PrusaSlicer-NonPlainar/src/libslic3r/TriangleMeshSlicer.cpp

#include "ClipperUtils.hpp"
#include "Geometry.hpp"
#include "Tesselate.hpp"
#include "TriangleMesh.hpp"
#include "TriangleMeshSlicer.hpp"

#include <algorithm>
#include <cmath>
#include <deque>
#include <queue>
#include <utility>

#include <boost/log/trivial.hpp>

#include <tbb/parallel_for.h>

#if 0
    #define DEBUG
    #define _DEBUG
    #undef NDEBUG
    #define SLIC3R_DEBUG
// #define SLIC3R_TRIANGLEMESH_DEBUG
#endif

#include <assert.h>
#include <boost/thread/mutex.hpp>
#include <boost/thread/lock_guard.hpp>

#if defined(SLIC3R_DEBUG) || defined(SLIC3R_DEBUG_SLICE_PROCESSING)
#include "SVG.hpp"
#endif

namespace Slic3r {

class IntersectionReference
{
public:
    IntersectionReference() = default;
    IntersectionReference(int point_id, int edge_id) : point_id(point_id), edge_id(edge_id) {}
    // Where is this intersection point located? On mesh vertex or mesh edge?
    // Only one of the following will be set, the other will remain set to -1.
    // Index of the mesh vertex.
    int point_id { -1 };
    // Index of the mesh edge.
    int edge_id { -1 };
};

class IntersectionPoint : public Point, public IntersectionReference
{
public:
    IntersectionPoint() = default;
    IntersectionPoint(int point_id, int edge_id, const Point &pt) : IntersectionReference(point_id, edge_id), Point(pt) {}
    IntersectionPoint(const IntersectionReference &ir, const Point &pt) : IntersectionReference(ir), Point(pt) {}
    // Inherits coord_t x, y
};

class IntersectionLine : public Line
{
public:
    IntersectionLine() = default;

    bool skip() const { return (this->flags & SKIP) != 0; }
    void set_skip() { this->flags |= SKIP; }

    bool is_seed_candidate() const { return (this->flags & NO_SEED) == 0 && ! this->skip(); }
    void set_no_seed(bool set) { if (set) this->flags |= NO_SEED; else this->flags &= ~NO_SEED; }
    
    // Inherits Point a, b
    // For each line end point, either {a,b}_id or {a,b}edge_a_id is set, the other is left to -1.
    // Vertex indices of the line end points.
    int             a_id { -1 };
    int             b_id { -1 };
    // Source mesh edges of the line end points.
    int             edge_a_id { -1 };
    int             edge_b_id { -1 };

    enum class FacetEdgeType { 
        // A general case, the cutting plane intersect a face at two different edges.
        General,
        // Two vertices are aligned with the cutting plane, the third vertex is below the cutting plane.
        Top,
        // Two vertices are aligned with the cutting plane, the third vertex is above the cutting plane.
        Bottom,
        // All three vertices of a face are aligned with the cutting plane.
        Horizontal
    };

    // feGeneral, feTop, feBottom, feHorizontal
    FacetEdgeType   edge_type { FacetEdgeType::General };
    // Used to skip duplicate edges.
    enum {
        // Triangle edge added, because it has no neighbor.
        EDGE0_NO_NEIGHBOR   = 0x001,
        EDGE1_NO_NEIGHBOR   = 0x002,
        EDGE2_NO_NEIGHBOR   = 0x004,
        // Triangle edge added, because it makes a fold with another horizontal edge.
        EDGE0_FOLD          = 0x010,
        EDGE1_FOLD          = 0x020,
        EDGE2_FOLD          = 0x040,
        // The edge cannot be a seed of a greedy loop extraction (folds are not safe to become seeds).
        NO_SEED             = 0x100,
        SKIP                = 0x200,
    };
    uint32_t        flags { 0 };
};

using IntersectionLines = std::vector<IntersectionLine>;

enum class FacetSliceType {
    NoSlice = 0,
    Slicing = 1,
    Cutting = 2
};

// Return true, if the facet has been sliced and line_out has been filled.
static FacetSliceType slice_facet(
    // Z height of the slice in XY plane. Scaled or unscaled (same as vertices[].z()).
    float                                slice_z,
    // 3 vertices of the triangle, XY scaled. Z scaled or unscaled (same as slice_z).
    const stl_vertex                    *vertices,
    const stl_triangle_vertex_indices   &indices,
    const Vec3i                         &edge_neighbor,
    const int                            idx_vertex_lowest,
    const bool                           horizontal,
    IntersectionLine                    &line_out)
{
    IntersectionPoint points[3];
    size_t            num_points = 0;
    auto              point_on_layer = size_t(-1);

    // Reorder vertices so that the first one is the one with lowest Z.
    // This is needed to get all intersection lines in a consistent order
    // (external on the right of the line)
    for (int j = 0; j < 3; ++ j) {  // loop through facet edges
        int               edge_id;
        const stl_vertex *a, *b;
        int               a_id, b_id;
        {
            int   k = (idx_vertex_lowest + j) % 3;
            int   l = (k + 1) % 3;
            edge_id = edge_neighbor(k);
            a_id    = indices[k];
            a       = vertices + k;
            b_id    = indices[l];
            b       = vertices + l;
        }

        // Is edge or face aligned with the cutting plane?
        if (a->z() == slice_z && b->z() == slice_z) {
            // Edge is horizontal and belongs to the current layer.
            // The following rotation of the three vertices may not be efficient, but this branch happens rarely.
            const stl_vertex &v0 = vertices[0];
            const stl_vertex &v1 = vertices[1];
            const stl_vertex &v2 = vertices[2];
            // We may ignore this edge for slicing purposes, but we may still use it for object cutting.
            FacetSliceType    result = FacetSliceType::Slicing;
            if (horizontal) {
                // All three vertices are aligned with slice_z.
                line_out.edge_type = IntersectionLine::FacetEdgeType::Horizontal;
                result = FacetSliceType::Cutting;
                double normal = (v1.x() - v0.x()) * (v2.y() - v1.y()) - (v1.y() - v0.y()) * (v2.x() - v1.x());
                if (normal < 0) {
                    // If normal points downwards this is a bottom horizontal facet so we reverse its point order.
                    std::swap(a, b);
                    std::swap(a_id, b_id);
                }
            } else {
                // Two vertices are aligned with the cutting plane, the third vertex is below or above the cutting plane.
                // Is the third vertex below the cutting plane?
                bool third_below = v0.z() < slice_z || v1.z() < slice_z || v2.z() < slice_z;
                // Two vertices on the cutting plane, the third vertex is below the plane. Consider the edge to be part of the slice
                // only if it is the upper edge.
                // (the bottom most edge resp. vertex of a triangle is not owned by the triangle, but the top most edge resp. vertex is part of the triangle
                // in respect to the cutting plane).
                result = third_below ? FacetSliceType::Slicing : FacetSliceType::Cutting;
                if (third_below) {
                    line_out.edge_type = IntersectionLine::FacetEdgeType::Top;
                    std::swap(a, b);
                    std::swap(a_id, b_id);
                } else
                    line_out.edge_type = IntersectionLine::FacetEdgeType::Bottom;
            }
            line_out.a.x()  = a->x();
            line_out.a.y()  = a->y();
            line_out.b.x()  = b->x();
            line_out.b.y()  = b->y();
            line_out.a_id   = a_id;
            line_out.b_id   = b_id;
            assert(line_out.a != line_out.b);
            return result;
        }

        if (a->z() == slice_z) {
            // Only point a alings with the cutting plane.
            if (point_on_layer == size_t(-1) || points[point_on_layer].point_id != a_id) {
                point_on_layer = num_points;
                IntersectionPoint &point = points[num_points ++];
                point.x()      = a->x();
                point.y()      = a->y();
                point.point_id = a_id;
            }
        } else if (b->z() == slice_z) {
            // Only point b alings with the cutting plane.
            if (point_on_layer == size_t(-1) || points[point_on_layer].point_id != b_id) {
                point_on_layer = num_points;
                IntersectionPoint &point = points[num_points ++];
                point.x()      = b->x();
                point.y()      = b->y();
                point.point_id = b_id;
            }
        } else if ((a->z() < slice_z && b->z() > slice_z) || (b->z() < slice_z && a->z() > slice_z)) {
            // A general case. The face edge intersects the cutting plane. Calculate the intersection point.
            assert(a_id != b_id);
            // Sort the edge to give a consistent answer.
            if (a_id > b_id) {
                std::swap(a_id, b_id);
                std::swap(a, b);
            }
            IntersectionPoint &point = points[num_points];
            double t = (double(slice_z) - double(b->z())) / (double(a->z()) - double(b->z()));
            if (t <= 0.) {
                if (point_on_layer == size_t(-1) || points[point_on_layer].point_id != a_id) {
                    point.x() = a->x();
                    point.y() = a->y();
                    point_on_layer = num_points ++;
                    point.point_id = a_id;
                }
            } else if (t >= 1.) {
                if (point_on_layer == size_t(-1) || points[point_on_layer].point_id != b_id) {
                    point.x() = b->x();
                    point.y() = b->y();
                    point_on_layer = num_points ++;
                    point.point_id = b_id;
                }
            } else {
                point.x() = coord_t(floor(double(b->x()) + (double(a->x()) - double(b->x())) * t + 0.5));
                point.y() = coord_t(floor(double(b->y()) + (double(a->y()) - double(b->y())) * t + 0.5));
                point.edge_id = edge_id;
                ++ num_points;
            }
        }
    }

    // Facets must intersect each plane 0 or 2 times, or it may touch the plane at a single vertex only.
    assert(num_points < 3);
    if (num_points == 2) {
        line_out.edge_type  = IntersectionLine::FacetEdgeType::General;
        line_out.a          = static_cast<const Point&>(points[1]);
        line_out.b          = static_cast<const Point&>(points[0]);
        line_out.a_id       = points[1].point_id;
        line_out.b_id       = points[0].point_id;
        line_out.edge_a_id  = points[1].edge_id;
        line_out.edge_b_id  = points[0].edge_id;
        // Not a zero lenght edge.
        //FIXME slice_facet() may create zero length edges due to rounding of doubles into coord_t.
        //assert(line_out.a != line_out.b);
        // The plane cuts at least one edge in a general position.
        assert(line_out.a_id == -1 || line_out.b_id == -1);
        assert(line_out.edge_a_id != -1 || line_out.edge_b_id != -1);
        // General slicing position, use the segment for both slicing and object cutting.
#if 0
        if (line_out.a_id != -1 && line_out.b_id != -1) {
            // Solving a degenerate case, where both the intersections snapped to an edge.
            // Correctly classify the face as below or above based on the position of the 3rd point.
            int i = indices[0];
            if (i == line_out.a_id || i == line_out.b_id)
                i = indices[1];
            if (i == line_out.a_id || i == line_out.b_id)
                i = indices[2];
            assert(i != line_out.a_id && i != line_out.b_id);
            line_out.edge_type = ((m_use_quaternion ?
                                    (m_quaternion * this->v_scaled_shared[i]).z()
                                    : this->v_scaled_shared[i].z()) < slice_z) ? IntersectionLine::FacetEdgeType::Top : IntersectionLine::FacetEdgeType::Bottom;
        }
#endif
        return FacetSliceType::Slicing;
    }
    return FacetSliceType::NoSlice;
}

template<typename TransformVertex>
void slice_facet_at_zs(
    // Scaled or unscaled vertices. transform_vertex_fn may scale zs.
    const std::vector<Vec3f>                         &mesh_vertices,
    const TransformVertex                            &transform_vertex_fn,
    const stl_triangle_vertex_indices                &indices,
    const Vec3i                                      &facet_neighbors,
    // Scaled or unscaled zs. If vertices have their zs scaled or transform_vertex_fn scales them, then zs have to be scaled as well.
    const std::vector<float>                         &zs,
    std::vector<IntersectionLines>                   &lines,
    boost::mutex                                     &lines_mutex)
{
    stl_vertex vertices[3] { transform_vertex_fn(mesh_vertices[indices(0)]), transform_vertex_fn(mesh_vertices[indices(1)]), transform_vertex_fn(mesh_vertices[indices(2)]) };

    // find facet extents
    const float min_z = fminf(vertices[0].z(), fminf(vertices[1].z(), vertices[2].z()));
    const float max_z = fmaxf(vertices[0].z(), fmaxf(vertices[1].z(), vertices[2].z()));
    
    // find layer extents
    auto min_layer = std::lower_bound(zs.begin(), zs.end(), min_z); // first layer whose slice_z is >= min_z
    auto max_layer = std::upper_bound(min_layer, zs.end(), max_z); // first layer whose slice_z is > max_z
    
    for (auto it = min_layer; it != max_layer; ++ it) {
        IntersectionLine il;
        int idx_vertex_lowest = (vertices[1].z() == min_z) ? 1 : ((vertices[2].z() == min_z) ? 2 : 0);
        if (slice_facet(*it, vertices, indices, facet_neighbors, idx_vertex_lowest, min_z == max_z, il) == FacetSliceType::Slicing &&
            il.edge_type != IntersectionLine::FacetEdgeType::Horizontal) {
            // Ignore horizontal triangles. Any valid horizontal triangle must have a vertical triangle connected, otherwise the part has zero volume.
            boost::lock_guard<boost::mutex> l(lines_mutex);
            lines[it - zs.begin()].emplace_back(il);
        }
    }
}

template<typename TransformVertex, typename ThrowOnCancel>
inline std::vector<IntersectionLines> slice_make_lines(
    const std::vector<stl_vertex>                   &vertices,
    const TransformVertex                           &transform_vertex_fn,
    const std::vector<stl_triangle_vertex_indices>  &indices,
    const std::vector<Vec3i>                        &face_neighbors,
    const std::vector<float>                        &zs,
    const ThrowOnCancel                              throw_on_cancel_fn)
{
    std::vector<IntersectionLines>  lines(zs.size(), IntersectionLines());
    boost::mutex                    lines_mutex;
    tbb::parallel_for(
        tbb::blocked_range<int>(0, int(indices.size())),
        [&vertices, &transform_vertex_fn, &indices, &face_neighbors, &zs, &lines, &lines_mutex, throw_on_cancel_fn](const tbb::blocked_range<int> &range) {
            for (int face_idx = range.begin(); face_idx < range.end(); ++ face_idx) {
                if ((face_idx & 0x0ffff) == 0)
                    throw_on_cancel_fn();
                slice_facet_at_zs(vertices, transform_vertex_fn, indices[face_idx], face_neighbors[face_idx], zs, lines, lines_mutex);
            }
        }
    );
    return lines;
}

#if 0
//FIXME Should this go away? For valid meshes the function slice_facet() returns Slicing
// and sets edges of vertical triangles to produce only a single edge per pair of neighbor faces.
// So the following code makes only sense now to handle degenerate meshes with more than two faces
// sharing a single edge.
static inline void remove_tangent_edges(std::vector<IntersectionLine> &lines)
{
    std::vector<IntersectionLine*> by_vertex_pair;
    by_vertex_pair.reserve(lines.size());
    for (IntersectionLine& line : lines)
        if (line.edge_type != IntersectionLine::FacetEdgeType::General && line.a_id != -1)
            // This is a face edge. Check whether there is its neighbor stored in lines.
            by_vertex_pair.emplace_back(&line);
    auto edges_lower_sorted = [](const IntersectionLine *l1, const IntersectionLine *l2) {
        // Sort vertices of l1, l2 lexicographically
        int l1a = l1->a_id;
        int l1b = l1->b_id;
        int l2a = l2->a_id;
        int l2b = l2->b_id;
        if (l1a > l1b)
            std::swap(l1a, l1b);
        if (l2a > l2b)
            std::swap(l2a, l2b);
        // Lexicographical "lower" operator on lexicographically sorted vertices should bring equal edges together when sored.
        return l1a < l2a || (l1a == l2a && l1b < l2b);
    };
    std::sort(by_vertex_pair.begin(), by_vertex_pair.end(), edges_lower_sorted);
    for (auto line = by_vertex_pair.begin(); line != by_vertex_pair.end(); ++ line) {
        IntersectionLine &l1 = **line;
        if (! l1.skip()) {
            // Iterate as long as line and line2 edges share the same end points.
            for (auto line2 = line + 1; line2 != by_vertex_pair.end() && ! edges_lower_sorted(*line, *line2); ++ line2) {
                // Lines must share the end points.
                assert(! edges_lower_sorted(*line, *line2));
                assert(! edges_lower_sorted(*line2, *line));
                IntersectionLine &l2 = **line2;
                if (l2.skip())
                    continue;
                if (l1.a_id == l2.a_id) {
                    assert(l1.b_id == l2.b_id);
                    l2.set_skip();
                    // If they are both oriented upwards or downwards (like a 'V'),
                    // then we can remove both edges from this layer since it won't 
                    // affect the sliced shape.
                    // If one of them is oriented upwards and the other is oriented
                    // downwards, let's only keep one of them (it doesn't matter which
                    // one since all 'top' lines were reversed at slicing).
                    if (l1.edge_type == l2.edge_type) {
                        l1.set_skip();
                        break;
                    }
                } else {
                    assert(l1.a_id == l2.b_id && l1.b_id == l2.a_id);
                    // If this edge joins two horizontal facets, remove both of them.
                    if (l1.edge_type == IntersectionLine::FacetEdgeType::Horizontal && l2.edge_type == IntersectionLine::FacetEdgeType::Horizontal) {
                        l1.set_skip();
                        l2.set_skip();
                        break;
                    }
                }
            }
        }
    }
}
#endif

struct OpenPolyline {
    OpenPolyline() = default;
    OpenPolyline(const IntersectionReference &start, const IntersectionReference &end, Points &&points) : 
        start(start), end(end), points(std::move(points)), consumed(false) { this->length = Slic3r::length(this->points); }
    void reverse() {
        std::swap(start, end);
        std::reverse(points.begin(), points.end());
    }
    IntersectionReference   start;
    IntersectionReference   end;
    Points                  points;
    double                  length;
    bool                    consumed;
};

// called by make_loops() to connect sliced triangles into closed loops and open polylines by the triangle connectivity.
// Only connects segments crossing triangles of the same orientation.
static void chain_lines_by_triangle_connectivity(IntersectionLines &lines, Polygons &loops, std::vector<OpenPolyline> &open_polylines)
{
    // Build a map of lines by edge_a_id and a_id.
    std::vector<IntersectionLine*> by_edge_a_id;
    std::vector<IntersectionLine*> by_a_id;
    by_edge_a_id.reserve(lines.size());
    by_a_id.reserve(lines.size());
    for (IntersectionLine &line : lines) {
        if (! line.skip()) {
            if (line.edge_a_id != -1)
                by_edge_a_id.emplace_back(&line);
            if (line.a_id != -1)
                by_a_id.emplace_back(&line);
        }
    }
    auto by_edge_lower = [](const IntersectionLine* il1, const IntersectionLine *il2) { return il1->edge_a_id < il2->edge_a_id; };
    auto by_vertex_lower = [](const IntersectionLine* il1, const IntersectionLine *il2) { return il1->a_id < il2->a_id; };
    std::sort(by_edge_a_id.begin(), by_edge_a_id.end(), by_edge_lower);
    std::sort(by_a_id.begin(), by_a_id.end(), by_vertex_lower);
    // Chain the segments with a greedy algorithm, collect the loops and unclosed polylines.
    IntersectionLines::iterator it_line_seed = lines.begin();
    for (;;) {
        // take first spare line and start a new loop
        IntersectionLine *first_line = nullptr;
        for (; it_line_seed != lines.end(); ++ it_line_seed)
            if (it_line_seed->is_seed_candidate()) {
            //if (! it_line_seed->skip()) {
                first_line = &(*it_line_seed ++);
                break;
            }
        if (first_line == nullptr)
            break;
        first_line->set_skip();
        Points loop_pts;
        loop_pts.emplace_back(first_line->a);
        IntersectionLine *last_line = first_line;
        
        /*
        printf("first_line edge_a_id = %d, edge_b_id = %d, a_id = %d, b_id = %d, a = %d,%d, b = %d,%d\n", 
            first_line->edge_a_id, first_line->edge_b_id, first_line->a_id, first_line->b_id,
            first_line->a.x, first_line->a.y, first_line->b.x, first_line->b.y);
        */
        
        IntersectionLine key;
        for (;;) {
            // find a line starting where last one finishes
            IntersectionLine* next_line = nullptr;
            if (last_line->edge_b_id != -1) {
                key.edge_a_id = last_line->edge_b_id;
                auto it_begin = std::lower_bound(by_edge_a_id.begin(), by_edge_a_id.end(), &key, by_edge_lower);
                if (it_begin != by_edge_a_id.end()) {
                    auto it_end = std::upper_bound(it_begin, by_edge_a_id.end(), &key, by_edge_lower);
                    for (auto it_line = it_begin; it_line != it_end; ++ it_line)
                        if (! (*it_line)->skip()) {
                            next_line = *it_line;
                            break;
                        }
                }
            }
            if (next_line == nullptr && last_line->b_id != -1) {
                key.a_id = last_line->b_id;
                auto it_begin = std::lower_bound(by_a_id.begin(), by_a_id.end(), &key, by_vertex_lower);
                if (it_begin != by_a_id.end()) {
                    auto it_end = std::upper_bound(it_begin, by_a_id.end(), &key, by_vertex_lower);
                    for (auto it_line = it_begin; it_line != it_end; ++ it_line)
                        if (! (*it_line)->skip()) {
                            next_line = *it_line;
                            break;
                        }
                }
            }
            if (next_line == nullptr) {
                // Check whether we closed this loop.
                if ((first_line->edge_a_id != -1 && first_line->edge_a_id == last_line->edge_b_id) || 
                    (first_line->a_id      != -1 && first_line->a_id      == last_line->b_id)) {
                    // The current loop is complete. Add it to the output.
                    loops.emplace_back(std::move(loop_pts));
                    #ifdef SLIC3R_TRIANGLEMESH_DEBUG
                    printf("  Discovered %s polygon of %d points\n", (p.is_counter_clockwise() ? "ccw" : "cw"), (int)p.points.size());
                    #endif
                } else {
                    // This is an open polyline. Add it to the list of open polylines. These open polylines will processed later.
                    loop_pts.emplace_back(last_line->b);
                    open_polylines.emplace_back(OpenPolyline(
                        IntersectionReference(first_line->a_id, first_line->edge_a_id), 
                        IntersectionReference(last_line->b_id, last_line->edge_b_id), std::move(loop_pts)));
                }
                break;
            }
            /*
            printf("next_line edge_a_id = %d, edge_b_id = %d, a_id = %d, b_id = %d, a = %d,%d, b = %d,%d\n", 
                next_line->edge_a_id, next_line->edge_b_id, next_line->a_id, next_line->b_id,
                next_line->a.x, next_line->a.y, next_line->b.x, next_line->b.y);
            */
            loop_pts.emplace_back(next_line->a);
            last_line = next_line;
            next_line->set_skip();
        }
    }
}

std::vector<OpenPolyline*> open_polylines_sorted(std::vector<OpenPolyline> &open_polylines, bool update_lengths)
{
    std::vector<OpenPolyline*> out;
    out.reserve(open_polylines.size());
    for (OpenPolyline &opl : open_polylines)
        if (! opl.consumed) {
            if (update_lengths)
                opl.length = Slic3r::length(opl.points);
            out.emplace_back(&opl);
        }
    std::sort(out.begin(), out.end(), [](const OpenPolyline *lhs, const OpenPolyline *rhs){ return lhs->length > rhs->length; });
    return out;
}

// called by make_loops() to connect remaining open polylines across shared triangle edges and vertices.
// Depending on "try_connect_reversed", it may or may not connect segments crossing triangles of opposite orientation.
static void chain_open_polylines_exact(std::vector<OpenPolyline> &open_polylines, Polygons &loops, bool try_connect_reversed)
{
    // Store the end points of open_polylines into vectors sorted
    struct OpenPolylineEnd {
        OpenPolylineEnd(OpenPolyline *polyline, bool start) : polyline(polyline), start(start) {}
        OpenPolyline    *polyline;
        // Is it the start or end point?
        bool             start;
        const IntersectionReference& ipref() const { return start ? polyline->start : polyline->end; }
        // Return a unique ID for the intersection point.
        // Return a positive id for a point, or a negative id for an edge.
        int id() const { const IntersectionReference &r = ipref(); return (r.point_id >= 0) ? r.point_id : - r.edge_id; }
        bool operator==(const OpenPolylineEnd &rhs) const { return this->polyline == rhs.polyline && this->start == rhs.start; }
    };
    auto by_id_lower = [](const OpenPolylineEnd &ope1, const OpenPolylineEnd &ope2) { return ope1.id() < ope2.id(); };
    std::vector<OpenPolylineEnd> by_id;
    by_id.reserve(2 * open_polylines.size());
    for (OpenPolyline &opl : open_polylines) {
        if (opl.start.point_id != -1 || opl.start.edge_id != -1)
            by_id.emplace_back(OpenPolylineEnd(&opl, true));
        if (try_connect_reversed && (opl.end.point_id != -1 || opl.end.edge_id != -1))
            by_id.emplace_back(OpenPolylineEnd(&opl, false));
    }
    std::sort(by_id.begin(), by_id.end(), by_id_lower);
    // Find an iterator to by_id_lower for the particular end of OpenPolyline (by comparing the OpenPolyline pointer and the start attribute).
    auto find_polyline_end = [&by_id, by_id_lower](const OpenPolylineEnd &end) -> std::vector<OpenPolylineEnd>::iterator {
        for (auto it = std::lower_bound(by_id.begin(), by_id.end(), end, by_id_lower);
                  it != by_id.end() && it->id() == end.id(); ++ it)
            if (*it == end)
                return it;
        return by_id.end();
    };
    // Try to connect the loops.
    std::vector<OpenPolyline*> sorted_by_length = open_polylines_sorted(open_polylines, false);
    for (OpenPolyline *opl : sorted_by_length) {
        if (opl->consumed)
            continue;
        opl->consumed = true;
        OpenPolylineEnd end(opl, false);
        for (;;) {
            // find a line starting where last one finishes
            auto it_next_start = std::lower_bound(by_id.begin(), by_id.end(), end, by_id_lower);
            for (; it_next_start != by_id.end() && it_next_start->id() == end.id(); ++ it_next_start)
                if (! it_next_start->polyline->consumed)
                    goto found;
            // The current loop could not be closed. Unmark the segment.
            opl->consumed = false;
            break;
        found:
            // Attach this polyline to the end of the initial polyline.
            if (it_next_start->start) {
                auto it = it_next_start->polyline->points.begin();
                std::copy(++ it, it_next_start->polyline->points.end(), back_inserter(opl->points));
            } else {
                auto it = it_next_start->polyline->points.rbegin();
                std::copy(++ it, it_next_start->polyline->points.rend(), back_inserter(opl->points));
            }
            opl->length += it_next_start->polyline->length;
            // Mark the next polyline as consumed.
            it_next_start->polyline->points.clear();
            it_next_start->polyline->length = 0.;
            it_next_start->polyline->consumed = true;
            if (try_connect_reversed) {
                // Running in a mode, where the polylines may be connected by mixing their orientations.
                // Update the end point lookup structure after the end point of the current polyline was extended.
                auto it_end      = find_polyline_end(end);
                auto it_next_end = find_polyline_end(OpenPolylineEnd(it_next_start->polyline, !it_next_start->start));
                // Swap the end points of the current and next polyline, but keep the polyline ptr and the start flag.
                std::swap(opl->end, it_next_end->start ? it_next_end->polyline->start : it_next_end->polyline->end);
                // Swap the positions of OpenPolylineEnd structures in the sorted array to match their respective end point positions.
                std::swap(*it_end, *it_next_end);
            }
            // Check whether we closed this loop.
            if ((opl->start.edge_id  != -1 && opl->start.edge_id  == opl->end.edge_id) ||
                (opl->start.point_id != -1 && opl->start.point_id == opl->end.point_id)) {
                // The current loop is complete. Add it to the output.
                //assert(opl->points.front().point_id == opl->points.back().point_id);
                //assert(opl->points.front().edge_id  == opl->points.back().edge_id);
                // Remove the duplicate last point.
                opl->points.pop_back();
                if (opl->points.size() >= 3) {
                    if (try_connect_reversed && area(opl->points) < 0)
                        // The closed polygon is patched from pieces with messed up orientation, therefore
                        // the orientation of the patched up polygon is not known.
                        // Orient the patched up polygons CCW. This heuristic may close some holes and cavities.
                        std::reverse(opl->points.begin(), opl->points.end());
                    loops.emplace_back(std::move(opl->points));
                }
                opl->points.clear();
                break;
            }
            // Continue with the current loop.
        }
    }
}

// called by make_loops() to connect remaining open polylines across shared triangle edges and vertices, 
// possibly closing small gaps.
// Depending on "try_connect_reversed", it may or may not connect segments crossing triangles of opposite orientation.
static void chain_open_polylines_close_gaps(std::vector<OpenPolyline> &open_polylines, Polygons &loops, double max_gap, bool try_connect_reversed)
{
    const coord_t max_gap_scaled = (coord_t)scale_(max_gap);

    // Sort the open polylines by their length, so the new loops will be seeded from longer chains.
    // Update the polyline lengths, return only not yet consumed polylines.
    std::vector<OpenPolyline*> sorted_by_length = open_polylines_sorted(open_polylines, true);

    // Store the end points of open_polylines into ClosestPointInRadiusLookup<OpenPolylineEnd>.
    struct OpenPolylineEnd {
        OpenPolylineEnd(OpenPolyline *polyline, bool start) : polyline(polyline), start(start) {}
        OpenPolyline    *polyline;
        // Is it the start or end point?
        bool             start;
        const Point&     point() const { return start ? polyline->points.front() : polyline->points.back(); }
        bool operator==(const OpenPolylineEnd &rhs) const { return this->polyline == rhs.polyline && this->start == rhs.start; }
    };
    struct OpenPolylineEndAccessor {
        const Point* operator()(const OpenPolylineEnd &pt) const { return pt.polyline->consumed ? nullptr : &pt.point(); }
    };
    typedef ClosestPointInRadiusLookup<OpenPolylineEnd, OpenPolylineEndAccessor> ClosestPointLookupType;
    ClosestPointLookupType closest_end_point_lookup(max_gap_scaled);
    for (OpenPolyline *opl : sorted_by_length) {
        closest_end_point_lookup.insert(OpenPolylineEnd(opl, true));
        if (try_connect_reversed)
            closest_end_point_lookup.insert(OpenPolylineEnd(opl, false));
    }
    // Try to connect the loops.
    for (OpenPolyline *opl : sorted_by_length) {
        if (opl->consumed)
            continue;
        OpenPolylineEnd end(opl, false);
        if (try_connect_reversed)
            // The end point of this polyline will be modified, thus the following entry will become invalid. Remove it.
            closest_end_point_lookup.erase(end);
        opl->consumed = true;
        size_t n_segments_joined = 1;
        for (;;) {
            // Find a line starting where last one finishes, only return non-consumed open polylines (OpenPolylineEndAccessor returns null for consumed).
            std::pair<const OpenPolylineEnd*, double> next_start_and_dist = closest_end_point_lookup.find(end.point());
            const OpenPolylineEnd *next_start = next_start_and_dist.first;
            // Check whether we closed this loop.
            double current_loop_closing_distance2 = (opl->points.back() - opl->points.front()).cast<double>().squaredNorm();
            bool   loop_closed = current_loop_closing_distance2 < coordf_t(max_gap_scaled) * coordf_t(max_gap_scaled);
            if (next_start != nullptr && loop_closed && current_loop_closing_distance2 < next_start_and_dist.second) {
                // Heuristics to decide, whether to close the loop, or connect another polyline.
                // One should avoid closing loops shorter than max_gap_scaled.
                loop_closed = sqrt(current_loop_closing_distance2) < 0.3 * length(opl->points);
            }
            if (loop_closed) {
                // Remove the start point of the current polyline from the lookup.
                // Mark the current segment as not consumed, otherwise the closest_end_point_lookup.erase() would fail.
                opl->consumed = false;
                closest_end_point_lookup.erase(OpenPolylineEnd(opl, true));
                if (current_loop_closing_distance2 == 0.) {
                    // Remove the duplicate last point.
                    opl->points.pop_back();
                } else {
                    // The end points are different, keep both of them.
                }
                if (opl->points.size() >= 3) {
                    if (try_connect_reversed && n_segments_joined > 1 && area(opl->points) < 0)
                        // The closed polygon is patched from pieces with messed up orientation, therefore
                        // the orientation of the patched up polygon is not known.
                        // Orient the patched up polygons CCW. This heuristic may close some holes and cavities.
                        std::reverse(opl->points.begin(), opl->points.end());
                    loops.emplace_back(std::move(opl->points));
                }
                opl->points.clear();
                opl->consumed = true;
                break;
            }
            if (next_start == nullptr) {
                // The current loop could not be closed. Unmark the segment.
                opl->consumed = false;
                if (try_connect_reversed)
                    // Re-insert the end point.
                    closest_end_point_lookup.insert(OpenPolylineEnd(opl, false));
                break;
            }
            // Attach this polyline to the end of the initial polyline.
            if (next_start->start) {
                auto it = next_start->polyline->points.begin();
                if (*it == opl->points.back())
                    ++ it;
                std::copy(it, next_start->polyline->points.end(), back_inserter(opl->points));
            } else {
                auto it = next_start->polyline->points.rbegin();
                if (*it == opl->points.back())
                    ++ it;
                std::copy(it, next_start->polyline->points.rend(), back_inserter(opl->points));
            }
            ++ n_segments_joined;
            // Remove the end points of the consumed polyline segment from the lookup.
            OpenPolyline *opl2 = next_start->polyline;
            closest_end_point_lookup.erase(OpenPolylineEnd(opl2, true));
            if (try_connect_reversed)
                closest_end_point_lookup.erase(OpenPolylineEnd(opl2, false));
            opl2->points.clear();
            opl2->consumed = true;
            // Continue with the current loop.
        }
    }
}

static Polygons make_loops(
    // Lines will have their flags modified.
    IntersectionLines   &lines)
{
    Polygons loops;
#if 0
//FIXME slice_facet() may create zero length edges due to rounding of doubles into coord_t.
//#ifdef _DEBUG
    for (const Line &l : lines)
        assert(l.a != l.b);
#endif /* _DEBUG */

    // There should be no tangent edges, as the horizontal triangles are ignored and if two triangles touch at a cutting plane,
    // only the bottom triangle is considered to be cutting the plane.
//    remove_tangent_edges(lines);

#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
        BoundingBox bbox_svg;
        {
            static int iRun = 0;
            for (const Line &line : lines) {
                bbox_svg.merge(line.a);
                bbox_svg.merge(line.b);
            }
            SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-raw_lines-%d.svg", iRun ++).c_str(), bbox_svg);
            for (const Line &line : lines)
                svg.draw(line);
            svg.Close();
        }
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */

    std::vector<OpenPolyline> open_polylines;
    chain_lines_by_triangle_connectivity(lines, loops, open_polylines);

#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
        {
            static int iRun = 0;
            SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines-%d.svg", iRun ++).c_str(), bbox_svg);
            svg.draw(union_ex(*loops));
            for (const OpenPolyline &pl : open_polylines)
                svg.draw(Polyline(pl.points), "red");
            svg.Close();
        }
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */

    // Now process the open polylines.
    // Do it in two rounds, first try to connect in the same direction only,
    // then try to connect the open polylines in reversed order as well.
    chain_open_polylines_exact(open_polylines, loops, false);
    chain_open_polylines_exact(open_polylines, loops, true);

#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
    {
        static int iRun = 0;
        SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines2-%d.svg", iRun++).c_str(), bbox_svg);
        svg.draw(union_ex(*loops));
        for (const OpenPolyline &pl : open_polylines) {
            if (pl.points.empty())
                continue;
            svg.draw(Polyline(pl.points), "red");
            svg.draw(pl.points.front(), "blue");
            svg.draw(pl.points.back(), "blue");
        }
        svg.Close();
    }
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */

    // Try to close gaps.
    // Do it in two rounds, first try to connect in the same direction only,
    // then try to connect the open polylines in reversed order as well.
#if 0
    for (double max_gap : { EPSILON, 0.001, 0.1, 1., 2. }) {
        chain_open_polylines_close_gaps(open_polylines, *loops, max_gap, false);
        chain_open_polylines_close_gaps(open_polylines, *loops, max_gap, true);
    }
#else
    const double max_gap = 2.; //mm
    chain_open_polylines_close_gaps(open_polylines, loops, max_gap, false);
    chain_open_polylines_close_gaps(open_polylines, loops, max_gap, true);
#endif

#ifdef SLIC3R_DEBUG_SLICE_PROCESSING
    {
        static int iRun = 0;
        SVG svg(debug_out_path("TriangleMeshSlicer_make_loops-polylines-final-%d.svg", iRun++).c_str(), bbox_svg);
        svg.draw(union_ex(*loops));
        for (const OpenPolyline &pl : open_polylines) {
            if (pl.points.empty())
                continue;
            svg.draw(Polyline(pl.points), "red");
            svg.draw(pl.points.front(), "blue");
            svg.draw(pl.points.back(), "blue");
        }
        svg.Close();
    }
#endif /* SLIC3R_DEBUG_SLICE_PROCESSING */

    return loops;
}

template<typename ThrowOnCancel>
static std::vector<Polygons> make_loops(
    // Lines will have their flags modified.
    std::vector<IntersectionLines> &lines, 
    const MeshSlicingParams        &params, 
    ThrowOnCancel                   throw_on_cancel)
{
    std::vector<Polygons> layers;
    layers.resize(lines.size());
    tbb::parallel_for(
        tbb::blocked_range<size_t>(0, lines.size()),
        [&lines, &layers, &params, throw_on_cancel](const tbb::blocked_range<size_t> &range) {
            for (size_t line_idx = range.begin(); line_idx < range.end(); ++ line_idx) {
                if ((line_idx & 0x0ffff) == 0)
                    throw_on_cancel();

                Polygons &polygons = layers[line_idx];
                polygons = make_loops(lines[line_idx]);

                auto this_mode = line_idx < params.slicing_mode_normal_below_layer ? params.mode_below : params.mode;
                if (! polygons.empty()) {
                    if (this_mode == MeshSlicingParams::SlicingMode::Positive) {
                        // Reorient all loops to be CCW.
                        for (Polygon& p : polygons)
                            p.make_counter_clockwise();
                    }
                    else if (this_mode == MeshSlicingParams::SlicingMode::PositiveLargestContour) {
                        // Keep just the largest polygon, make it CCW.
                        double   max_area = 0.;
                        Polygon* max_area_polygon = nullptr;
                        for (Polygon& p : polygons) {
                            double a = p.area();
                            if (std::abs(a) > std::abs(max_area)) {
                                max_area = a;
                                max_area_polygon = &p;
                            }
                        }
                        assert(max_area_polygon != nullptr);
                        if (max_area < 0.)
                            max_area_polygon->reverse();
                        Polygon p(std::move(*max_area_polygon));
                        polygons.clear();
                        polygons.emplace_back(std::move(p));
                    }
                }
            }
        }
    );

    return layers;
}

// Used to cut the mesh into two halves.
static ExPolygons make_expolygons_simple(std::vector<IntersectionLine> &lines)
{
    ExPolygons slices;
    Polygons holes;

    for (Polygon &loop : make_loops(lines))
        if (loop.area() >= 0.)
            slices.emplace_back(std::move(loop));
        else
            holes.emplace_back(std::move(loop));

    // If there are holes, then there should also be outer contours.
    assert(holes.empty() || ! slices.empty());
    if (! slices.empty())
    {
        // Assign holes to outer contours.
        for (Polygon &hole : holes) {
            // Find an outer contour to a hole.
            int     slice_idx            = -1;
            double  current_contour_area = std::numeric_limits<double>::max();
            for (ExPolygon &slice : slices)
                if (slice.contour.contains(hole.points.front())) {
                    double area = slice.contour.area();
                    if (area < current_contour_area) {
                        slice_idx = &slice - slices.data();
                        current_contour_area = area;
                    }
                }
            // assert(slice_idx != -1);
            if (slice_idx == -1)
                // Ignore this hole.
                continue;
            assert(current_contour_area < std::numeric_limits<double>::max() && current_contour_area >= -hole.area());
            slices[slice_idx].holes.emplace_back(std::move(hole));
        }

#if 0
        // If the input mesh is not valid, the holes may intersect with the external contour.
        // Rather subtract them from the outer contour.
        Polygons poly;
        for (auto it_slice = slices->begin(); it_slice != slices->end(); ++ it_slice) {
            if (it_slice->holes.empty()) {
                poly.emplace_back(std::move(it_slice->contour));
            } else {
                Polygons contours;
                contours.emplace_back(std::move(it_slice->contour));
                for (auto it = it_slice->holes.begin(); it != it_slice->holes.end(); ++ it)
                    it->reverse();
                polygons_append(poly, diff(contours, it_slice->holes));
            }
        }
        // If the input mesh is not valid, the input contours may intersect.
        *slices = union_ex(poly);
#endif

#if 0
        // If the input mesh is not valid, the holes may intersect with the external contour.
        // Rather subtract them from the outer contour.
        ExPolygons poly;
        for (auto it_slice = slices->begin(); it_slice != slices->end(); ++ it_slice) {
            Polygons contours;
            contours.emplace_back(std::move(it_slice->contour));
            for (auto it = it_slice->holes.begin(); it != it_slice->holes.end(); ++ it)
                it->reverse();
            expolygons_append(poly, diff_ex(contours, it_slice->holes));
        }
        // If the input mesh is not valid, the input contours may intersect.
        *slices = std::move(poly);
#endif
    }

    return slices;
}

static void make_expolygons(const Polygons &loops, const float closing_radius, const float extra_offset, ClipperLib::PolyFillType fill_type, ExPolygons* slices)
{
    /*
        Input loops are not suitable for evenodd nor nonzero fill types, as we might get
        two consecutive concentric loops having the same winding order - and we have to 
        respect such order. In that case, evenodd would create wrong inversions, and nonzero
        would ignore holes inside two concentric contours.
        So we're ordering loops and collapse consecutive concentric loops having the same 
        winding order.
        TODO: find a faster algorithm for this, maybe with some sort of binary search.
        If we computed a "nesting tree" we could also just remove the consecutive loops
        having the same winding order, and remove the extra one(s) so that we could just
        supply everything to offset() instead of performing several union/diff calls.
    
        we sort by area assuming that the outermost loops have larger area;
        the previous sorting method, based on $b->contains($a->[0]), failed to nest
        loops correctly in some edge cases when original model had overlapping facets
    */

    /* The following lines are commented out because they can generate wrong polygons,
       see for example issue #661 */

    //std::vector<double> area;
    //std::vector<size_t> sorted_area;  // vector of indices
    //for (Polygons::const_iterator loop = loops.begin(); loop != loops.end(); ++ loop) {
    //    area.emplace_back(loop->area());
    //    sorted_area.emplace_back(loop - loops.begin());
    //}
    //
    //// outer first
    //std::sort(sorted_area.begin(), sorted_area.end(),
    //    [&area](size_t a, size_t b) { return std::abs(area[a]) > std::abs(area[b]); });

    //// we don't perform a safety offset now because it might reverse cw loops
    //Polygons p_slices;
    //for (std::vector<size_t>::const_iterator loop_idx = sorted_area.begin(); loop_idx != sorted_area.end(); ++ loop_idx) {
    //    /* we rely on the already computed area to determine the winding order
    //       of the loops, since the Orientation() function provided by Clipper
    //       would do the same, thus repeating the calculation */
    //    Polygons::const_iterator loop = loops.begin() + *loop_idx;
    //    if (area[*loop_idx] > +EPSILON)
    //        p_slices.emplace_back(*loop);
    //    else if (area[*loop_idx] < -EPSILON)
    //        //FIXME This is arbitrary and possibly very slow.
    //        // If the hole is inside a polygon, then there is no need to diff.
    //        // If the hole intersects a polygon boundary, then diff it, but then
    //        // there is no guarantee of an ordering of the loops.
    //        // Maybe we can test for the intersection before running the expensive diff algorithm?
    //        p_slices = diff(p_slices, *loop);
    //}

    // Perform a safety offset to merge very close facets (TODO: find test case for this)
    // 0.0499 comes from https://github.com/slic3r/Slic3r/issues/959
//    double safety_offset = scale_(0.0499);
    // 0.0001 is set to satisfy GH #520, #1029, #1364
    assert(closing_radius >= 0);
    // Allowing negative extra_offset for shrinking a contour. This likely only makes sense if slicing a single region only.
    //assert(extra_offset >= 0);
    double offset_out;
    double offset_in;
    if (closing_radius >= extra_offset) {
        offset_out = + scale_(closing_radius);
        offset_in  = - scale_(closing_radius - extra_offset);
    } else {
        offset_out = + scale_(extra_offset);
        offset_in  = 0.;
    }

    /* The following line is commented out because it can generate wrong polygons,
       see for example issue #661 */
    //ExPolygons ex_slices = offset2_ex(p_slices, +safety_offset, -safety_offset);
    
    #ifdef SLIC3R_TRIANGLEMESH_DEBUG
    size_t holes_count = 0;
    for (ExPolygons::const_iterator e = ex_slices.begin(); e != ex_slices.end(); ++ e)
        holes_count += e->holes.size();
    printf("%zu surface(s) having %zu holes detected from %zu polylines\n",
        ex_slices.size(), holes_count, loops.size());
    #endif
    
    // append to the supplied collection
    expolygons_append(*slices,
        offset_out > 0 && offset_in < 0 ? offset2_ex(union_ex(loops, fill_type), offset_out, offset_in) :
        offset_out > 0 ? offset_ex(union_ex(loops, fill_type), offset_out) :
        offset_in  < 0 ? offset_ex(union_ex(loops, fill_type), offset_in) :
        union_ex(loops, fill_type));
}

std::vector<Polygons> slice_mesh(
    const indexed_triangle_set       &mesh,
    // Unscaled Zs
    const std::vector<float>         &zs,
    const MeshSlicingParams          &params,
    std::function<void()>             throw_on_cancel)
{
    BOOST_LOG_TRIVIAL(debug) << "slice_mesh to polygons";
       
    std::vector<IntersectionLines> lines;

    {
        //FIXME facets_edges is likely not needed and quite costly to calculate.
        // Instead of edge identifiers, one shall use a sorted pair of edge vertex indices.
        // However facets_edges assigns a single edge ID to two triangles only, thus when factoring facets_edges out, one will have
        // to make sure that no code relies on it.
        std::vector<Vec3i>            facets_edges = create_face_neighbors_index(mesh);
        const bool                    identity     = params.trafo.matrix() == Transform3d::Identity().matrix();
        static constexpr const double s            = 1. / SCALING_FACTOR;
        if (zs.size() <= 1) {
            // It likely is not worthwile to copy the vertices. Apply the transformation in place.
            if (identity)
                lines = slice_make_lines(
                    mesh.vertices, [](const Vec3f &p) { return Vec3f(scaled<float>(p.x()), scaled<float>(p.y()), p.z()); }, 
                    mesh.indices, facets_edges, zs, throw_on_cancel);
            else {
                // Transform the vertices, scale up in XY, not in Y.
                auto t = params.trafo;
                t.prescale(Vec3d(s, s, 1.));
                auto tf = t.cast<float>();
                lines = slice_make_lines(mesh.vertices, [tf](const Vec3f &p) { return tf * p; }, mesh.indices, facets_edges, zs, throw_on_cancel);
            }
        } else {
            // Copy and scale vertices in XY, don't scale in Z.
            // Possibly apply the transformation.
            std::vector<stl_vertex> vertices(mesh.vertices);
            if (identity) {
                for (stl_vertex &v : vertices) {
                    // Scale just XY, leave Z unscaled.
                    v.x() *= float(s);
                    v.y() *= float(s);
                }
            } else {
                // Transform the vertices, scale up in XY, not in Y.
                auto t = params.trafo;
                t.prescale(Vec3d(s, s, 1.));
                auto tf = t.cast<float>();
                for (stl_vertex &v : vertices)
                    v = tf * v;
            }
            lines = slice_make_lines(vertices, [](const Vec3f &p) { return p; },  mesh.indices, facets_edges, zs, throw_on_cancel);
        }
    }

    throw_on_cancel();

    std::vector<Polygons> layers = make_loops(lines, params, throw_on_cancel);

#ifdef SLIC3R_DEBUG
    {
        static int iRun = 0;
        for (size_t i = 0; i < z.size(); ++ i) {
            Polygons  &polygons   = (*layers)[i];
            ExPolygons expolygons = union_ex(polygons, true);
            SVG::export_expolygons(debug_out_path("slice_%d_%d.svg", iRun, i).c_str(), expolygons);
            {
                BoundingBox bbox;
                for (const IntersectionLine &l : lines[i]) {
                    bbox.merge(l.a);
                    bbox.merge(l.b);
                }
                SVG svg(debug_out_path("slice_loops_%d_%d.svg", iRun, i).c_str(), bbox);
                svg.draw(expolygons);
                for (const IntersectionLine &l : lines[i])
                    svg.draw(l, "red", 0);
                svg.draw_outline(expolygons, "black", "blue", 0);
                svg.Close();
            }
#if 0
//FIXME slice_facet() may create zero length edges due to rounding of doubles into coord_t.
            for (Polygon &poly : polygons) {
                for (size_t i = 1; i < poly.points.size(); ++ i)
                    assert(poly.points[i-1] != poly.points[i]);
                assert(poly.points.front() != poly.points.back());
            }
#endif
        }
        ++ iRun;
    }
#endif

    return layers;
}

std::vector<ExPolygons> slice_mesh_ex(
    const indexed_triangle_set       &mesh,
    const std::vector<float>         &zs,
    const MeshSlicingParamsEx        &params,
    std::function<void()>             throw_on_cancel)
{
    std::vector<Polygons> layers_p;
    {
        MeshSlicingParams slicing_params(params);
        if (params.mode == MeshSlicingParams::SlicingMode::PositiveLargestContour)
            slicing_params.mode = MeshSlicingParams::SlicingMode::Positive;
        if (params.mode_below == MeshSlicingParams::SlicingMode::PositiveLargestContour)
            slicing_params.mode_below = MeshSlicingParams::SlicingMode::Positive;
        layers_p = slice_mesh(mesh, zs, slicing_params, throw_on_cancel);
    }
    
//    BOOST_LOG_TRIVIAL(debug) << "slice_mesh make_expolygons in parallel - start";
    std::vector<ExPolygons> layers(layers_p.size(), ExPolygons{});
    tbb::parallel_for(
        tbb::blocked_range<size_t>(0, layers_p.size()),
        [&layers_p, &params, &layers, throw_on_cancel]
        (const tbb::blocked_range<size_t>& range) {
            auto resolution = scaled<float>(params.resolution);
            for (size_t layer_id = range.begin(); layer_id < range.end(); ++ layer_id) {
                throw_on_cancel();
                ExPolygons &expolygons = layers[layer_id];
                const auto this_mode = layer_id < params.slicing_mode_normal_below_layer ? params.mode_below : params.mode;
                Slic3r::make_expolygons(
                    layers_p[layer_id], params.closing_radius, params.extra_offset,
                    this_mode == MeshSlicingParams::SlicingMode::EvenOdd ? ClipperLib::pftEvenOdd : 
                    this_mode == MeshSlicingParams::SlicingMode::PositiveLargestContour ? ClipperLib::pftNonZero : ClipperLib::pftPositive,
                    &expolygons);
                //FIXME simplify
                if (this_mode == MeshSlicingParams::SlicingMode::PositiveLargestContour)
                    keep_largest_contour_only(expolygons);
                if (resolution != 0.)
                    for (ExPolygon &ex : expolygons)
                        ex.simplify(resolution);
            }
        });
//    BOOST_LOG_TRIVIAL(debug) << "slice_mesh make_expolygons in parallel - end";

    return layers;
}

// Remove duplicates of slice_vertices, optionally triangulate the cut.
static void triangulate_slice(
    indexed_triangle_set    &its, 
    IntersectionLines       &lines, 
    std::vector<int>        &slice_vertices,
    // Vertices of the original (unsliced) mesh. Newly added vertices are those on the slice.
    int                      num_original_vertices,
    // Z height of the slice.
    float                    z, 
    bool                     triangulate)
{
    sort_remove_duplicates(slice_vertices);

    // 1) Create map of the slice vertices from positions to mesh indices.
    // As the caller will likely add duplicate points when intersecting triangle edges, there will be duplicates.
    std::vector<std::pair<Vec2f, int>> map_vertex_to_index;
    map_vertex_to_index.reserve(slice_vertices.size());
    for (int i : slice_vertices)
        map_vertex_to_index.emplace_back(to_2d(its.vertices[i]), i);
    std::sort(map_vertex_to_index.begin(), map_vertex_to_index.end(), 
        [](const std::pair<Vec2f, int> &l, const std::pair<Vec2f, int> &r) { 
            return l.first.x() < r.first.x() || 
                   (l.first.x() == r.first.x() && (l.first.y() < r.first.y() || 
                                                   (l.first.y() == r.first.y() && l.second < r.second))); });

    // 2) Discover duplicate points on the slice. Remap duplicate vertices to a vertex with a lowest index.
    {
        std::vector<int> map_duplicate_vertex(int(its.vertices.size()) - num_original_vertices, -1);
        int i = 0;
        int k = 0;
        for (; i < int(map_vertex_to_index.size()); ++ i) {
            map_vertex_to_index[k ++] = map_vertex_to_index[i];
            const Vec2f &ipos = map_vertex_to_index[i].first;
            const int    iidx = map_vertex_to_index[i].second;
            if (iidx >= num_original_vertices)
                // map to itself
                map_duplicate_vertex[iidx - num_original_vertices] = iidx;
            int j = i;
            for (++ j; j < int(map_vertex_to_index.size()) && ipos.x() == map_vertex_to_index[j].first.x() && ipos.y() == map_vertex_to_index[j].first.y(); ++ j) {
                const int jidx = map_vertex_to_index[j].second;
                assert(jidx >= num_original_vertices);
                if (jidx >= num_original_vertices)
                    // map to the first vertex
                    map_duplicate_vertex[jidx - num_original_vertices] = iidx;
            }
        }
        map_vertex_to_index.erase(map_vertex_to_index.begin() + k, map_vertex_to_index.end());
        for (stl_triangle_vertex_indices &f : its.indices)
            for (i = 0; i < 3; ++ i)
                if (f(i) >= num_original_vertices)
                    f(i) = map_duplicate_vertex[f(i) - num_original_vertices];
    }

    if (triangulate) {
        size_t idx_vertex_new_first = its.vertices.size();
        Pointf3s triangles = triangulate_expolygons_3d(make_expolygons_simple(lines), z, true);
        for (size_t i = 0; i < triangles.size(); ) {
            stl_triangle_vertex_indices facet;
            for (size_t j = 0; j < 3; ++ j) {
                Vec3f v = triangles[i ++].cast<float>();
                auto it = lower_bound_by_predicate(map_vertex_to_index.begin(), map_vertex_to_index.end(), 
                    [&v](const std::pair<Vec2f, int> &l) { return l.first.x() < v.x() || (l.first.x() == v.x() && l.first.y() < v.y()); });
                int   idx = -1;
                if (it != map_vertex_to_index.end() && it->first.x() == v.x() && it->first.y() == v.y())
                    idx = it->second;
                else {
                    // Try to find the vertex in the list of newly added vertices. Those vertices are not matched on the cut and they shall be rare.
                    for (size_t k = idx_vertex_new_first; k < its.vertices.size(); ++ k)
                        if (its.vertices[k] == v) {
                            idx = int(k);
                            break;
                        }
                    if (idx == -1) {
                        idx = int(its.vertices.size());
                        its.vertices.emplace_back(v);
                    }
                }
                facet(j) = idx;
            }
            if (facet(0) != facet(1) && facet(0) != facet(2) && facet(1) != facet(2))
                its.indices.emplace_back(facet);
        }
    }

    // Remove vertices, which are not referenced by any face.
    its_compactify_vertices(its);

    // Degenerate faces should not be created.
    // its_remove_degenerate_faces(its);
}

void cut_mesh(const indexed_triangle_set &mesh, float z, indexed_triangle_set *upper, indexed_triangle_set *lower, bool triangulate_caps)
{
    assert(upper || lower);
    if (upper == nullptr && lower == nullptr)
        return;

    BOOST_LOG_TRIVIAL(trace) << "cut_mesh - slicing object";

    if (upper) {
        upper->clear();
        upper->vertices = mesh.vertices;
        upper->indices.reserve(mesh.indices.size());
    }

    if (lower) {
        lower->clear();
        lower->vertices = mesh.vertices;
        lower->indices.reserve(mesh.indices.size());
    }

    // To triangulate the caps after slicing.
    IntersectionLines  upper_lines, lower_lines;
    std::vector<int>   upper_slice_vertices, lower_slice_vertices;
    std::vector<Vec3i> facets_edges = create_face_neighbors_index(mesh);

    for (int facet_idx = 0; facet_idx < int(mesh.indices.size()); ++ facet_idx) {
        const stl_triangle_vertex_indices &facet = mesh.indices[facet_idx];
        Vec3f vertices[3] { mesh.vertices[facet(0)], mesh.vertices[facet(1)], mesh.vertices[facet(2)] };
        float min_z = std::min(vertices[0].z(), std::min(vertices[1].z(), vertices[2].z()));
        float max_z = std::max(vertices[0].z(), std::max(vertices[1].z(), vertices[2].z()));
        
        // intersect facet with cutting plane
        IntersectionLine line;
        int              idx_vertex_lowest = (vertices[1].z() == min_z) ? 1 : ((vertices[2].z() == min_z) ? 2 : 0);
        FacetSliceType   slice_type = FacetSliceType::NoSlice;
        if (z > min_z - EPSILON && z < max_z + EPSILON) {
            Vec3f vertices_scaled[3];
            for (int i = 0; i < 3; ++ i) {
                const Vec3f &src = vertices[i];
                Vec3f       &dst = vertices_scaled[i];
                dst.x() = scale_(src.x());
                dst.y() = scale_(src.y());
                dst.z() = src.z();
            }
            slice_type = slice_facet(z, vertices_scaled, mesh.indices[facet_idx], facets_edges[facet_idx], idx_vertex_lowest, min_z == max_z, line);
        }

        if (slice_type != FacetSliceType::NoSlice) {
            // Save intersection lines for generating correct triangulations.
            if (line.edge_type == IntersectionLine::FacetEdgeType::Top) {
                lower_lines.emplace_back(line);
                lower_slice_vertices.emplace_back(line.a_id);
                lower_slice_vertices.emplace_back(line.b_id);
            } else if (line.edge_type == IntersectionLine::FacetEdgeType::Bottom) {
                upper_lines.emplace_back(line);
                upper_slice_vertices.emplace_back(line.a_id);
                upper_slice_vertices.emplace_back(line.b_id);
            } else if (line.edge_type == IntersectionLine::FacetEdgeType::General) {
                lower_lines.emplace_back(line);
                upper_lines.emplace_back(line);
            }
        }
        
        if (min_z > z || (min_z == z && max_z > z)) {
            // facet is above the cut plane and does not belong to it
            if (upper != nullptr)
                upper->indices.emplace_back(facet);
        } else if (max_z < z || (max_z == z && min_z < z)) {
            // facet is below the cut plane and does not belong to it
            if (lower != nullptr)
                lower->indices.emplace_back(facet);
        } else if (min_z < z && max_z > z) {
            // Facet is cut by the slicing plane.
            assert(slice_type == FacetSliceType::Slicing);
            assert(line.edge_type == IntersectionLine::FacetEdgeType::General);
            assert(line.edge_a_id != -1);
            assert(line.edge_b_id != -1);

            // look for the vertex on whose side of the slicing plane there are no other vertices
            int isolated_vertex = 
                (vertices[0].z() > z) == (vertices[1].z() > z) ? 2 :
                (vertices[1].z() > z) == (vertices[2].z() > z) ? 0 : 1;
            
            // get vertices starting from the isolated one
            int iv = isolated_vertex;
            stl_vertex v0v1, v2v0;
            assert(facets_edges[facet_idx](iv) == line.edge_a_id ||facets_edges[facet_idx](iv) == line.edge_b_id);
            if (facets_edges[facet_idx](iv) == line.edge_a_id) {
                v0v1 = to_3d(unscaled<float>(line.a), z);
                v2v0 = to_3d(unscaled<float>(line.b), z);
            } else {
                v0v1 = to_3d(unscaled<float>(line.b), z);
                v2v0 = to_3d(unscaled<float>(line.a), z);
            }
            const stl_vertex &v0  = vertices[iv];
            const int         iv0 = facet[iv];
            if (++ iv == 3)
                iv = 0;
            const stl_vertex &v1  = vertices[iv];
            const int         iv1 = facet[iv];
            if (++ iv == 3)
                iv = 0;
            const stl_vertex &v2  = vertices[iv];
            const int         iv2 = facet[iv];

            // intersect v0-v1 and v2-v0 with cutting plane and make new vertices
            auto new_vertex = [upper, lower, &upper_slice_vertices, &lower_slice_vertices](const Vec3f &a, const int ia, const Vec3f &b, const int ib, const Vec3f &c) {
                int iupper, ilower;
                if (c == a)
                    iupper = ilower = ia;
                else if (c == b)
                    iupper = ilower = ib;
                else {
                    // Insert a new vertex into upper / lower.
                    if (upper) {
                        iupper = int(upper->vertices.size());
                        upper->vertices.emplace_back(c);
                        upper_slice_vertices.emplace_back(iupper);
                    }
                    if (lower) {
                        ilower = int(lower->vertices.size());
                        lower->vertices.emplace_back(c);
                        lower_slice_vertices.emplace_back(ilower);
                    }
                }
                return std::make_pair(iupper, ilower);
            };
            auto [iv0v1_upper, iv0v1_lower] = new_vertex(v1, iv1, v0, iv0, v0v1);
            auto [iv2v0_upper, iv2v0_lower] = new_vertex(v2, iv2, v0, iv0, v2v0);
            auto new_face = [](indexed_triangle_set *its, int i, int j, int k) {
                if (its != nullptr && i != j && i != k && j != k)
                    its->indices.emplace_back(i, j, k);
            };

            if (v0.z() > z) {
                new_face(upper, iv0, iv0v1_upper, iv2v0_upper);
                new_face(lower, iv1, iv2, iv0v1_lower);
                new_face(lower, iv2, iv2v0_lower, iv0v1_lower);
            } else {
                new_face(upper, iv1, iv2, iv0v1_upper);
                new_face(upper, iv2, iv2v0_upper, iv0v1_upper);
                new_face(lower, iv0, iv0v1_lower, iv2v0_lower);
            }
        }
    }
    
    if (upper != nullptr)
        triangulate_slice(*upper, upper_lines, upper_slice_vertices, int(mesh.vertices.size()), z, triangulate_caps);

    if (lower != nullptr)
        triangulate_slice(*lower, lower_lines, lower_slice_vertices, int(mesh.vertices.size()), z, triangulate_caps);
}

}