#include <catch2/catch.hpp>
#include <test_utils.hpp>

#include <stack>

#include <libslic3r/Polygon.hpp>
#include <libslic3r/Polyline.hpp>
#include <libslic3r/EdgeGrid.hpp>
#include <libslic3r/Geometry.hpp>

#define BOOST_VORONOI_USE_GMP 1
#include "boost/polygon/voronoi.hpp"

using boost::polygon::voronoi_builder;
using boost::polygon::voronoi_diagram;

using namespace Slic3r;

struct VD : public boost::polygon::voronoi_diagram<double> {
    typedef double                                          coord_type;
    typedef boost::polygon::point_data<coordinate_type>     point_type;
    typedef boost::polygon::segment_data<coordinate_type>   segment_type;
    typedef boost::polygon::rectangle_data<coordinate_type> rect_type;
};

// #define VORONOI_DEBUG_OUT

#ifdef VORONOI_DEBUG_OUT
#include <libslic3r/SVG.hpp>
#endif

#ifdef VORONOI_DEBUG_OUT
namespace boost { namespace polygon {

// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_graphic_utils.hpp header file
//          Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE_1_0.txt or copy at
//          http://www.boost.org/LICENSE_1_0.txt)
template <typename CT>
class voronoi_visual_utils {
 public:
  // Discretize parabolic Voronoi edge.
  // Parabolic Voronoi edges are always formed by one point and one segment
  // from the initial input set.
  //
  // Args:
  //   point: input point.
  //   segment: input segment.
  //   max_dist: maximum discretization distance.
  //   discretization: point discretization of the given Voronoi edge.
  //
  // Template arguments:
  //   InCT: coordinate type of the input geometries (usually integer).
  //   Point: point type, should model point concept.
  //   Segment: segment type, should model segment concept.
  //
  // Important:
  //   discretization should contain both edge endpoints initially.
  template <class InCT1, class InCT2,
            template<class> class Point,
            template<class> class Segment>
  static
  typename enable_if<
    typename gtl_and<
      typename gtl_if<
        typename is_point_concept<
          typename geometry_concept< Point<InCT1> >::type
        >::type
      >::type,
      typename gtl_if<
        typename is_segment_concept<
          typename geometry_concept< Segment<InCT2> >::type
        >::type
      >::type
    >::type,
    void
  >::type discretize(
      const Point<InCT1>& point,
      const Segment<InCT2>& segment,
      const CT max_dist,
      std::vector< Point<CT> >* discretization) {
    // Apply the linear transformation to move start point of the segment to
    // the point with coordinates (0, 0) and the direction of the segment to
    // coincide the positive direction of the x-axis.
    CT segm_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
    CT segm_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
    CT sqr_segment_length = segm_vec_x * segm_vec_x + segm_vec_y * segm_vec_y;

    // Compute x-coordinates of the endpoints of the edge
    // in the transformed space.
    CT projection_start = sqr_segment_length *
        get_point_projection((*discretization)[0], segment);
    CT projection_end = sqr_segment_length *
        get_point_projection((*discretization)[1], segment);

    // Compute parabola parameters in the transformed space.
    // Parabola has next representation:
    // f(x) = ((x-rot_x)^2 + rot_y^2) / (2.0*rot_y).
    CT point_vec_x = cast(x(point)) - cast(x(low(segment)));
    CT point_vec_y = cast(y(point)) - cast(y(low(segment)));
    CT rot_x = segm_vec_x * point_vec_x + segm_vec_y * point_vec_y;
    CT rot_y = segm_vec_x * point_vec_y - segm_vec_y * point_vec_x;

    // Save the last point.
    Point<CT> last_point = (*discretization)[1];
    discretization->pop_back();

    // Use stack to avoid recursion.
    std::stack<CT> point_stack;
    point_stack.push(projection_end);
    CT cur_x = projection_start;
    CT cur_y = parabola_y(cur_x, rot_x, rot_y);

    // Adjust max_dist parameter in the transformed space.
    const CT max_dist_transformed = max_dist * max_dist * sqr_segment_length;
    while (!point_stack.empty()) {
      CT new_x = point_stack.top();
      CT new_y = parabola_y(new_x, rot_x, rot_y);

      // Compute coordinates of the point of the parabola that is
      // furthest from the current line segment.
      CT mid_x = (new_y - cur_y) / (new_x - cur_x) * rot_y + rot_x;
      CT mid_y = parabola_y(mid_x, rot_x, rot_y);

      // Compute maximum distance between the given parabolic arc
      // and line segment that discretize it.
      CT dist = (new_y - cur_y) * (mid_x - cur_x) -
          (new_x - cur_x) * (mid_y - cur_y);
      dist = dist * dist / ((new_y - cur_y) * (new_y - cur_y) +
          (new_x - cur_x) * (new_x - cur_x));
      if (dist <= max_dist_transformed) {
        // Distance between parabola and line segment is less than max_dist.
        point_stack.pop();
        CT inter_x = (segm_vec_x * new_x - segm_vec_y * new_y) /
            sqr_segment_length + cast(x(low(segment)));
        CT inter_y = (segm_vec_x * new_y + segm_vec_y * new_x) /
            sqr_segment_length + cast(y(low(segment)));
        discretization->push_back(Point<CT>(inter_x, inter_y));
        cur_x = new_x;
        cur_y = new_y;
      } else {
        point_stack.push(mid_x);
      }
    }

    // Update last point.
    discretization->back() = last_point;
  }

 private:
  // Compute y(x) = ((x - a) * (x - a) + b * b) / (2 * b).
  static CT parabola_y(CT x, CT a, CT b) {
    return ((x - a) * (x - a) + b * b) / (b + b);
  }

  // Get normalized length of the distance between:
  //   1) point projection onto the segment
  //   2) start point of the segment
  // Return this length divided by the segment length. This is made to avoid
  // sqrt computation during transformation from the initial space to the
  // transformed one and vice versa. The assumption is made that projection of
  // the point lies between the start-point and endpoint of the segment.
  template <class InCT,
            template<class> class Point,
            template<class> class Segment>
  static
  typename enable_if<
    typename gtl_and<
      typename gtl_if<
        typename is_point_concept<
          typename geometry_concept< Point<int> >::type
        >::type
      >::type,
      typename gtl_if<
        typename is_segment_concept<
          typename geometry_concept< Segment<long> >::type
        >::type
      >::type
    >::type,
    CT
  >::type get_point_projection(
      const Point<CT>& point, const Segment<InCT>& segment) {
    CT segment_vec_x = cast(x(high(segment))) - cast(x(low(segment)));
    CT segment_vec_y = cast(y(high(segment))) - cast(y(low(segment)));
    CT point_vec_x = x(point) - cast(x(low(segment)));
    CT point_vec_y = y(point) - cast(y(low(segment)));
    CT sqr_segment_length =
        segment_vec_x * segment_vec_x + segment_vec_y * segment_vec_y;
    CT vec_dot = segment_vec_x * point_vec_x + segment_vec_y * point_vec_y;
    return vec_dot / sqr_segment_length;
  }

  template <typename InCT>
  static CT cast(const InCT& value) {
    return static_cast<CT>(value);
  }
};

} } // namespace boost::polygon

// The following code for the visualization of the boost Voronoi diagram is based on:
//
// Boost.Polygon library voronoi_visualizer.cpp file
//          Copyright Andrii Sydorchuk 2010-2012.
// Distributed under the Boost Software License, Version 1.0.
//    (See accompanying file LICENSE_1_0.txt or copy at
//          http://www.boost.org/LICENSE_1_0.txt)
namespace Voronoi { namespace Internal {

    typedef double coordinate_type;
    typedef boost::polygon::point_data<coordinate_type> point_type;
    typedef boost::polygon::segment_data<coordinate_type> segment_type;
    typedef boost::polygon::rectangle_data<coordinate_type> rect_type;
    typedef boost::polygon::voronoi_diagram<coordinate_type> VD;
    typedef VD::cell_type cell_type;
    typedef VD::cell_type::source_index_type source_index_type;
    typedef VD::cell_type::source_category_type source_category_type;
    typedef VD::edge_type edge_type;
    typedef VD::cell_container_type cell_container_type;
    typedef VD::cell_container_type vertex_container_type;
    typedef VD::edge_container_type edge_container_type;
    typedef VD::const_cell_iterator const_cell_iterator;
    typedef VD::const_vertex_iterator const_vertex_iterator;
    typedef VD::const_edge_iterator const_edge_iterator;

    static const std::size_t EXTERNAL_COLOR = 1;

    inline void color_exterior(const VD::edge_type* edge)
    {
        if (edge->color() == EXTERNAL_COLOR)
            return;
        edge->color(EXTERNAL_COLOR);
        edge->twin()->color(EXTERNAL_COLOR);
        const VD::vertex_type* v = edge->vertex1();
        if (v == NULL || !edge->is_primary())
            return;
        v->color(EXTERNAL_COLOR);
        const VD::edge_type* e = v->incident_edge();
        do {
            color_exterior(e);
            e = e->rot_next();
        } while (e != v->incident_edge());
    }

    inline point_type retrieve_point(const Points &points, const std::vector<segment_type> &segments, const cell_type& cell)
    {
        assert(cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT || cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_END_POINT ||
               cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT);
        return cell.source_category() == boost::polygon::SOURCE_CATEGORY_SINGLE_POINT ?
                    Voronoi::Internal::point_type(double(points[cell.source_index()].x()), double(points[cell.source_index()].y())) :
                    (cell.source_category() == boost::polygon::SOURCE_CATEGORY_SEGMENT_START_POINT) ?
                        low(segments[cell.source_index()]) : high(segments[cell.source_index()]);
    }

    inline void clip_infinite_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, coordinate_type bbox_max_size, std::vector<point_type>* clipped_edge)
    {
        const cell_type& cell1 = *edge.cell();
        const cell_type& cell2 = *edge.twin()->cell();
        point_type origin, direction;
        // Infinite edges could not be created by two segment sites.
        if (! cell1.contains_point() && ! cell2.contains_point()) {
            printf("Error! clip_infinite_edge - infinite edge separates two segment cells\n");
            return;
        }
        if (cell1.contains_point() && cell2.contains_point()) {
            point_type p1 = retrieve_point(points, segments, cell1);
            point_type p2 = retrieve_point(points, segments, cell2);
            origin.x((p1.x() + p2.x()) * 0.5);
            origin.y((p1.y() + p2.y()) * 0.5);
            direction.x(p1.y() - p2.y());
            direction.y(p2.x() - p1.x());
        } else {
            origin = cell1.contains_segment() ? retrieve_point(points, segments, cell2) : retrieve_point(points, segments, cell1);
            segment_type segment = cell1.contains_segment() ? segments[cell1.source_index()] : segments[cell2.source_index()];
            coordinate_type dx = high(segment).x() - low(segment).x();
            coordinate_type dy = high(segment).y() - low(segment).y();
            if ((low(segment) == origin) ^ cell1.contains_point()) {
                direction.x(dy);
                direction.y(-dx);
            } else {
                direction.x(-dy);
                direction.y(dx);
            }
        }
        coordinate_type koef = bbox_max_size / (std::max)(fabs(direction.x()), fabs(direction.y()));
        if (edge.vertex0() == NULL) {
            clipped_edge->push_back(point_type(
                origin.x() - direction.x() * koef,
                origin.y() - direction.y() * koef));
        } else {
            clipped_edge->push_back(
                point_type(edge.vertex0()->x(), edge.vertex0()->y()));
        }
        if (edge.vertex1() == NULL) {
            clipped_edge->push_back(point_type(
                origin.x() + direction.x() * koef,
                origin.y() + direction.y() * koef));
        } else {
            clipped_edge->push_back(
                point_type(edge.vertex1()->x(), edge.vertex1()->y()));
        }
    }

    inline void sample_curved_edge(const Points &points, const std::vector<segment_type> &segments, const edge_type& edge, std::vector<point_type> &sampled_edge, coordinate_type max_dist)
    {
        point_type point = edge.cell()->contains_point() ?
            retrieve_point(points, segments, *edge.cell()) :
            retrieve_point(points, segments, *edge.twin()->cell());
        segment_type segment = edge.cell()->contains_point() ?
            segments[edge.twin()->cell()->source_index()] :
            segments[edge.cell()->source_index()];
        ::boost::polygon::voronoi_visual_utils<coordinate_type>::discretize(point, segment, max_dist, &sampled_edge);
    }

} /* namespace Internal */ } // namespace Voronoi

static inline void dump_voronoi_to_svg(
    const char          *path,
    /* const */ VD      &vd,
    const Points        &points,
    const Lines         &lines,
    const double         scale = 0.7) // 0.2?
{
    const std::string   inputSegmentPointColor      = "lightseagreen";
    const coord_t       inputSegmentPointRadius     = coord_t(0.09 * scale / SCALING_FACTOR);
    const std::string   inputSegmentColor           = "lightseagreen";
    const coord_t       inputSegmentLineWidth       = coord_t(0.03 * scale / SCALING_FACTOR);

    const std::string   voronoiPointColor           = "black";
    const coord_t       voronoiPointRadius          = coord_t(0.06 * scale / SCALING_FACTOR);
    const std::string   voronoiLineColorPrimary     = "black";
    const std::string   voronoiLineColorSecondary   = "green";
    const std::string   voronoiArcColor             = "red";
    const coord_t       voronoiLineWidth            = coord_t(0.02 * scale / SCALING_FACTOR);

    const bool          internalEdgesOnly           = false;
    const bool          primaryEdgesOnly            = false;

    BoundingBox bbox;
    bbox.merge(get_extents(points));
    bbox.merge(get_extents(lines));
    bbox.min -= (0.01 * bbox.size().cast<double>()).cast<coord_t>();
    bbox.max += (0.01 * bbox.size().cast<double>()).cast<coord_t>();

    ::Slic3r::SVG svg(path, bbox);

//    bbox.scale(1.2);
    // For clipping of half-lines to some reasonable value.
    // The line will then be clipped by the SVG viewer anyway.
    const double bbox_dim_max = double(std::max(bbox.size().x(), bbox.size().y()));
    // For the discretization of the Voronoi parabolic segments.
    const double discretization_step = 0.05 * bbox_dim_max;

    // Make a copy of the input segments with the double type.
    std::vector<Voronoi::Internal::segment_type> segments;
    for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++ it)
        segments.push_back(Voronoi::Internal::segment_type(
            Voronoi::Internal::point_type(double(it->a(0)), double(it->a(1))),
            Voronoi::Internal::point_type(double(it->b(0)), double(it->b(1)))));

    // Color exterior edges.
    for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it)
        if (!it->is_finite())
            Voronoi::Internal::color_exterior(&(*it));

    // Draw the end points of the input polygon.
    for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it) {
        svg.draw(it->a, inputSegmentPointColor, inputSegmentPointRadius);
        svg.draw(it->b, inputSegmentPointColor, inputSegmentPointRadius);
    }
    // Draw the input polygon.
    for (Lines::const_iterator it = lines.begin(); it != lines.end(); ++it)
        svg.draw(Line(Point(coord_t(it->a(0)), coord_t(it->a(1))), Point(coord_t(it->b(0)), coord_t(it->b(1)))), inputSegmentColor, inputSegmentLineWidth);

#if 1
    // Draw voronoi vertices.
    for (boost::polygon::voronoi_diagram<double>::const_vertex_iterator it = vd.vertices().begin(); it != vd.vertices().end(); ++it)
        if (! internalEdgesOnly || it->color() != Voronoi::Internal::EXTERNAL_COLOR)
            svg.draw(Point(coord_t(it->x()), coord_t(it->y())), voronoiPointColor, voronoiPointRadius);

    for (boost::polygon::voronoi_diagram<double>::const_edge_iterator it = vd.edges().begin(); it != vd.edges().end(); ++it) {
        if (primaryEdgesOnly && !it->is_primary())
            continue;
        if (internalEdgesOnly && (it->color() == Voronoi::Internal::EXTERNAL_COLOR))
            continue;
        std::vector<Voronoi::Internal::point_type> samples;
        std::string color = voronoiLineColorPrimary;
        if (!it->is_finite()) {
            Voronoi::Internal::clip_infinite_edge(points, segments, *it, bbox_dim_max, &samples);
            if (! it->is_primary())
                color = voronoiLineColorSecondary;
        } else {
            // Store both points of the segment into samples. sample_curved_edge will split the initial line
            // until the discretization_step is reached.
            samples.push_back(Voronoi::Internal::point_type(it->vertex0()->x(), it->vertex0()->y()));
            samples.push_back(Voronoi::Internal::point_type(it->vertex1()->x(), it->vertex1()->y()));
            if (it->is_curved()) {
                Voronoi::Internal::sample_curved_edge(points, segments, *it, samples, discretization_step);
                color = voronoiArcColor;
            } else if (! it->is_primary())
                color = voronoiLineColorSecondary;
        }
        for (std::size_t i = 0; i + 1 < samples.size(); ++i)
            svg.draw(Line(Point(coord_t(samples[i].x()), coord_t(samples[i].y())), Point(coord_t(samples[i+1].x()), coord_t(samples[i+1].y()))), color, voronoiLineWidth);
    }
#endif

    svg.Close();
}
#endif

// https://svn.boost.org/trac10/ticket/12067
// This bug seems to be confirmed.
// Vojtech supposes that there may be no Voronoi edges produced for
// the 1st and last sweep line positions.
TEST_CASE("Voronoi missing edges - points 12067", "[Voronoi]")
{
    Points pts {
        { -10, -20 },
        {  10, -20 },
        {   5,   0 },
        {  10,  20 },
        { -10,  20 },
        {  -5,   0 }
    };

    // Construction of the Voronoi Diagram.
    VD vd;
    construct_voronoi(pts.begin(), pts.end(), &vd);

#ifdef VORONOI_DEBUG_OUT
    dump_voronoi_to_svg(debug_out_path("voronoi-pts.svg").c_str(),
        vd, pts, Lines());
#endif

//    REQUIRE(closest_point.z() == Approx(1.));
}

// https://svn.boost.org/trac10/ticket/12707
// This issue is confirmed, there are no self intersections in the polygon.
// A minimal test case is created at the end of this test,
// a new issue opened with the minimal test case:
// https://github.com/boostorg/polygon/issues/43
TEST_CASE("Voronoi missing edges - Alessandro gapfill 12707", "[Voronoi]")
{
    Lines lines0 {
        { { 42127548,   699996}, { 42127548, 10135750 } },
        { { 42127548, 10135750}, { 50487352, 10135750 } },
        { { 50487352, 10135750}, { 50487352,   699995 } },
        { { 50487352,   699995}, { 51187348,        0 } },
        { { 51187348,        0}, { 64325952,        0 } },
        { { 64325952,        0}, { 64325952,   699996 } },
        { { 64325952,   699996}, { 51187348,   699996 } },
        { { 51187348,   699996}, { 51187348, 10835701 } },
        { { 51187348, 10835701}, { 41427552, 10835701 } },
        { { 41427552, 10835701}, { 41427552,   699996 } },
        { { 41427552,   699996}, { 28664848,   699996 } },
        { { 28664848,   699996}, { 28664848, 10835701 } },
        { { 28664848, 10835701}, { 19280052, 10835701 } },
        { { 19280052, 10835701}, { 27964852,   699996 } },
        { { 27964852,   699996}, { 28664848,        0 } },
        { { 28664848,        0}, { 41427551,        0 } },
        { { 41427551,        0}, { 42127548,   699996 } }
    };

    Lines lines1 {
        { { 42127548,   699996}, { 42127548, 10135750 } },
        { { 42127548, 10135750}, { 50487352, 10135750 } },
        { { 50487352, 10135750}, { 50487352,   699995 } },
        { { 50487352,   699995}, { 51187348,        0 } },
        { { 51187348,        0}, { 51187348, 10835701 } },
        { { 51187348, 10835701}, { 41427552, 10835701 } },
        { { 41427552, 10835701}, { 41427552,   699996 } },
        { { 41427552,   699996}, { 28664848,   699996 } },
        { { 28664848,   699996}, { 28664848, 10835701 } },
        { { 28664848, 10835701}, { 19280052, 10835701 } },
        { { 19280052, 10835701}, { 27964852,   699996 } },
        { { 27964852,   699996}, { 28664848,        0 } },
        { { 28664848,        0}, { 41427551,        0 } },
        { { 41427551,        0}, { 42127548,   699996 } }
    };

    Lines lines2 {
        { { 42127548,   699996}, { 42127548, 10135750 } },
        { { 42127548, 10135750}, { 50487352, 10135750 } },
        { { 50487352, 10135750}, { 50487352,   699995 } },
        { { 50487352,   699995}, { 51187348,        0 } },
        { { 51187348,        0}, { 51187348, 10835701 } },
        { { 51187348, 10835701}, { 41427552, 10835701 } },
        { { 41427552, 10835701}, { 41427552,   699996 } },
        { { 41427552,   699996}, { 28664848,   699996 } },
        { { 28664848,   699996}, { 28664848, 10835701 } },
        { { 28664848, 10835701}, { 19280052, 10835701 } },
        { { 19280052, 10835701}, { 28664848,        0 } },
        { { 28664848,        0}, { 41427551,        0 } },
        { { 41427551,        0}, { 42127548,   699996 } }
    };

    Lines lines3 {
        { { 42127548,   699996}, { 42127548, 10135750 } },
        { { 42127548, 10135750}, { 50487352, 10135750 } },
        { { 50487352, 10135750}, { 50487352,   699995 } },
        { { 50487352,   699995}, { 51187348,        0 } },
        { { 51187348,        0}, { 51187348, 10835701 } },
        { { 51187348, 10835701}, { 41427552, 10835701 } },
        { { 41427552, 10835701}, { 41427552,   699996 } },
        { { 41427552,   699996}, { 41427551,        0 } },
        { { 41427551,        0}, { 42127548,   699996 } }
    };

    Lines lines4 {
        { { 42127548,   699996}, { 42127548, 10135750 } },
        { { 42127548, 10135750}, { 50487352, 10135750 } },
        { { 50487352, 10135750}, { 50487352,   699995 } },
        { { 50487352,   699995}, { 51187348,        0 } },
        { { 51187348,        0}, { 51187348, 10835701 } },
        { { 51187348, 10835701}, { 41427552, 10835701 } },
        { { 41427552, 10835701}, { 41427551,        0 } },
        { { 41427551,        0}, { 42127548,   699996 } }
    };

    Lines lines = to_lines(Polygon {
        {       0, 10000000},
        {  700000,        1}, // it has to be 1, higher number, zero or -1 work.
        {  700000,  9000000},
        { 9100000,  9000000},
        { 9100000,        0},
        {10000000, 10000000}
        });

    Polygon poly;
    std::mt19937 gen;
    std::uniform_int_distribution<size_t> dist(-100, 100);
    for (size_t i = 0; i < lines.size(); ++ i) {
      Line &l1 = lines[i];
      Line &l2 = lines[(i + 1) % lines.size()];
      REQUIRE(l1.b.x() == l2.a.x());
      REQUIRE(l1.b.y() == l2.a.y());
#if 0
      // Wiggle the points a bit to find out whether this fixes the voronoi diagram for this particular polygon.
      l1.b.x() = (l2.a.x() += dist(gen));
      l1.b.y() = (l2.a.y() += dist(gen));
#endif
      poly.points.emplace_back(l1.a);
    }

    REQUIRE(intersecting_edges({ poly }).empty());

    VD vd;
    construct_voronoi(lines.begin(), lines.end(), &vd);

#ifdef VORONOI_DEBUG_OUT
    dump_voronoi_to_svg(debug_out_path("voronoi-lines.svg").c_str(),
        vd, Points(), lines);
#endif
}

// https://svn.boost.org/trac10/ticket/12903
// division by zero reported, but this issue is most likely a non-issue, as it produces an infinity for the interval of validity
// of the floating point calculation, therefore forcing a recalculation with extended accuracy.
TEST_CASE("Voronoi division by zero 12903", "[Voronoi]")
{
    Points pts { { 1, 1 }, { 3, 1 }, { 1, 3 }, { 3, 3 },
                 { -1, 1 }, { 1, -1 }, { 5, 1 }, { 3, -1 },
                 { -1, 3 }, { 1, 5 }, { 5, 3 }, { 3, 5 } };
    {
        auto pts2 { pts };
        std::sort(pts2.begin(), pts2.end(), [](auto &l, auto &r) { return (l.x() == r.x()) ? l.y() < r.y() : l.x() < r.x(); });
        // No point removed -> no duplicate.
        REQUIRE(std::unique(pts2.begin(), pts2.end()) == pts2.end());
    }

    VD vd;
    construct_voronoi(pts.begin(), pts.end(), &vd);

#ifdef VORONOI_DEBUG_OUT
    // Scale the voronoi vertices and input points, so that the dump_voronoi_to_svg will display them correctly.
    for (auto &pt : vd.vertices()) {
        const_cast<double&>(pt.x()) = scale_(pt.x());
        const_cast<double&>(pt.y()) = scale_(pt.y());
    }
    for (auto &pt : pts)
        pt = Point::new_scale(pt.x(), pt.y());
    dump_voronoi_to_svg(debug_out_path("voronoi-div-by-zero.svg").c_str(), vd, pts, Lines());
#endif
}

// https://svn.boost.org/trac10/ticket/12139
// Funny sample from a dental industry?
// Vojtech confirms this test fails and rightly so, because the input data contain self intersections.
// This test is suppressed.
TEST_CASE("Voronoi NaN coordinates 12139", "[Voronoi][!hide][!mayfail]")
{
    Lines lines = {
        { {  260500,1564400 }, { 261040,1562960 } },
        { {  261040,1562960 }, { 260840,1561780 } },
        { {  260840,1561780 }, { 262620,1561480 } },
        { {  262620,1561480 }, { 263160,1561220 } },
        { {  263160,1561220 }, { 264100,1563259 } },
        { {  264100,1563259 }, { 262380,1566980 } },
        { {  262380,1566980 }, { 260500,1564400 } },
        { {  137520,1851640 }, { 132160,1851100 } },
        { {  132160,1851100 }, { 126460,1848779 } },
        { {  126460,1848779 }, { 123960,1847320 } },
        { {  123960,1847320 }, { 120960,1844559 } },
        { {  120960,1844559 }, { 119640,1843040 } },
        { {  119640,1843040 }, { 118320,1840900 } },
        { {  118320,1840900 }, { 117920,1838120 } },
        { {  117920,1838120 }, { 118219,1833340 } },
        { {  118219,1833340 }, { 116180,1835000 } },
        { {  116180,1835000 }, { 115999,1834820 } },
        { {  115999,1834820 }, { 114240,1836340 } },
        { {  114240,1836340 }, { 112719,1837260 } },
        { {  112719,1837260 }, { 109460,1838239 } },
        { {  109460,1838239 }, { 103639,1837480 } },
        { {  103639,1837480 }, { 99819,1835460 } },
        { {  99819,1835460 }, { 96320,1834260 } },
        { {  96320,1834260 }, { 95339,1834260 } },
        { {  95339,1834260 }, { 93660,1833720 } },
        { {  93660,1833720 }, { 90719,1833300 } },
        { {  90719,1833300 }, { 87860,1831660 } },
        { {  87860,1831660 }, { 84580,1830499 } },
        { {  84580,1830499 }, { 79780,1827419 } },
        { {  79780,1827419 }, { 76020,1824280 } },
        { {  76020,1824280 }, { 73680,1821180 } },
        { {  73680,1821180 }, { 72560,1818960 } },
        { {  72560,1818960 }, { 71699,1817719 } },
        { {  71699,1817719 }, { 70280,1814260 } },
        { {  70280,1814260 }, { 69460,1811060 } },
        { {  69460,1811060 }, { 69659,1807320 } },
        { {  69659,1807320 }, { 69640,1803300 } },
        { {  69640,1803300 }, { 69360,1799780 } },
        { {  69360,1799780 }, { 69320,1796720 } },
        { {  69320,1796720 }, { 69640,1793980 } },
        { {  69640,1793980 }, { 70160,1791780 } },
        { {  70160,1791780 }, { 72460,1784879 } },
        { {  72460,1784879 }, { 74420,1780780 } },
        { {  74420,1780780 }, { 76500,1772899 } },
        { {  76500,1772899 }, { 76760,1769359 } },
        { {  76760,1769359 }, { 76480,1766259 } },
        { {  76480,1766259 }, { 76839,1760360 } },
        { {  76839,1760360 }, { 77539,1756680 } },
        { {  77539,1756680 }, { 80540,1748140 } },
        { {  80540,1748140 }, { 84200,1742619 } },
        { {  84200,1742619 }, { 90900,1735220 } },
        { {  90900,1735220 }, { 94159,1732679 } },
        { {  94159,1732679 }, { 101259,1729559 } },
        { {  101259,1729559 }, { 107299,1727939 } },
        { {  107299,1727939 }, { 110979,1727919 } },
        { {  110979,1727919 }, { 113499,1727240 } },
        { {  113499,1727240 }, { 113619,1727359 } },
        { {  113619,1727359 }, { 114280,1727280 } },
        { {  114280,1727280 }, { 131440,1732560 } },
        { {  131440,1732560 }, { 118140,1727119 } },
        { {  118140,1727119 }, { 117120,1723759 } },
        { {  117120,1723759 }, { 113840,1720660 } },
        { {  113840,1720660 }, { 111399,1716760 } },
        { {  111399,1716760 }, { 109700,1712979 } },
        { {  109700,1712979 }, { 108879,1708400 } },
        { {  108879,1708400 }, { 108060,1696360 } },
        { {  108060,1696360 }, { 110040,1687760 } },
        { {  110040,1687760 }, { 112140,1682480 } },
        { {  112140,1682480 }, { 112540,1681780 } },
        { {  112540,1681780 }, { 115260,1678320 } },
        { {  115260,1678320 }, { 118720,1675320 } },
        { {  118720,1675320 }, { 126100,1670980 } },
        { {  126100,1670980 }, { 132400,1668080 } },
        { {  132400,1668080 }, { 136700,1667440 } },
        { {  136700,1667440 }, { 142440,1667159 } },
        { {  142440,1667159 }, { 143340,1666720 } },
        { {  143340,1666720 }, { 138679,1661319 } },
        { {  138679,1661319 }, { 137240,1657480 } },
        { {  137240,1657480 }, { 136760,1650739 } },
        { {  136760,1650739 }, { 136780,1647339 } },
        { {  136780,1647339 }, { 135940,1644280 } },
        { {  135940,1644280 }, { 136000,1640820 } },
        { {  136000,1640820 }, { 135480,1638020 } },
        { {  135480,1638020 }, { 137060,1634220 } },
        { {  137060,1634220 }, { 136320,1631340 } },
        { {  136320,1631340 }, { 134620,1629700 } },
        { {  134620,1629700 }, { 132460,1628199 } },
        { {  132460,1628199 }, { 132299,1627860 } },
        { {  132299,1627860 }, { 138360,1618020 } },
        { {  138360,1618020 }, { 142440,1611859 } },
        { {  142440,1611859 }, { 143180,1611299 } },
        { {  143180,1611299 }, { 144000,1611259 } },
        { {  144000,1611259 }, { 145960,1612540 } },
        { {  145960,1612540 }, { 146720,1613700 } },
        { {  146720,1613700 }, { 147700,1613539 } },
        { {  147700,1613539 }, { 148520,1614039 } },
        { {  148520,1614039 }, { 149840,1613740 } },
        { {  149840,1613740 }, { 150620,1614079 } },
        { {  150620,1614079 }, { 154760,1612740 } },
        { {  154760,1612740 }, { 159000,1608420 } },
        { {  159000,1608420 }, { 161120,1606780 } },
        { {  161120,1606780 }, { 164060,1605139 } },
        { {  164060,1605139 }, { 168079,1603620 } },
        { {  168079,1603620 }, { 170240,1603400 } },
        { {  170240,1603400 }, { 172400,1603499 } },
        { {  172400,1603499 }, { 194440,1613740 } },
        { {  194440,1613740 }, { 195880,1616460 } },
        { {  195880,1616460 }, { 197060,1618140 } },
        { {  197060,1618140 }, { 198039,1617860 } },
        { {  198039,1617860 }, { 198739,1618900 } },
        { {  198739,1618900 }, { 200259,1619200 } },
        { {  200259,1619200 }, { 201940,1618920 } },
        { {  201940,1618920 }, { 201700,1617139 } },
        { {  201700,1617139 }, { 203860,1618179 } },
        { {  203860,1618179 }, { 203500,1617540 } },
        { {  203500,1617540 }, { 205000,1616579 } },
        { {  205000,1616579 }, { 206780,1615020 } },
        { {  206780,1615020 }, { 210159,1614059 } },
        { {  210159,1614059 }, { 217080,1611080 } },
        { {  217080,1611080 }, { 219200,1611579 } },
        { {  219200,1611579 }, { 223219,1610980 } },
        { {  223219,1610980 }, { 224580,1610540 } },
        { {  224580,1610540 }, { 227460,1611440 } },
        { {  227460,1611440 }, { 229359,1611859 } },
        { {  229359,1611859 }, { 230620,1612580 } },
        { {  230620,1612580 }, { 232340,1614460 } },
        { {  232340,1614460 }, { 232419,1617040 } },
        { {  232419,1617040 }, { 231740,1619480 } },
        { {  231740,1619480 }, { 231880,1624899 } },
        { {  231880,1624899 }, { 231540,1625820 } },
        { {  231540,1625820 }, { 231700,1627079 } },
        { {  231700,1627079 }, { 231320,1628239 } },
        { {  231320,1628239 }, { 231420,1636080 } },
        { {  231420,1636080 }, { 231099,1637200 } },
        { {  231099,1637200 }, { 228660,1643280 } },
        { {  228660,1643280 }, { 227699,1644960 } },
        { {  227699,1644960 }, { 226080,1651140 } },
        { {  226080,1651140 }, { 225259,1653420 } },
        { {  225259,1653420 }, { 225159,1655399 } },
        { {  225159,1655399 }, { 223760,1659260 } },
        { {  223760,1659260 }, { 219860,1666360 } },
        { {  219860,1666360 }, { 219180,1667220 } },
        { {  219180,1667220 }, { 212580,1673680 } },
        { {  212580,1673680 }, { 207880,1676460 } },
        { {  207880,1676460 }, { 205560,1677560 } },
        { {  205560,1677560 }, { 199700,1678920 } },
        { {  199700,1678920 }, { 195280,1679420 } },
        { {  195280,1679420 }, { 193939,1679879 } },
        { {  193939,1679879 }, { 188780,1679440 } },
        { {  188780,1679440 }, { 188100,1679639 } },
        { {  188100,1679639 }, { 186680,1679339 } },
        { {  186680,1679339 }, { 184760,1679619 } },
        { {  184760,1679619 }, { 183520,1681440 } },
        { {  183520,1681440 }, { 183860,1682200 } },
        { {  183860,1682200 }, { 186620,1686120 } },
        { {  186620,1686120 }, { 190380,1688380 } },
        { {  190380,1688380 }, { 192780,1690739 } },
        { {  192780,1690739 }, { 195860,1694839 } },
        { {  195860,1694839 }, { 196620,1696539 } },
        { {  196620,1696539 }, { 197540,1701819 } },
        { {  197540,1701819 }, { 198939,1705699 } },
        { {  198939,1705699 }, { 198979,1711819 } },
        { {  198979,1711819 }, { 198240,1716900 } },
        { {  198240,1716900 }, { 197440,1720139 } },
        { {  197440,1720139 }, { 195340,1724639 } },
        { {  195340,1724639 }, { 194040,1726140 } },
        { {  194040,1726140 }, { 192559,1728239 } },
        { {  192559,1728239 }, { 187780,1732339 } },
        { {  187780,1732339 }, { 182519,1735520 } },
        { {  182519,1735520 }, { 181239,1736140 } },
        { {  181239,1736140 }, { 177340,1737619 } },
        { {  177340,1737619 }, { 175439,1738140 } },
        { {  175439,1738140 }, { 171380,1738880 } },
        { {  171380,1738880 }, { 167860,1739059 } },
        { {  167860,1739059 }, { 166040,1738920 } },
        { {  166040,1738920 }, { 163680,1738539 } },
        { {  163680,1738539 }, { 157660,1736859 } },
        { {  157660,1736859 }, { 154900,1735460 } },
        { {  154900,1735460 }, { 151420,1735159 } },
        { {  151420,1735159 }, { 142100,1736160 } },
        { {  142100,1736160 }, { 140880,1735920 } },
        { {  140880,1735920 }, { 142820,1736859 } },
        { {  142820,1736859 }, { 144080,1737240 } },
        { {  144080,1737240 }, { 144280,1737460 } },
        { {  144280,1737460 }, { 144239,1738120 } },
        { {  144239,1738120 }, { 144980,1739420 } },
        { {  144980,1739420 }, { 146340,1741039 } },
        { {  146340,1741039 }, { 147160,1741720 } },
        { {  147160,1741720 }, { 154260,1745800 } },
        { {  154260,1745800 }, { 156560,1746879 } },
        { {  156560,1746879 }, { 165180,1752679 } },
        { {  165180,1752679 }, { 168240,1755860 } },
        { {  168240,1755860 }, { 170940,1759260 } },
        { {  170940,1759260 }, { 173440,1762079 } },
        { {  173440,1762079 }, { 174540,1764079 } },
        { {  174540,1764079 }, { 176479,1766640 } },
        { {  176479,1766640 }, { 178900,1768960 } },
        { {  178900,1768960 }, { 180819,1772780 } },
        { {  180819,1772780 }, { 181479,1776859 } },
        { {  181479,1776859 }, { 181660,1788499 } },
        { {  181660,1788499 }, { 181460,1791740 } },
        { {  181460,1791740 }, { 181160,1792840 } },
        { {  181160,1792840 }, { 179580,1797180 } },
        { {  179580,1797180 }, { 174620,1808960 } },
        { {  174620,1808960 }, { 174100,1809839 } },
        { {  174100,1809839 }, { 171660,1812419 } },
        { {  171660,1812419 }, { 169639,1813840 } },
        { {  169639,1813840 }, { 168880,1814720 } },
        { {  168880,1814720 }, { 168960,1815980 } },
        { {  168960,1815980 }, { 169979,1819160 } },
        { {  169979,1819160 }, { 170080,1820159 } },
        { {  170080,1820159 }, { 168280,1830540 } },
        { {  168280,1830540 }, { 167580,1832200 } },
        { {  167580,1832200 }, { 165679,1835720 } },
        { {  165679,1835720 }, { 164720,1836819 } },
        { {  164720,1836819 }, { 161840,1841740 } },
        { {  161840,1841740 }, { 159880,1843519 } },
        { {  159880,1843519 }, { 158959,1844120 } },
        { {  158959,1844120 }, { 154960,1847500 } },
        { {  154960,1847500 }, { 152140,1848580 } },
        { {  152140,1848580 }, { 150440,1849520 } },
        { {  150440,1849520 }, { 144940,1850980 } },
        { {  144940,1850980 }, { 138340,1851700 } },
        { {  138340,1851700 }, { 137520,1851640 } },
        { {  606940,1873860 }, { 602860,1872460 } },
        { {  602860,1872460 }, { 600680,1871539 } },
        { {  600680,1871539 }, { 599300,1870640 } },
        { {  599300,1870640 }, { 598120,1869579 } },
        { {  598120,1869579 }, { 594680,1867180 } },
        { {  594680,1867180 }, { 589680,1861460 } },
        { {  589680,1861460 }, { 586300,1855020 } },
        { {  586300,1855020 }, { 584700,1848060 } },
        { {  584700,1848060 }, { 585199,1843499 } },
        { {  585199,1843499 }, { 584000,1842079 } },
        { {  584000,1842079 }, { 582900,1841480 } },
        { {  582900,1841480 }, { 581020,1839899 } },
        { {  581020,1839899 }, { 579440,1838040 } },
        { {  579440,1838040 }, { 577840,1834299 } },
        { {  577840,1834299 }, { 576160,1831859 } },
        { {  576160,1831859 }, { 574540,1828499 } },
        { {  574540,1828499 }, { 572140,1822860 } },
        { {  572140,1822860 }, { 570180,1815219 } },
        { {  570180,1815219 }, { 570080,1812280 } },
        { {  570080,1812280 }, { 570340,1808300 } },
        { {  570340,1808300 }, { 570160,1807119 } },
        { {  570160,1807119 }, { 570140,1804039 } },
        { {  570140,1804039 }, { 571640,1796660 } },
        { {  571640,1796660 }, { 571740,1794680 } },
        { {  571740,1794680 }, { 572279,1794039 } },
        { {  572279,1794039 }, { 575480,1788300 } },
        { {  575480,1788300 }, { 576379,1787419 } },
        { {  576379,1787419 }, { 577020,1786120 } },
        { {  577020,1786120 }, { 578000,1785100 } },
        { {  578000,1785100 }, { 579960,1783720 } },
        { {  579960,1783720 }, { 581420,1782079 } },
        { {  581420,1782079 }, { 585480,1778440 } },
        { {  585480,1778440 }, { 586680,1777079 } },
        { {  586680,1777079 }, { 590520,1774639 } },
        { {  590520,1774639 }, { 592440,1773199 } },
        { {  592440,1773199 }, { 595160,1772260 } },
        { {  595160,1772260 }, { 598079,1770920 } },
        { {  598079,1770920 }, { 601420,1769019 } },
        { {  601420,1769019 }, { 606400,1767280 } },
        { {  606400,1767280 }, { 607320,1766620 } },
        { {  607320,1766620 }, { 605760,1766460 } },
        { {  605760,1766460 }, { 604420,1766780 } },
        { {  604420,1766780 }, { 601660,1766579 } },
        { {  601660,1766579 }, { 597160,1766980 } },
        { {  597160,1766980 }, { 591420,1766720 } },
        { {  591420,1766720 }, { 585360,1765460 } },
        { {  585360,1765460 }, { 578540,1763680 } },
        { {  578540,1763680 }, { 574020,1761599 } },
        { {  574020,1761599 }, { 572520,1760560 } },
        { {  572520,1760560 }, { 570959,1759000 } },
        { {  570959,1759000 }, { 566580,1755620 } },
        { {  566580,1755620 }, { 563820,1752000 } },
        { {  563820,1752000 }, { 563140,1751380 } },
        { {  563140,1751380 }, { 560800,1747899 } },
        { {  560800,1747899 }, { 558640,1742280 } },
        { {  558640,1742280 }, { 557860,1741620 } },
        { {  557860,1741620 }, { 555820,1739099 } },
        { {  555820,1739099 }, { 553920,1737540 } },
        { {  553920,1737540 }, { 551900,1735179 } },
        { {  551900,1735179 }, { 551180,1733880 } },
        { {  551180,1733880 }, { 549540,1729559 } },
        { {  549540,1729559 }, { 548860,1720720 } },
        { {  548860,1720720 }, { 549080,1719099 } },
        { {  549080,1719099 }, { 548200,1714700 } },
        { {  548200,1714700 }, { 547560,1713860 } },
        { {  547560,1713860 }, { 544500,1711259 } },
        { {  544500,1711259 }, { 543939,1709780 } },
        { {  543939,1709780 }, { 544520,1705439 } },
        { {  544520,1705439 }, { 543520,1701519 } },
        { {  543520,1701519 }, { 543920,1699319 } },
        { {  543920,1699319 }, { 546360,1697440 } },
        { {  546360,1697440 }, { 546680,1695419 } },
        { {  546680,1695419 }, { 545600,1694180 } },
        { {  545600,1694180 }, { 543220,1692000 } },
        { {  543220,1692000 }, { 538260,1685139 } },
        { {  538260,1685139 }, { 537540,1683000 } },
        { {  537540,1683000 }, { 537020,1682220 } },
        { {  537020,1682220 }, { 535560,1675940 } },
        { {  535560,1675940 }, { 535940,1671220 } },
        { {  535940,1671220 }, { 536320,1669379 } },
        { {  536320,1669379 }, { 535420,1666400 } },
        { {  535420,1666400 }, { 533540,1664460 } },
        { {  533540,1664460 }, { 530720,1662860 } },
        { {  530720,1662860 }, { 529240,1662260 } },
        { {  529240,1662260 }, { 528780,1659160 } },
        { {  528780,1659160 }, { 528820,1653560 } },
        { {  528820,1653560 }, { 529779,1650900 } },
        { {  529779,1650900 }, { 536760,1640840 } },
        { {  536760,1640840 }, { 540360,1636120 } },
        { {  540360,1636120 }, { 541160,1635380 } },
        { {  541160,1635380 }, { 544719,1629480 } },
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        { {  637760,1879859 }, { 640899,1881500 } },
        { {  640899,1881500 }, { 644220,1883980 } },
        { {  644220,1883980 }, { 643900,1890860 } },
        { {  643900,1890860 }, { 643060,1894160 } },
        { {  643060,1894160 }, { 642459,1900320 } },
        { {  642459,1900320 }, { 642400,1903120 } },
        { {  642400,1903120 }, { 643819,1908519 } },
        { {  643819,1908519 }, { 644700,1912560 } },
        { {  644700,1912560 }, { 644640,1916380 } },
        { {  644640,1916380 }, { 644959,1918600 } },
        { {  644959,1918600 }, { 642540,1925620 } },
        { {  642540,1925620 }, { 642439,1926640 } },
        { {  642439,1926640 }, { 641860,1928300 } },
        { {  641860,1928300 }, { 638700,1932939 } },
        { {  638700,1932939 }, { 634820,1934200 } },
        { {  634820,1934200 }, { 631980,1936539 } },
        { {  631980,1936539 }, { 630160,1940600 } },
        { {  630160,1940600 }, { 627740,1941640 } },
        { {  627740,1941640 }, { 627400,1941660 } },
        { {  627400,1941660 }, { 627100,1941519 } }
    };

#if 0
    // Verify whether two any two non-neighbor line segments intersect. They should not, otherwise the Voronoi builder
    // is not guaranteed to succeed.
    for (size_t i = 0; i < lines.size(); ++ i)
        for (size_t j = i + 1; j < lines.size(); ++ j) {
            Point &ip1 = lines[i].a;
            Point &ip2 = lines[i].b;
            Point &jp1 = lines[j].a;
            Point &jp2 = lines[j].b;
            if (&ip1 != &jp2 && &jp1 != &ip2) {
                REQUIRE(! Slic3r::Geometry::segments_intersect(ip1, ip2, jp1, jp2));
            }
        }
#endif

    VD vd;
    construct_voronoi(lines.begin(), lines.end(), &vd);

    for (const auto& edge : vd.edges())
        if (edge.is_finite()) {
            auto v0 = edge.vertex0();
            auto v1 = edge.vertex1();
            REQUIRE((v0->x() == 0 || std::isnormal(v0->x())));
            REQUIRE((v0->y() == 0 || std::isnormal(v0->y())));
            REQUIRE((v1->x() == 0 || std::isnormal(v1->x())));
            REQUIRE((v1->y() == 0 || std::isnormal(v1->y())));
        }

#ifdef VORONOI_DEBUG_OUT
    dump_voronoi_to_svg(debug_out_path("voronoi-NaNs.svg").c_str(),
        vd, Points(), lines, 0.015);
#endif
}