 3, 1>;
Vector origin_d = ray_intersector.origin.template cast<double>();
Vector dir_d = ray_intersector.dir .template cast<double>();
auto face = ray_intersector.faces[node.idx];
Vector v0 = ray_intersector.vertices[face(0)].template cast<double>();
Vector v1 = ray_intersector.vertices[face(1)].template cast<double>();
Vector v2 = ray_intersector.vertices[face(2)].template cast<double>();
// shoot ray, record hit
double t, u, v;
if (intersect_triangle1(origin_d.data(), dir_d.data(), v0.data(), v1.data(), v2.data(), &t, &u, &v) && t > 0.)
ray_intersector.hits.emplace_back(igl::Hit{ int(node.idx), -1, float(u), float(v), float(t) });
return;
}
// Left / right child node index.
size_t left = node_idx * 2 + 1;
size_t right = left + 1;
intersect_ray_recursive_all_hits(ray_intersector, left);
intersect_ray_recursive_all_hits(ray_intersector, right);
}
template<typename AVertexType, typename AIndexedFaceType, typename ATreeType, typename AVectorType>
struct IndexedTriangleSetDistancer {
using VertexType = AVertexType;
using IndexedFaceType = AIndexedFaceType;
using TreeType = ATreeType;
using VectorType = AVectorType;
const std::vector<VertexType> &vertices;
const std::vector<IndexedFaceType> &faces;
const TreeType &tree;
const VectorType origin;
};
// Real-time collision detection, Ericson, Chapter 5
template<typename Vector>
static inline Vector closest_point_to_triangle(const Vector &p, const Vector &a, const Vector &b, const Vector &c)
{
using Scalar = typename Vector::Scalar;
// Check if P in vertex region outside A
Vector ab = b - a;
Vector ac = c - a;
Vector ap = p - a;
Scalar d1 = ab.dot(ap);
Scalar d2 = ac.dot(ap);
if (d1 <= Scalar(0) && d2 <= Scalar(0))
return a;
// Check if P in vertex region outside B
Vector bp = p - b;
Scalar d3 = ab.dot(bp);
Scalar d4 = ac.dot(bp);
if (d3 >= Scalar(0) && d4 <= d3)
return b;
// Check if P in edge region of AB, if so return projection of P onto AB
Scalar vc = d1*d4 - d3*d2;
if (a != b && vc <= Scalar(0) && d1 >= Scalar(0) && d3 <= Scalar(0)) {
Scalar v = d1 / (d1 - d3);
return a + v * ab;
}
// Check if P in vertex region outside C
Vector cp = p - c;
Scalar d5 = ab.dot(cp);
Scalar d6 = ac.dot(cp);
if (d6 >= Scalar(0) && d5 <= d6)
return c;
// Check if P in edge region of AC, if so return projection of P onto AC
Scalar vb = d5*d2 - d1*d6;
if (vb <= Scalar(0) && d2 >= Scalar(0) && d6 <= Scalar(0)) {
Scalar w = d2 / (d2 - d6);
return a + w * ac;
}
// Check if P in edge region of BC, if so return projection of P onto BC
Scalar va = d3*d6 - d5*d4;
if (va <= Scalar(0) && (d4 - d3) >= Scalar(0) && (d5 - d6) >= Scalar(0)) {
Scalar w = (d4 - d3) / ((d4 - d3) + (d5 - d6));
return b + w * (c - b);
}
// P inside face region. Compute Q through its barycentric coordinates (u,v,w)
Scalar denom = Scalar(1.0) / (va + vb + vc);
Scalar v = vb * denom;
Scalar w = vc * denom;
return a + ab * v + ac * w; // = u*a + v*b + w*c, u = va * denom = 1.0-v-w
};
template<typename IndexedTriangleSetDistancerType, typename Scalar>
static inline Scalar squared_distance_recursive(
IndexedTriangleSetDistancerType &distancer,
size_t node_idx,
Scalar low_sqr_d,
Scalar up_sqr_d,
size_t &i,
Eigen::PlainObjectBase<typename IndexedTriangleSetDistancerType::VectorType> &c)
{
using Vector = typename IndexedTriangleSetDistancerType::VectorType;
if (low_sqr_d > up_sqr_d)
return low_sqr_d;
auto set_min = [&i, &c, &up_sqr_d](const Scalar sqr_d_candidate, const size_t i_candidate, const Vector &c_candidate) {
if (sqr_d_candidate < up_sqr_d) {
i = i_candidate;
c = c_candidate;
up_sqr_d = sqr_d_candidate;
}
};
const auto &node = distancer.tree.node(node_idx);
assert(node.is_valid());
if (node.is_leaf())
{
const auto &triangle = distancer.faces[node.idx];
Vector c_candidate = closest_point_to_triangle<Vector>(
distancer.origin,
distancer.vertices[triangle(0)].template cast<Scalar>(),
distancer.vertices[triangle(1)].template cast<Scalar>(),
distancer.vertices[triangle(2)].template cast<Scalar>());
set_min((c_candidate - distancer.origin).squaredNorm(), node.idx, c_candidate);
}
else
{
size_t left_node_idx = node_idx * 2 + 1;
size_t right_node_idx = left_node_idx + 1;
const auto &node_left = distancer.tree.node(left_node_idx);
const auto &node_right = distancer.tree.node(right_node_idx);
assert(node_left.is_valid());
assert(node_right.is_valid());
bool looked_left = false;
bool looked_right = false;
const auto &look_left = [&]()
{
size_t i_left;
Vector c_left = c;
Scalar sqr_d_left = squared_distance_recursive(distancer, left_node_idx, low_sqr_d, up_sqr_d, i_left, c_left);
set_min(sqr_d_left, i_left, c_left);
looked_left = true;
};
const auto &look_right = [&]()
{
size_t i_right;
Vector c_right = c;
Scalar sqr_d_right = squared_distance_recursive(distancer, right_node_idx, low_sqr_d, up_sqr_d, i_right, c_right);
set_min(sqr_d_right, i_right, c_right);
looked_right = true;
};
// must look left or right if in box
using BBoxScalar = typename IndexedTriangleSetDistancerType::TreeType::BoundingBox::Scalar;
if (node_left.bbox.contains(distancer.origin.template cast<BBoxScalar>()))
look_left();
if (node_right.bbox.contains(distancer.origin.template cast<BBoxScalar>()))
look_right();
// if haven't looked left and could be less than current min, then look
Scalar left_up_sqr_d = node_left.bbox.squaredExteriorDistance(distancer.origin);
Scalar right_up_sqr_d = node_right.bbox.squaredExteriorDistance(distancer.origin);
if (left_up_sqr_d < right_up_sqr_d) {
if (! looked_left && left_up_sqr_d < up_sqr_d)
look_left();
if (! looked_right && right_up_sqr_d < up_sqr_d)
look_right();
} else {
if (! looked_right && right_up_sqr_d < up_sqr_d)
look_right();
if (! looked_left && left_up_sqr_d < up_sqr_d)
look_left();
}
}
return up_sqr_d;
}
} // namespace detail
template<typename VertexType, typename IndexedFaceType, typename TreeType, typename VectorType>
inline bool intersect_ray_first_hit(
const std::vector<VertexType> &vertices,
const std::vector<IndexedFaceType> &faces,
const TreeType &tree,
const VectorType &origin,
const VectorType &dir,
igl::Hit &hit)
{
using Scalar = typename VectorType::Scalar;
auto ray_intersector = detail::RayIntersector<VertexType, IndexedFaceType, TreeType, VectorType> {
vertices, faces, tree,
origin, dir
};
return ! tree.empty() && detail::intersect_ray_recursive_first_hit(
ray_intersector, size_t(0), std::numeric_limits<Scalar>::infinity(), hit);
}
template<typename VertexType, typename IndexedFaceType, typename TreeType, typename VectorType>
inline bool intersect_ray_all_hits(
const std::vector<VertexType> &vertices,
const std::vector<IndexedFaceType> &faces,
const TreeType &tree,
const VectorType &origin,
const VectorType &dir,
std::vector<igl::Hit> &hits)
{
auto ray_intersector = detail::RayIntersectorHits<VertexType, IndexedFaceType, TreeType, VectorType> {
vertices, faces, tree,
origin, dir
};
if (! tree.empty()) {
ray_intersector.hits.reserve(8);
detail::intersect_ray_recursive_all_hits(ray_intersector, 0);
std::swap(hits, ray_intersector.hits);
std::sort(hits.begin(), hits.end(), [](const auto &l, const auto &r) { return l.t < r.t; });
}
return ! hits.empty();
}
// Closest point to triangle test will be performed with the accuracy of VectorType::Scalar.
template<typename VertexType, typename IndexedFaceType, typename TreeType, typename VectorType>
inline typename VectorType::Scalar squared_distance(
const std::vector<VertexType> &vertices,
const std::vector<IndexedFaceType> &faces,
const TreeType &tree,
const VectorType &point,
size_t &hit_idx_out,
Eigen::PlainObjectBase<VectorType> &hit_point_out)
{
using Scalar = typename VectorType::Scalar;
auto distancer = detail::IndexedTriangleSetDistancer<VertexType, IndexedFaceType, TreeType, VectorType>
{ vertices, faces, tree, point };
return detail::squared_distance_recursive(distancer, size_t(0), Scalar(0), std::numeric_limits<Scalar>::infinity(), hit_idx_out, hit_point_out);
}
} // namespace AABBTreeIndirect
} // namespace Slic3r
#endif /* slic3r_AABBTreeIndirect_hpp_ */

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@ -3,6 +3,7 @@ get_filename_component(_TEST_NAME ${CMAKE_CURRENT_LIST_DIR} NAME)
add_executable(${_TEST_NAME}_tests
${_TEST_NAME}_tests.cpp
test_3mf.cpp
test_aabbindirect.cpp
test_clipper_offset.cpp
test_clipper_utils.cpp
test_config.cpp

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#include <catch2/catch.hpp>
#include <test_utils.hpp>
#include <libslic3r/TriangleMesh.hpp>
#include <libslic3r/AABBTreeIndirect.hpp>
using namespace Slic3r;
TEST_CASE("Building a tree over a box, ray caster and closest query", "[AABBIndirect]")
{
TriangleMesh tmesh = make_cube(1., 1., 1.);
tmesh.repair();
auto tree = AABBTreeIndirect::build_aabb_tree(tmesh.its.vertices, tmesh.its.indices);
REQUIRE(! tree.empty());
igl::Hit hit;
bool intersected = AABBTreeIndirect::intersect_ray_first_hit(
tmesh.its.vertices, tmesh.its.indices,
tree,
Vec3d(0.5, 0.5, -5.),
Vec3d(0., 0., 1.),
hit);
REQUIRE(intersected);
REQUIRE(hit.t == Approx(5.));
std::vector<igl::Hit> hits;
bool intersected2 = AABBTreeIndirect::intersect_ray_all_hits(
tmesh.its.vertices, tmesh.its.indices,
tree,
Vec3d(0.3, 0.5, -5.),
Vec3d(0., 0., 1.),
hits);
REQUIRE(intersected2);
REQUIRE(hits.size() == 2);
REQUIRE(hits.front().t == Approx(5.));
REQUIRE(hits.back().t == Approx(6.));
size_t hit_idx;
Vec3d closest_point;
double squared_distance = AABBTreeIndirect::squared_distance(
tmesh.its.vertices, tmesh.its.indices,
tree,
Vec3d(0.3, 0.5, -5.),
hit_idx, closest_point);
REQUIRE(squared_distance == Approx(5. * 5.));
REQUIRE(closest_point.x() == Approx(0.3));
REQUIRE(closest_point.y() == Approx(0.5));
REQUIRE(closest_point.z() == Approx(0.));
squared_distance = AABBTreeIndirect::squared_distance(
tmesh.its.vertices, tmesh.its.indices,
tree,
Vec3d(0.3, 0.5, 5.),
hit_idx, closest_point);
REQUIRE(squared_distance == Approx(4. * 4.));
REQUIRE(closest_point.x() == Approx(0.3));
REQUIRE(closest_point.y() == Approx(0.5));
REQUIRE(closest_point.z() == Approx(1.));
}