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BambuStudio/libslic3r/Geometry/VoronoiUtilsCgal.cpp

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#include <CGAL/Exact_predicates_exact_constructions_kernel.h>
#include <CGAL/Arr_segment_traits_2.h>
#include <CGAL/Surface_sweep_2_algorithms.h>
#include "libslic3r/Geometry/Voronoi.hpp"
#include "libslic3r/Geometry/VoronoiUtils.hpp"
#include "libslic3r/Arachne/utils/PolygonsSegmentIndex.hpp"
#include "libslic3r/MultiMaterialSegmentation.hpp"
#include "VoronoiUtilsCgal.hpp"
using VD = Slic3r::Geometry::VoronoiDiagram;
namespace Slic3r::Geometry {
using PolygonsSegmentIndexConstIt = std::vector<Arachne::PolygonsSegmentIndex>::const_iterator;
using LinesIt = Lines::iterator;
using ColoredLinesConstIt = ColoredLines::const_iterator;
// Explicit template instantiation.
template bool VoronoiUtilsCgal::is_voronoi_diagram_planar_angle(const VD &, LinesIt, LinesIt);
template bool VoronoiUtilsCgal::is_voronoi_diagram_planar_angle(const VD &, VD::SegmentIt, VD::SegmentIt);
template bool VoronoiUtilsCgal::is_voronoi_diagram_planar_angle(const VD &, ColoredLinesConstIt, ColoredLinesConstIt);
template bool VoronoiUtilsCgal::is_voronoi_diagram_planar_angle(const VD &, PolygonsSegmentIndexConstIt, PolygonsSegmentIndexConstIt);
// The tangent vector of the parabola is computed based on the Proof of the reflective property.
// https://en.wikipedia.org/wiki/Parabola#Proof_of_the_reflective_property
// https://math.stackexchange.com/q/2439647/2439663#comment5039739_2439663
namespace impl {
using K = CGAL::Simple_cartesian<double>;
using FK = CGAL::Simple_cartesian<CGAL::Interval_nt_advanced>;
using EK = CGAL::Simple_cartesian<CGAL::MP_Float>;
using C2E = CGAL::Cartesian_converter<K, EK>;
using C2F = CGAL::Cartesian_converter<K, FK>;
class Epick : public CGAL::Filtered_kernel_adaptor<CGAL::Type_equality_wrapper<K::Base<Epick>::Type, Epick>, true> {};
template<typename K>
inline typename K::Vector_2 calculate_parabolic_tangent_vector(
// Test point on the parabola, where the tangent will be calculated.
const typename K::Point_2 &p,
// Focus point of the parabola.
const typename K::Point_2 &f,
// Points of a directrix of the parabola.
const typename K::Point_2 &u,
const typename K::Point_2 &v,
// On which side of the parabolic segment endpoints the focus point is, which determines the orientation of the tangent.
const typename K::Orientation &tangent_orientation)
{
using RT = typename K::RT;
using Vector_2 = typename K::Vector_2;
const Vector_2 directrix_vec = v - u;
const RT directrix_vec_sqr_length = CGAL::scalar_product(directrix_vec, directrix_vec);
Vector_2 focus_vec = (f - u) * directrix_vec_sqr_length - directrix_vec * CGAL::scalar_product(directrix_vec, p - u);
Vector_2 tangent_vec = focus_vec.perpendicular(tangent_orientation);
return tangent_vec;
}
template<typename K> struct ParabolicTangentToSegmentOrientationPredicate
{
using Point_2 = typename K::Point_2;
using Vector_2 = typename K::Vector_2;
using Orientation = typename K::Orientation;
using result_type = typename K::Orientation;
result_type operator()(
// Test point on the parabola, where the tangent will be calculated.
const Point_2 &p,
// End of the linear segment (p, q), for which orientation towards the tangent to parabola will be evaluated.
const Point_2 &q,
// Focus point of the parabola.
const Point_2 &f,
// Points of a directrix of the parabola.
const Point_2 &u,
const Point_2 &v,
// On which side of the parabolic segment endpoints the focus point is, which determines the orientation of the tangent.
const Orientation &tangent_orientation) const
{
assert(tangent_orientation == CGAL::Orientation::LEFT_TURN || tangent_orientation == CGAL::Orientation::RIGHT_TURN);
Vector_2 tangent_vec = calculate_parabolic_tangent_vector<K>(p, f, u, v, tangent_orientation);
Vector_2 linear_vec = q - p;
return CGAL::sign(tangent_vec.x() * linear_vec.y() - tangent_vec.y() * linear_vec.x());
}
};
template<typename K> struct ParabolicTangentToParabolicTangentOrientationPredicate
{
using Point_2 = typename K::Point_2;
using Vector_2 = typename K::Vector_2;
using Orientation = typename K::Orientation;
using result_type = typename K::Orientation;
result_type operator()(
// Common point on both parabolas, where the tangent will be calculated.
const Point_2 &p,
// Focus point of the first parabola.
const Point_2 &f_0,
// Points of a directrix of the first parabola.
const Point_2 &u_0,
const Point_2 &v_0,
// On which side of the parabolic segment endpoints the focus point is, which determines the orientation of the tangent.
const Orientation &tangent_orientation_0,
// Focus point of the second parabola.
const Point_2 &f_1,
// Points of a directrix of the second parabola.
const Point_2 &u_1,
const Point_2 &v_1,
// On which side of the parabolic segment endpoints the focus point is, which determines the orientation of the tangent.
const Orientation &tangent_orientation_1) const
{
assert(tangent_orientation_0 == CGAL::Orientation::LEFT_TURN || tangent_orientation_0 == CGAL::Orientation::RIGHT_TURN);
assert(tangent_orientation_1 == CGAL::Orientation::LEFT_TURN || tangent_orientation_1 == CGAL::Orientation::RIGHT_TURN);
Vector_2 tangent_vec_0 = calculate_parabolic_tangent_vector<K>(p, f_0, u_0, v_0, tangent_orientation_0);
Vector_2 tangent_vec_1 = calculate_parabolic_tangent_vector<K>(p, f_1, u_1, v_1, tangent_orientation_1);
return CGAL::sign(tangent_vec_0.x() * tangent_vec_1.y() - tangent_vec_0.y() * tangent_vec_1.x());
}
};
using ParabolicTangentToSegmentOrientationPredicateFiltered = CGAL::Filtered_predicate<ParabolicTangentToSegmentOrientationPredicate<EK>, ParabolicTangentToSegmentOrientationPredicate<FK>, C2E, C2F>;
using ParabolicTangentToParabolicTangentOrientationPredicateFiltered = CGAL::Filtered_predicate<ParabolicTangentToParabolicTangentOrientationPredicate<EK>, ParabolicTangentToParabolicTangentOrientationPredicate<FK>, C2E, C2F>;
} // namespace impl
using ParabolicTangentToSegmentOrientation = impl::ParabolicTangentToSegmentOrientationPredicateFiltered;
using ParabolicTangentToParabolicTangentOrientation = impl::ParabolicTangentToParabolicTangentOrientationPredicateFiltered;
using CGAL_Point = impl::K::Point_2;
inline CGAL_Point to_cgal_point(const VD::vertex_type *pt) { return {pt->x(), pt->y()}; }
inline CGAL_Point to_cgal_point(const Point &pt) { return {pt.x(), pt.y()}; }
inline CGAL_Point to_cgal_point(const Vec2d &pt) { return {pt.x(), pt.y()}; }
inline Linef make_linef(const VD::edge_type &edge)
{
const VD::vertex_type *v0 = edge.vertex0();
const VD::vertex_type *v1 = edge.vertex1();
return {Vec2d(v0->x(), v0->y()), Vec2d(v1->x(), v1->y())};
}
[[maybe_unused]] inline bool is_equal(const VD::vertex_type &vertex_first, const VD::vertex_type &vertex_second) { return vertex_first.x() == vertex_second.x() && vertex_first.y() == vertex_second.y(); }
// FIXME Lukas H.: Also includes parabolic segments.
bool VoronoiUtilsCgal::is_voronoi_diagram_planar_intersection(const VD &voronoi_diagram)
{
using CGAL_E_Point = CGAL::Exact_predicates_exact_constructions_kernel::Point_2;
using CGAL_E_Segment = CGAL::Arr_segment_traits_2<CGAL::Exact_predicates_exact_constructions_kernel>::Curve_2;
auto to_cgal_point = [](const VD::vertex_type &pt) -> CGAL_E_Point { return {pt.x(), pt.y()}; };
assert(std::all_of(voronoi_diagram.edges().cbegin(), voronoi_diagram.edges().cend(),
[](const VD::edge_type &edge) { return edge.color() == 0; }));
std::vector<CGAL_E_Segment> segments;
segments.reserve(voronoi_diagram.num_edges());
for (const VD::edge_type &edge : voronoi_diagram.edges()) {
if (edge.color() != 0)
continue;
if (edge.is_finite() && edge.is_linear() && edge.vertex0() != nullptr && edge.vertex1() != nullptr &&
VoronoiUtils::is_finite(*edge.vertex0()) && VoronoiUtils::is_finite(*edge.vertex1())) {
segments.emplace_back(to_cgal_point(*edge.vertex0()), to_cgal_point(*edge.vertex1()));
edge.color(1);
assert(edge.twin() != nullptr);
edge.twin()->color(1);
}
}
for (const VD::edge_type &edge : voronoi_diagram.edges())
edge.color(0);
std::vector<CGAL_E_Point> intersections_pt;
CGAL::compute_intersection_points(segments.begin(), segments.end(), std::back_inserter(intersections_pt));
return intersections_pt.empty();
}
struct ParabolicSegment
{
const Point focus;
const Line directrix;
// Two points on the parabola;
const Linef segment;
// Indicate if focus point is on the left side or right side relative to parabolic segment endpoints.
const CGAL::Orientation is_focus_on_left;
};
template<typename SegmentIterator>
inline static typename boost::polygon::enable_if<
typename boost::polygon::gtl_if<typename boost::polygon::is_segment_concept<
typename boost::polygon::geometry_concept<typename std::iterator_traits<SegmentIterator>::value_type>::type>::type>::type,
ParabolicSegment>::type
get_parabolic_segment(const VD::edge_type &edge, const SegmentIterator segment_begin, const SegmentIterator segment_end)
{
using Segment = typename std::iterator_traits<SegmentIterator>::value_type;
assert(edge.is_curved());
const VD::cell_type *left_cell = edge.cell();
const VD::cell_type *right_cell = edge.twin()->cell();
const Point focus_pt = VoronoiUtils::get_source_point(*(left_cell->contains_point() ? left_cell : right_cell), segment_begin, segment_end);
const Segment &directrix = VoronoiUtils::get_source_segment(*(left_cell->contains_point() ? right_cell : left_cell), segment_begin, segment_end);
CGAL::Orientation focus_side = CGAL::opposite(CGAL::orientation(to_cgal_point(edge.vertex0()), to_cgal_point(edge.vertex1()), to_cgal_point(focus_pt)));
assert(focus_side == CGAL::Orientation::LEFT_TURN || focus_side == CGAL::Orientation::RIGHT_TURN);
const Point directrix_from = boost::polygon::segment_traits<Segment>::get(directrix, boost::polygon::LOW);
const Point directrix_to = boost::polygon::segment_traits<Segment>::get(directrix, boost::polygon::HIGH);
return {focus_pt, Line(directrix_from, directrix_to), make_linef(edge), focus_side};
}
template<typename SegmentIterator>
inline static typename boost::polygon::enable_if<
typename boost::polygon::gtl_if<typename boost::polygon::is_segment_concept<
typename boost::polygon::geometry_concept<typename std::iterator_traits<SegmentIterator>::value_type>::type>::type>::type,
CGAL::Orientation>::type
orientation_of_two_edges(const VD::edge_type &edge_a, const VD::edge_type &edge_b, const SegmentIterator segment_begin, const SegmentIterator segment_end)
{
assert(is_equal(*edge_a.vertex0(), *edge_b.vertex0()));
CGAL::Orientation orientation;
if (edge_a.is_linear() && edge_b.is_linear()) {
orientation = CGAL::orientation(to_cgal_point(edge_a.vertex0()), to_cgal_point(edge_a.vertex1()), to_cgal_point(edge_b.vertex1()));
} else if (edge_a.is_curved() && edge_b.is_curved()) {
const ParabolicSegment parabolic_a = get_parabolic_segment(edge_a, segment_begin, segment_end);
const ParabolicSegment parabolic_b = get_parabolic_segment(edge_b, segment_begin, segment_end);
orientation = ParabolicTangentToParabolicTangentOrientation{}(to_cgal_point(parabolic_a.segment.a),
to_cgal_point(parabolic_a.focus),
to_cgal_point(parabolic_a.directrix.a),
to_cgal_point(parabolic_a.directrix.b),
parabolic_a.is_focus_on_left,
to_cgal_point(parabolic_b.focus),
to_cgal_point(parabolic_b.directrix.a),
to_cgal_point(parabolic_b.directrix.b),
parabolic_b.is_focus_on_left);
return orientation;
} else {
assert(edge_a.is_curved() != edge_b.is_curved());
const VD::edge_type &linear_edge = edge_a.is_curved() ? edge_b : edge_a;
const VD::edge_type &parabolic_edge = edge_a.is_curved() ? edge_a : edge_b;
const ParabolicSegment parabolic = get_parabolic_segment(parabolic_edge, segment_begin, segment_end);
orientation = ParabolicTangentToSegmentOrientation{}(to_cgal_point(parabolic.segment.a), to_cgal_point(linear_edge.vertex1()),
to_cgal_point(parabolic.focus),
to_cgal_point(parabolic.directrix.a),
to_cgal_point(parabolic.directrix.b),
parabolic.is_focus_on_left);
if (edge_b.is_curved())
orientation = CGAL::opposite(orientation);
}
return orientation;
}
template<typename SegmentIterator>
static typename boost::polygon::enable_if<
typename boost::polygon::gtl_if<typename boost::polygon::is_segment_concept<
typename boost::polygon::geometry_concept<typename std::iterator_traits<SegmentIterator>::value_type>::type>::type>::type,
bool>::type
check_if_three_edges_are_ccw(const VD::edge_type &edge_first,
const VD::edge_type &edge_second,
const VD::edge_type &edge_third,
const SegmentIterator segment_begin,
const SegmentIterator segment_end)
{
assert(is_equal(*edge_first.vertex0(), *edge_second.vertex0()) && is_equal(*edge_second.vertex0(), *edge_third.vertex0()));
CGAL::Orientation orientation = orientation_of_two_edges(edge_first, edge_second, segment_begin, segment_end);
if (orientation == CGAL::Orientation::COLLINEAR) {
// The first two edges are collinear, so the third edge must be on the right side on the first of them.
return orientation_of_two_edges(edge_first, edge_third, segment_begin, segment_end) == CGAL::Orientation::RIGHT_TURN;
} else if (orientation == CGAL::Orientation::LEFT_TURN) {
// CCW oriented angle between vectors (common_pt, pt1) and (common_pt, pt2) is bellow PI.
// So we need to check if test_pt isn't between them.
CGAL::Orientation orientation1 = orientation_of_two_edges(edge_first, edge_third, segment_begin, segment_end);
CGAL::Orientation orientation2 = orientation_of_two_edges(edge_second, edge_third, segment_begin, segment_end);
return (orientation1 != CGAL::Orientation::LEFT_TURN || orientation2 != CGAL::Orientation::RIGHT_TURN);
} else {
assert(orientation == CGAL::Orientation::RIGHT_TURN);
// CCW oriented angle between vectors (common_pt, pt1) and (common_pt, pt2) is upper PI.
// So we need to check if test_pt is between them.
CGAL::Orientation orientation1 = orientation_of_two_edges(edge_first, edge_third, segment_begin, segment_end);
CGAL::Orientation orientation2 = orientation_of_two_edges(edge_second, edge_third, segment_begin, segment_end);
return (orientation1 == CGAL::Orientation::RIGHT_TURN || orientation2 == CGAL::Orientation::LEFT_TURN);
}
}
template<typename SegmentIterator>
typename boost::polygon::enable_if<
typename boost::polygon::gtl_if<typename boost::polygon::is_segment_concept<
typename boost::polygon::geometry_concept<typename std::iterator_traits<SegmentIterator>::value_type>::type>::type>::type,
bool>::type
VoronoiUtilsCgal::is_voronoi_diagram_planar_angle(const VD &voronoi_diagram,
const SegmentIterator segment_begin,
const SegmentIterator segment_end)
{
for (const VD::vertex_type &vertex : voronoi_diagram.vertices()) {
std::vector<const VD::edge_type *> edges;
const VD::edge_type *edge = vertex.incident_edge();
do {
if (edge->is_finite() && edge->vertex0() != nullptr && edge->vertex1() != nullptr && VoronoiUtils::is_finite(*edge->vertex0()) && VoronoiUtils::is_finite(*edge->vertex1()))
edges.emplace_back(edge);
edge = edge->rot_next();
} while (edge != vertex.incident_edge());
// Checking for CCW make sense for three and more edges.
if (edges.size() > 2) {
for (auto edge_it = edges.begin() ; edge_it != edges.end(); ++edge_it) {
const VD::edge_type *prev_edge = edge_it == edges.begin() ? edges.back() : *std::prev(edge_it);
const VD::edge_type *curr_edge = *edge_it;
const VD::edge_type *next_edge = std::next(edge_it) == edges.end() ? edges.front() : *std::next(edge_it);
if (!check_if_three_edges_are_ccw(*prev_edge, *curr_edge, *next_edge, segment_begin, segment_end))
return false;
}
}
}
return true;
}
} // namespace Slic3r::Geometry
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