mirror of https://github.com/CGAL/cgal
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This commit is contained in:
Sebastian Morr
parent
6c354e34da
commit
1bc8f28969
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@ -9,40 +9,48 @@ namespace CGAL {
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// Tests whether two polygons P and Q overlap for different translations of Q.
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template <class Kernel_, class Container_>
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class AABB_collision_detector_2 {
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class AABB_collision_detector_2
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{
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public:
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typedef typename Kernel_::Point_2 Point_2;
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typedef typename Kernel_::Vector_2 Vector_2;
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typedef typename CGAL::Polygon_2<Kernel_> Polygon_2;
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typedef typename Polygon_2::Edge_const_iterator Edge_iterator;
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typedef AABB_segment_2_primitive<Kernel_, Edge_iterator, Polygon_2> Tree_segment_2;
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typedef AABB_traits_2<Kernel_, Tree_segment_2> Tree_traits;
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typedef AABB_tree<Tree_traits> Tree_2;
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typedef typename Kernel_::Point_2 Point_2;
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typedef typename Kernel_::Vector_2 Vector_2;
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typedef typename CGAL::Polygon_2<Kernel_> Polygon_2;
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typedef typename Polygon_2::Edge_const_iterator Edge_iterator;
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typedef AABB_segment_2_primitive<Kernel_, Edge_iterator, Polygon_2>
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Tree_segment_2;
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typedef AABB_traits_2<Kernel_, Tree_segment_2> Tree_traits;
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typedef AABB_tree<Tree_traits> Tree_2;
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public:
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AABB_collision_detector_2(const Polygon_2 &p, const Polygon_2 &q)
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: m_stationary_tree((p.edges_begin()), (p.edges_end())), m_translating_tree((q.edges_begin()), (q.edges_end())), m_p(q), m_q(p) {
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AABB_collision_detector_2(const Polygon_2 &p, const Polygon_2 &q)
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: m_stationary_tree((p.edges_begin()), (p.edges_end())),
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m_translating_tree((q.edges_begin()), (q.edges_end())), m_p(q), m_q(p)
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{
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}
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// Returns true iff the polygons' boundaries intersect or one polygon is completely inside of the other one. Q is translated by t.
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bool check_collision(const Point_2 &t)
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{
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if (m_stationary_tree.do_intersect(m_translating_tree, t))
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{
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return true;
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}
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// Returns true iff the polygons' boundaries intersect or one polygon is completely inside of the other one. Q is translated by t.
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bool check_collision(const Point_2 &t) {
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if (m_stationary_tree.do_intersect(m_translating_tree, t)) {
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return true;
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}
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Polygon_2 translated_p = transform(typename Kernel_::Aff_transformation_2(Translation(), Vector_2(ORIGIN, t)), m_p);
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return (translated_p.has_on_bounded_side(*(m_q.vertices_begin())) || m_q.has_on_bounded_side(*(translated_p.vertices_begin())));
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}
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Polygon_2 translated_p = transform(typename Kernel_::Aff_transformation_2(
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Translation(), Vector_2(ORIGIN, t)), m_p);
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return (translated_p.has_on_bounded_side(*(m_q.vertices_begin()))
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|| m_q.has_on_bounded_side(*(translated_p.vertices_begin())));
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}
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private:
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Tree_2 m_stationary_tree;
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Tree_2 m_translating_tree;
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const Polygon_2 &m_p;
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const Polygon_2 &m_q;
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Tree_2 m_stationary_tree;
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Tree_2 m_translating_tree;
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const Polygon_2 &m_p;
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const Polygon_2 &m_q;
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};
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} // namespace CGAL
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@ -5,40 +5,46 @@ namespace CGAL {
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// Wraps around a Segment_2 and provides its iterator as Id
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template <class GeomTraits, class Iterator_, class ContainerType>
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class AABB_segment_2_primitive {
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class AABB_segment_2_primitive
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{
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public:
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typedef Iterator_ Id;
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typedef typename GeomTraits::Segment_2 Datum;
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typedef typename GeomTraits::Point_2 Point;
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typedef ContainerType Container;
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typedef Iterator_ Id;
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typedef typename GeomTraits::Segment_2 Datum;
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typedef typename GeomTraits::Point_2 Point;
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typedef ContainerType Container;
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AABB_segment_2_primitive() {}
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AABB_segment_2_primitive() {}
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AABB_segment_2_primitive(Id it) : m_it(it) {
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}
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AABB_segment_2_primitive(Id it) : m_it(it)
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{
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}
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AABB_segment_2_primitive(const AABB_segment_2_primitive &primitive) {
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m_it = primitive.id();
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}
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AABB_segment_2_primitive(const AABB_segment_2_primitive &primitive)
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{
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m_it = primitive.id();
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}
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const Id &id() const {
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return m_it;
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}
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const Id &id() const
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{
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return m_it;
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}
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const Datum datum() const {
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return *m_it;
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}
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const Datum datum() const
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{
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return *m_it;
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}
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// Return a point on the primitive
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Point reference_point() const {
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return datum().source();
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}
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// Return a point on the primitive
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Point reference_point() const
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{
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return datum().source();
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}
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private:
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Id m_it;
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Id m_it;
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};
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@ -4,164 +4,200 @@
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namespace CGAL {
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template<typename GeomTraits, typename AABB_primitive_>
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class AABB_traits_2 {
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class AABB_traits_2
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{
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public:
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typedef AABB_primitive_ Primitive;
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typedef typename Primitive::Id Id;
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typedef typename Primitive::Datum Datum;
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typedef typename Primitive::Container Container;
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typedef AABB_primitive_ Primitive;
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typedef typename Primitive::Id Id;
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typedef typename Primitive::Datum Datum;
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typedef typename Primitive::Container Container;
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typedef typename GeomTraits::Point_2 Point;
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typedef typename GeomTraits::Vector_2 Vector_2;
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typedef typename CGAL::Bbox_2 Bounding_box;
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typedef typename GeomTraits::Point_2 Point;
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typedef typename GeomTraits::Vector_2 Vector_2;
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typedef typename CGAL::Bbox_2 Bounding_box;
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typedef typename std::pair<Object, Id> Object_and_primitive_id;
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typedef typename std::pair<Point, Id> Point_and_primitive_id;
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typedef typename std::pair<Object, Id> Object_and_primitive_id;
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typedef typename std::pair<Point, Id> Point_and_primitive_id;
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// Types for AABB_tree
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Point_2 Point_3;
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typedef typename GeomTraits::Circle_2 Sphere_3;
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typedef typename GeomTraits::Iso_rectangle_2 Iso_cuboid_3;
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typedef typename GeomTraits::Construct_center_2 Construct_center_3;
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typedef typename GeomTraits::Construct_iso_rectangle_2 Construct_iso_cuboid_3;
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typedef typename GeomTraits::Construct_min_vertex_2 Construct_min_vertex_3;
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typedef typename GeomTraits::Construct_max_vertex_2 Construct_max_vertex_3;
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typedef typename GeomTraits::Compute_squared_radius_2 Compute_squared_radius_3;
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typedef typename GeomTraits::Cartesian_const_iterator_2 Cartesian_const_iterator_3;
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typedef typename GeomTraits::Construct_cartesian_const_iterator_2 Construct_cartesian_const_iterator_3;
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// Types for AABB_tree
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typedef typename GeomTraits::FT FT;
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typedef typename GeomTraits::Point_2 Point_3;
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typedef typename GeomTraits::Circle_2 Sphere_3;
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typedef typename GeomTraits::Iso_rectangle_2 Iso_cuboid_3;
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typedef typename GeomTraits::Construct_center_2 Construct_center_3;
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typedef typename GeomTraits::Construct_iso_rectangle_2 Construct_iso_cuboid_3;
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typedef typename GeomTraits::Construct_min_vertex_2 Construct_min_vertex_3;
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typedef typename GeomTraits::Construct_max_vertex_2 Construct_max_vertex_3;
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typedef typename GeomTraits::Compute_squared_radius_2 Compute_squared_radius_3;
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typedef typename GeomTraits::Cartesian_const_iterator_2
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Cartesian_const_iterator_3;
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typedef typename GeomTraits::Construct_cartesian_const_iterator_2
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Construct_cartesian_const_iterator_3;
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AABB_traits_2(const Point &translation_point): m_translation_point(translation_point) {
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m_interval_x = Interval_nt<true>(to_interval(translation_point.x()));
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m_interval_y = Interval_nt<true>(to_interval(translation_point.y()));
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};
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AABB_traits_2(const Point &translation_point): m_translation_point(
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translation_point)
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{
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m_interval_x = Interval_nt<true>(to_interval(translation_point.x()));
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m_interval_y = Interval_nt<true>(to_interval(translation_point.y()));
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};
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AABB_traits_2() {
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m_translation_point = Point(0, 0);
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m_interval_x = Interval_nt<true>(0);
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m_interval_y = Interval_nt<true>(0);
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};
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AABB_traits_2()
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{
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m_translation_point = Point(0, 0);
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m_interval_x = Interval_nt<true>(0);
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m_interval_y = Interval_nt<true>(0);
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};
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Interval_nt<true> get_interval_x() const {
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return m_interval_x;
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Interval_nt<true> get_interval_x() const
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{
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return m_interval_x;
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}
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Interval_nt<true> get_interval_y() const
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{
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return m_interval_y;
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}
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Point get_translation_point() const
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{
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return m_translation_point;
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}
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// Put the n/2 smallest primitives in the front, the n/2 largest primitives
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// in the back. They are compared along the bbox' longest axis.
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class Sort_primitives
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{
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public:
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template<typename PrimitiveIterator>
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void operator()(PrimitiveIterator first,
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PrimitiveIterator beyond,
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const Bounding_box &bbox) const
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{
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PrimitiveIterator middle = first + (beyond - first) / 2;
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if (bbox.xmax()-bbox.xmin() >= bbox.ymax()-bbox.ymin())
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{
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std::nth_element(first, middle, beyond, less_x); // sort along x
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}
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else
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{
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std::nth_element(first, middle, beyond, less_y); // sort along y
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}
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}
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};
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Sort_primitives sort_primitives_object() const
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{
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return Sort_primitives();
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}
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// Computes the bounding box of a set of primitives
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class Compute_bbox
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{
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public:
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template<typename ConstPrimitiveIterator>
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Bounding_box operator()(ConstPrimitiveIterator first,
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ConstPrimitiveIterator beyond) const
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{
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Bounding_box bbox = first->datum().bbox();
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for (++first; first != beyond; ++first)
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{
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bbox = bbox + first->datum().bbox();
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}
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return bbox;
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}
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};
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Compute_bbox compute_bbox_object() const
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{
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return Compute_bbox();
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}
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class Do_intersect
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{
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private:
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AABB_traits_2 *m_traits;
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public:
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Do_intersect(AABB_traits_2 *_traits): m_traits(_traits) {}
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bool operator()(const Bounding_box &q, const Bounding_box &bbox) const
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{
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Interval_nt<true> x1 = Interval_nt<true>(q.xmin(), q.xmax());
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Interval_nt<true> y1 = Interval_nt<true>(q.ymin(), q.ymax());
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Interval_nt<true> x2 = Interval_nt<true>(bbox.xmin(),
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bbox.xmax()) + m_traits->get_interval_x();
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Interval_nt<true> y2 = Interval_nt<true>(bbox.ymin(),
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bbox.ymax()) + m_traits->get_interval_y();
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return x1.do_overlap(x2) && y1.do_overlap(y2);
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}
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Interval_nt<true> get_interval_y() const {
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return m_interval_y;
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bool operator()(const Primitive &q, const Bounding_box &bbox) const
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{
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Interval_nt<true> x1 = Interval_nt<true>(q.datum().bbox().xmin(),
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q.datum().bbox().xmax());
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Interval_nt<true> y1 = Interval_nt<true>(q.datum().bbox().ymin(),
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q.datum().bbox().ymax());
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Interval_nt<true> x2 = Interval_nt<true>(bbox.xmin(),
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bbox.xmax()) + m_traits->get_interval_x();
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Interval_nt<true> y2 = Interval_nt<true>(bbox.ymin(),
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bbox.ymax()) + m_traits->get_interval_y();
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return x1.do_overlap(x2) && y1.do_overlap(y2);
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}
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Point get_translation_point() const {
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return m_translation_point;
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bool operator()(const Bounding_box &q, const Primitive &pr) const
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{
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Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(
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Translation(),
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Vector_2(ORIGIN, m_traits->get_translation_point())));
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return do_overlap(q, tr_pr.bbox());
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}
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// Put the n/2 smallest primitives in the front, the n/2 largest primitives
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// in the back. They are compared along the bbox' longest axis.
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class Sort_primitives {
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public:
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template<typename PrimitiveIterator>
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void operator()(PrimitiveIterator first,
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PrimitiveIterator beyond,
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const Bounding_box &bbox) const {
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PrimitiveIterator middle = first + (beyond - first) / 2;
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bool operator()(const Primitive &q, const Primitive &pr) const
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{
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Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(
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Translation(), Vector_2(ORIGIN, m_traits->get_translation_point())));
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if (bbox.xmax()-bbox.xmin() >= bbox.ymax()-bbox.ymin()) {
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std::nth_element(first, middle, beyond, less_x); // sort along x
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} else {
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std::nth_element(first, middle, beyond, less_y); // sort along y
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}
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}
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};
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if (!do_overlap(q.datum().bbox(), tr_pr.bbox()))
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{
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return false;
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}
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Sort_primitives sort_primitives_object() const {
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return Sort_primitives();
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return do_intersect(q.datum(), tr_pr);
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}
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};
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// Computes the bounding box of a set of primitives
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class Compute_bbox {
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public:
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template<typename ConstPrimitiveIterator>
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Bounding_box operator()(ConstPrimitiveIterator first,
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ConstPrimitiveIterator beyond) const {
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Bounding_box bbox = first->datum().bbox();
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for (++first; first != beyond; ++first) {
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bbox = bbox + first->datum().bbox();
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}
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return bbox;
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}
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};
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Compute_bbox compute_bbox_object() const {
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return Compute_bbox();
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}
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class Do_intersect {
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private:
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AABB_traits_2 *m_traits;
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public:
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Do_intersect(AABB_traits_2 *_traits): m_traits(_traits) {}
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bool operator()(const Bounding_box &q, const Bounding_box &bbox) const {
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Interval_nt<true> x1 = Interval_nt<true>(q.xmin(), q.xmax());
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Interval_nt<true> y1 = Interval_nt<true>(q.ymin(), q.ymax());
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Interval_nt<true> x2 = Interval_nt<true>(bbox.xmin(), bbox.xmax()) + m_traits->get_interval_x();
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Interval_nt<true> y2 = Interval_nt<true>(bbox.ymin(), bbox.ymax()) + m_traits->get_interval_y();
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return x1.do_overlap(x2) && y1.do_overlap(y2);
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}
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bool operator()(const Primitive &q, const Bounding_box &bbox) const {
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Interval_nt<true> x1 = Interval_nt<true>(q.datum().bbox().xmin(), q.datum().bbox().xmax());
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Interval_nt<true> y1 = Interval_nt<true>(q.datum().bbox().ymin(), q.datum().bbox().ymax());
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Interval_nt<true> x2 = Interval_nt<true>(bbox.xmin(), bbox.xmax()) + m_traits->get_interval_x();
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Interval_nt<true> y2 = Interval_nt<true>(bbox.ymin(), bbox.ymax()) + m_traits->get_interval_y();
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return x1.do_overlap(x2) && y1.do_overlap(y2);
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}
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bool operator()(const Bounding_box &q, const Primitive &pr) const {
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Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(Translation(),
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Vector_2(ORIGIN, m_traits->get_translation_point())));
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return do_overlap(q, tr_pr.bbox());
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}
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bool operator()(const Primitive &q, const Primitive &pr) const {
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Datum tr_pr = pr.datum().transform(typename GeomTraits::Aff_transformation_2(Translation(), Vector_2(ORIGIN, m_traits->get_translation_point())));
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if (!do_overlap(q.datum().bbox(), tr_pr.bbox())) {
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return false;
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}
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return do_intersect(q.datum(), tr_pr);
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}
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};
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|
||||
Do_intersect do_intersect_object() {
|
||||
return Do_intersect(this);
|
||||
}
|
||||
Do_intersect do_intersect_object()
|
||||
{
|
||||
return Do_intersect(this);
|
||||
}
|
||||
|
||||
private:
|
||||
|
||||
Point m_translation_point;
|
||||
Interval_nt<true> m_interval_x;
|
||||
Interval_nt<true> m_interval_y;
|
||||
Point m_translation_point;
|
||||
Interval_nt<true> m_interval_x;
|
||||
Interval_nt<true> m_interval_y;
|
||||
|
||||
// Comparison functions
|
||||
static bool less_x(const Primitive &pr1, const Primitive &pr2) {
|
||||
return pr1.reference_point().x() < pr2.reference_point().x();
|
||||
}
|
||||
// Comparison functions
|
||||
static bool less_x(const Primitive &pr1, const Primitive &pr2)
|
||||
{
|
||||
return pr1.reference_point().x() < pr2.reference_point().x();
|
||||
}
|
||||
|
||||
static bool less_y(const Primitive &pr1, const Primitive &pr2) {
|
||||
return pr1.reference_point().y() < pr2.reference_point().y();
|
||||
}
|
||||
static bool less_y(const Primitive &pr1, const Primitive &pr2)
|
||||
{
|
||||
return pr1.reference_point().y() < pr2.reference_point().y();
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
|
|
|||
|
|
@ -16,331 +16,393 @@
|
|||
namespace CGAL {
|
||||
|
||||
template <class Kernel_, class Container_>
|
||||
class Minkowski_sum_by_reduced_convolution_2 {
|
||||
class Minkowski_sum_by_reduced_convolution_2
|
||||
{
|
||||
|
||||
private:
|
||||
|
||||
typedef Kernel_ Kernel;
|
||||
typedef Container_ Container;
|
||||
typedef Kernel_ Kernel;
|
||||
typedef Container_ Container;
|
||||
|
||||
// Basic types:
|
||||
typedef CGAL::Polygon_2<Kernel, Container> Polygon_2;
|
||||
typedef typename Kernel::Point_2 Point_2;
|
||||
typedef typename Kernel::Vector_2 Vector_2;
|
||||
typedef typename Kernel::Direction_2 Direction_2;
|
||||
typedef typename Kernel::Triangle_2 Triangle_2;
|
||||
typedef typename Kernel::FT FT;
|
||||
// Basic types:
|
||||
typedef CGAL::Polygon_2<Kernel, Container> Polygon_2;
|
||||
typedef typename Kernel::Point_2 Point_2;
|
||||
typedef typename Kernel::Vector_2 Vector_2;
|
||||
typedef typename Kernel::Direction_2 Direction_2;
|
||||
typedef typename Kernel::Triangle_2 Triangle_2;
|
||||
typedef typename Kernel::FT FT;
|
||||
|
||||
// Segment-related types:
|
||||
typedef Arr_segment_traits_2<Kernel> Traits_2;
|
||||
typedef typename Traits_2::X_monotone_curve_2 Segment_2;
|
||||
typedef std::list<Segment_2> Segment_list;
|
||||
typedef Arr_default_dcel<Traits_2> Dcel;
|
||||
typedef std::pair<int, int> State;
|
||||
// Segment-related types:
|
||||
typedef Arr_segment_traits_2<Kernel> Traits_2;
|
||||
typedef typename Traits_2::X_monotone_curve_2 Segment_2;
|
||||
typedef std::list<Segment_2> Segment_list;
|
||||
typedef Arr_default_dcel<Traits_2> Dcel;
|
||||
typedef std::pair<int, int> State;
|
||||
|
||||
// Arrangement-related types:
|
||||
typedef Arrangement_with_history_2<Traits_2, Dcel> Arrangement_history_2;
|
||||
typedef typename Arrangement_history_2::Halfedge_handle Halfedge_handle;
|
||||
typedef typename Arrangement_history_2::Face_iterator Face_iterator;
|
||||
typedef typename Arrangement_history_2::Face_handle Face_handle;
|
||||
typedef typename Arrangement_history_2::Ccb_halfedge_circulator Ccb_halfedge_circulator;
|
||||
typedef typename Arrangement_history_2::Originating_curve_iterator Originating_curve_iterator;
|
||||
// Arrangement-related types:
|
||||
typedef Arrangement_with_history_2<Traits_2, Dcel> Arrangement_history_2;
|
||||
typedef typename Arrangement_history_2::Halfedge_handle Halfedge_handle;
|
||||
typedef typename Arrangement_history_2::Face_iterator Face_iterator;
|
||||
typedef typename Arrangement_history_2::Face_handle Face_handle;
|
||||
typedef typename Arrangement_history_2::Ccb_halfedge_circulator
|
||||
Ccb_halfedge_circulator;
|
||||
typedef typename Arrangement_history_2::Originating_curve_iterator
|
||||
Originating_curve_iterator;
|
||||
|
||||
// Function object types:
|
||||
typename Kernel::Construct_translated_point_2 f_add;
|
||||
typename Kernel::Construct_vector_2 f_vector;
|
||||
typename Kernel::Construct_direction_2 f_direction;
|
||||
typename Kernel::Orientation_2 f_orientation;
|
||||
typename Kernel::Compare_xy_2 f_compare_xy;
|
||||
typename Kernel::Counterclockwise_in_between_2 f_ccw_in_between;
|
||||
// Function object types:
|
||||
typename Kernel::Construct_translated_point_2 f_add;
|
||||
typename Kernel::Construct_vector_2 f_vector;
|
||||
typename Kernel::Construct_direction_2 f_direction;
|
||||
typename Kernel::Orientation_2 f_orientation;
|
||||
typename Kernel::Compare_xy_2 f_compare_xy;
|
||||
typename Kernel::Counterclockwise_in_between_2 f_ccw_in_between;
|
||||
|
||||
public:
|
||||
|
||||
Minkowski_sum_by_reduced_convolution_2() {
|
||||
// Obtain kernel functors
|
||||
Kernel ker;
|
||||
f_add = ker.construct_translated_point_2_object();
|
||||
f_vector = ker.construct_vector_2_object();
|
||||
f_direction = ker.construct_direction_2_object();
|
||||
f_orientation = ker.orientation_2_object();
|
||||
f_compare_xy = ker.compare_xy_2_object();
|
||||
f_ccw_in_between = ker.counterclockwise_in_between_2_object();
|
||||
Minkowski_sum_by_reduced_convolution_2()
|
||||
{
|
||||
// Obtain kernel functors
|
||||
Kernel ker;
|
||||
f_add = ker.construct_translated_point_2_object();
|
||||
f_vector = ker.construct_vector_2_object();
|
||||
f_direction = ker.construct_direction_2_object();
|
||||
f_orientation = ker.orientation_2_object();
|
||||
f_compare_xy = ker.compare_xy_2_object();
|
||||
f_ccw_in_between = ker.counterclockwise_in_between_2_object();
|
||||
}
|
||||
|
||||
template <class OutputIterator>
|
||||
void operator()(const Polygon_2 &pgn1, const Polygon_2 &pgn2,
|
||||
Polygon_2 &outer_boundary, OutputIterator holes) const
|
||||
{
|
||||
|
||||
Timer timer; // TODO: remove when optimization is done
|
||||
timer.start();
|
||||
|
||||
CGAL_precondition(pgn1.is_simple());
|
||||
CGAL_precondition(pgn2.is_simple());
|
||||
CGAL_precondition(pgn1.orientation() == COUNTERCLOCKWISE);
|
||||
CGAL_precondition(pgn2.orientation() == COUNTERCLOCKWISE);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Preconditions" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Initialize collision detector. It operates on pgn2 and on the inversed pgn1:
|
||||
const Polygon_2 inversed_pgn1 = transform(Aff_transformation_2<Kernel>(SCALING,
|
||||
-1), pgn1);
|
||||
AABB_collision_detector_2<Kernel, Container> collision_detector(pgn2,
|
||||
inversed_pgn1);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: AABB init" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Compute the reduced convolution
|
||||
Segment_list reduced_convolution;
|
||||
build_reduced_convolution(pgn1, pgn2, reduced_convolution);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Convolution" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Insert the segments into an arrangement
|
||||
Arrangement_history_2 arr;
|
||||
insert(arr, reduced_convolution.begin(), reduced_convolution.end());
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Arrangement" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Trace the outer loop and put it in 'outer_boundary'
|
||||
get_outer_loop(arr, outer_boundary);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Outer Loop" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Check for each face whether it is a hole in the M-sum. If it is, add it to 'holes'.
|
||||
for (Face_iterator face = arr.faces_begin(); face != arr.faces_end(); ++face)
|
||||
{
|
||||
handle_face(arr, face, holes, collision_detector);
|
||||
}
|
||||
|
||||
template <class OutputIterator>
|
||||
void operator()(const Polygon_2 &pgn1, const Polygon_2 &pgn2,
|
||||
Polygon_2 &outer_boundary, OutputIterator holes) const {
|
||||
|
||||
Timer timer; // TODO: remove when optimization is done
|
||||
timer.start();
|
||||
|
||||
CGAL_precondition(pgn1.is_simple());
|
||||
CGAL_precondition(pgn2.is_simple());
|
||||
CGAL_precondition(pgn1.orientation() == COUNTERCLOCKWISE);
|
||||
CGAL_precondition(pgn2.orientation() == COUNTERCLOCKWISE);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Preconditions" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Initialize collision detector. It operates on pgn2 and on the inversed pgn1:
|
||||
const Polygon_2 inversed_pgn1 = transform(Aff_transformation_2<Kernel>(SCALING, -1), pgn1);
|
||||
AABB_collision_detector_2<Kernel, Container> collision_detector(pgn2, inversed_pgn1);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: AABB init" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Compute the reduced convolution
|
||||
Segment_list reduced_convolution;
|
||||
build_reduced_convolution(pgn1, pgn2, reduced_convolution);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Convolution" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Insert the segments into an arrangement
|
||||
Arrangement_history_2 arr;
|
||||
insert(arr, reduced_convolution.begin(), reduced_convolution.end());
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Arrangement" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Trace the outer loop and put it in 'outer_boundary'
|
||||
get_outer_loop(arr, outer_boundary);
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Outer Loop" << std::endl;
|
||||
timer.reset();
|
||||
timer.start();
|
||||
|
||||
// Check for each face whether it is a hole in the M-sum. If it is, add it to 'holes'.
|
||||
for (Face_iterator face = arr.faces_begin(); face != arr.faces_end(); ++face) {
|
||||
handle_face(arr, face, holes, collision_detector);
|
||||
}
|
||||
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Holes" << std::endl;
|
||||
}
|
||||
timer.stop();
|
||||
std::cout << timer.time() << " s: Holes" << std::endl;
|
||||
}
|
||||
|
||||
private:
|
||||
|
||||
// Builds the reduced convolution using a fiber grid approach. For each
|
||||
// starting vertex, try to add two outgoing next states. If a visited
|
||||
// vertex is reached, then do not explore further. This is a BFS-like
|
||||
// iteration beginning from each vertex in the first column of the fiber
|
||||
// grid.
|
||||
void build_reduced_convolution(const Polygon_2 &pgn1, const Polygon_2 &pgn2, Segment_list &reduced_convolution) const {
|
||||
unsigned int n1 = pgn1.size();
|
||||
unsigned int n2 = pgn2.size();
|
||||
// Builds the reduced convolution using a fiber grid approach. For each
|
||||
// starting vertex, try to add two outgoing next states. If a visited
|
||||
// vertex is reached, then do not explore further. This is a BFS-like
|
||||
// iteration beginning from each vertex in the first column of the fiber
|
||||
// grid.
|
||||
void build_reduced_convolution(const Polygon_2 &pgn1, const Polygon_2 &pgn2,
|
||||
Segment_list &reduced_convolution) const
|
||||
{
|
||||
unsigned int n1 = pgn1.size();
|
||||
unsigned int n2 = pgn2.size();
|
||||
|
||||
// Init the direcions of both polygons
|
||||
std::vector<Direction_2> p1_dirs = directions_of_polygon(pgn1);
|
||||
std::vector<Direction_2> p2_dirs = directions_of_polygon(pgn2);
|
||||
// Init the direcions of both polygons
|
||||
std::vector<Direction_2> p1_dirs = directions_of_polygon(pgn1);
|
||||
std::vector<Direction_2> p2_dirs = directions_of_polygon(pgn2);
|
||||
|
||||
// Contains states that were already visited
|
||||
boost::unordered_set<State> visited_states;
|
||||
// Contains states that were already visited
|
||||
boost::unordered_set<State> visited_states;
|
||||
|
||||
// Init the queue with vertices from the first column
|
||||
std::queue<State> state_queue;
|
||||
for (int i = n1-1; i >= 0; --i) {
|
||||
state_queue.push(State(i, 0));
|
||||
}
|
||||
|
||||
while (state_queue.size() > 0) {
|
||||
State curr_state = state_queue.front();
|
||||
state_queue.pop();
|
||||
|
||||
int i1 = curr_state.first;
|
||||
int i2 = curr_state.second;
|
||||
|
||||
// If this state was already visited, skip it
|
||||
if (visited_states.count(curr_state) > 0) {
|
||||
continue;
|
||||
}
|
||||
visited_states.insert(curr_state);
|
||||
|
||||
int next_i1 = (i1+1) % n1;
|
||||
int next_i2 = (i2+1) % n2;
|
||||
int prev_i1 = (n1+i1-1) % n1;
|
||||
int prev_i2 = (n2+i2-1) % n2;
|
||||
|
||||
// Try two transitions: From (i,j) to (i+1,j) and to (i,j+1). Add
|
||||
// the respective segments, if they are in the reduced convolution.
|
||||
for(int step_in_pgn1 = 0; step_in_pgn1 <= 1; step_in_pgn1++) {
|
||||
int new_i1, new_i2;
|
||||
if (step_in_pgn1) {
|
||||
new_i1 = next_i1;
|
||||
new_i2 = i2;
|
||||
} else {
|
||||
new_i1 = i1;
|
||||
new_i2 = next_i2;
|
||||
}
|
||||
|
||||
// If the segment's direction lies counterclockwise in between
|
||||
// the other polygon's vertex' ingoing and outgoing directions,
|
||||
// the segment belongs to the full convolution.
|
||||
bool belongs_to_convolution;
|
||||
if (step_in_pgn1) {
|
||||
belongs_to_convolution = f_ccw_in_between(p1_dirs[i1], p2_dirs[prev_i2], p2_dirs[i2]) ||
|
||||
p1_dirs[i1] == p2_dirs[i2];
|
||||
} else {
|
||||
belongs_to_convolution = f_ccw_in_between(p2_dirs[i2], p1_dirs[prev_i1], p1_dirs[i1]) ||
|
||||
p2_dirs[i2] == p1_dirs[prev_i1];
|
||||
}
|
||||
|
||||
if (belongs_to_convolution) {
|
||||
state_queue.push(State(new_i1, new_i2));
|
||||
|
||||
// Only edges added to convex vertices can be on the M-sum's boundary.
|
||||
// This filter only leaves the *reduced* convolution.
|
||||
bool convex;
|
||||
if (step_in_pgn1) {
|
||||
convex = is_convex(pgn2[prev_i2], pgn2[i2], pgn2[next_i2]);
|
||||
} else {
|
||||
convex = is_convex(pgn1[prev_i1], pgn1[i1], pgn1[next_i1]);
|
||||
}
|
||||
|
||||
if (convex) {
|
||||
Point_2 start_point = get_point(i1, i2, pgn1, pgn2);
|
||||
Point_2 end_point = get_point(new_i1, new_i2, pgn1, pgn2);
|
||||
reduced_convolution.push_back(Segment_2(start_point, end_point));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
// Init the queue with vertices from the first column
|
||||
std::queue<State> state_queue;
|
||||
for (int i = n1-1; i >= 0; --i)
|
||||
{
|
||||
state_queue.push(State(i, 0));
|
||||
}
|
||||
|
||||
// Returns a sorted list of the polygon's edges
|
||||
std::vector<Direction_2> directions_of_polygon(const Polygon_2 &p) const {
|
||||
std::vector<Direction_2> directions;
|
||||
unsigned int n = p.size();
|
||||
while (state_queue.size() > 0)
|
||||
{
|
||||
State curr_state = state_queue.front();
|
||||
state_queue.pop();
|
||||
|
||||
for (int i = 0; i < n-1; ++i) {
|
||||
directions.push_back(f_direction(f_vector(p[i], p[i+1])));
|
||||
int i1 = curr_state.first;
|
||||
int i2 = curr_state.second;
|
||||
|
||||
// If this state was already visited, skip it
|
||||
if (visited_states.count(curr_state) > 0)
|
||||
{
|
||||
continue;
|
||||
}
|
||||
visited_states.insert(curr_state);
|
||||
|
||||
int next_i1 = (i1+1) % n1;
|
||||
int next_i2 = (i2+1) % n2;
|
||||
int prev_i1 = (n1+i1-1) % n1;
|
||||
int prev_i2 = (n2+i2-1) % n2;
|
||||
|
||||
// Try two transitions: From (i,j) to (i+1,j) and to (i,j+1). Add
|
||||
// the respective segments, if they are in the reduced convolution.
|
||||
for(int step_in_pgn1 = 0; step_in_pgn1 <= 1; step_in_pgn1++)
|
||||
{
|
||||
int new_i1, new_i2;
|
||||
if (step_in_pgn1)
|
||||
{
|
||||
new_i1 = next_i1;
|
||||
new_i2 = i2;
|
||||
}
|
||||
directions.push_back(f_direction(f_vector(p[n-1], p[0])));
|
||||
|
||||
return directions;
|
||||
}
|
||||
|
||||
bool is_convex(const Point_2 &prev, const Point_2 &curr, const Point_2 &next) const {
|
||||
return f_orientation(prev, curr, next) == LEFT_TURN;
|
||||
}
|
||||
|
||||
// Returns the point corresponding to a state (i,j).
|
||||
Point_2 get_point(int i1, int i2, const Polygon_2 &pgn1, const Polygon_2 &pgn2) const {
|
||||
|
||||
return f_add(pgn1[i1], Vector_2(Point_2(ORIGIN), pgn2[i2]));
|
||||
}
|
||||
|
||||
// Put the outer loop of the arrangement in 'outer_boundary'
|
||||
void get_outer_loop(Arrangement_history_2 &arr, Polygon_2 &outer_boundary) const {
|
||||
Ccb_halfedge_circulator circ_start = *(arr.unbounded_face()->holes_begin());
|
||||
Ccb_halfedge_circulator circ = circ_start;
|
||||
|
||||
do {
|
||||
outer_boundary.push_back(circ->source()->point());
|
||||
} while (--circ != circ_start);
|
||||
}
|
||||
|
||||
// Check whether the face is on the M-sum's border. Add it to 'holes' if it is.
|
||||
template <class OutputIterator>
|
||||
void handle_face(const Arrangement_history_2 &arr, const Face_handle face, OutputIterator holes, AABB_collision_detector_2<Kernel, Container> &collision_detector) const {
|
||||
|
||||
// If the face contains holes, it can't be on the Minkowski sum's border
|
||||
if (face->holes_begin() != face->holes_end()) {
|
||||
return;
|
||||
else
|
||||
{
|
||||
new_i1 = i1;
|
||||
new_i2 = next_i2;
|
||||
}
|
||||
|
||||
Ccb_halfedge_circulator start = face->outer_ccb();
|
||||
Ccb_halfedge_circulator circ = start;
|
||||
|
||||
// The face needs to be orientable
|
||||
do {
|
||||
if (!do_original_edges_have_same_direction(arr, circ)) {
|
||||
return;
|
||||
}
|
||||
} while (++circ != start);
|
||||
|
||||
// When the reversed polygon 1, translated by a point inside of this face, collides with polygon 2, this cannot be a hole
|
||||
Point_2 inner_point = get_point_in_face(face);
|
||||
if (collision_detector.check_collision(inner_point)) {
|
||||
return;
|
||||
// If the segment's direction lies counterclockwise in between
|
||||
// the other polygon's vertex' ingoing and outgoing directions,
|
||||
// the segment belongs to the full convolution.
|
||||
bool belongs_to_convolution;
|
||||
if (step_in_pgn1)
|
||||
{
|
||||
belongs_to_convolution = f_ccw_in_between(p1_dirs[i1], p2_dirs[prev_i2],
|
||||
p2_dirs[i2]) ||
|
||||
p1_dirs[i1] == p2_dirs[i2];
|
||||
}
|
||||
else
|
||||
{
|
||||
belongs_to_convolution = f_ccw_in_between(p2_dirs[i2], p1_dirs[prev_i1],
|
||||
p1_dirs[i1]) ||
|
||||
p2_dirs[i2] == p1_dirs[prev_i1];
|
||||
}
|
||||
|
||||
// At this point, the face is a real hole, add it to 'holes'
|
||||
Polygon_2 pgn_hole;
|
||||
circ = start;
|
||||
if (belongs_to_convolution)
|
||||
{
|
||||
state_queue.push(State(new_i1, new_i2));
|
||||
|
||||
do {
|
||||
pgn_hole.push_back(circ->source()->point());
|
||||
} while (--circ != start);
|
||||
// Only edges added to convex vertices can be on the M-sum's boundary.
|
||||
// This filter only leaves the *reduced* convolution.
|
||||
bool convex;
|
||||
if (step_in_pgn1)
|
||||
{
|
||||
convex = is_convex(pgn2[prev_i2], pgn2[i2], pgn2[next_i2]);
|
||||
}
|
||||
else
|
||||
{
|
||||
convex = is_convex(pgn1[prev_i1], pgn1[i1], pgn1[next_i1]);
|
||||
}
|
||||
|
||||
*holes = pgn_hole;
|
||||
++holes;
|
||||
if (convex)
|
||||
{
|
||||
Point_2 start_point = get_point(i1, i2, pgn1, pgn2);
|
||||
Point_2 end_point = get_point(new_i1, new_i2, pgn1, pgn2);
|
||||
reduced_convolution.push_back(Segment_2(start_point, end_point));
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// Returns a sorted list of the polygon's edges
|
||||
std::vector<Direction_2> directions_of_polygon(const Polygon_2 &p) const
|
||||
{
|
||||
std::vector<Direction_2> directions;
|
||||
unsigned int n = p.size();
|
||||
|
||||
for (int i = 0; i < n-1; ++i)
|
||||
{
|
||||
directions.push_back(f_direction(f_vector(p[i], p[i+1])));
|
||||
}
|
||||
directions.push_back(f_direction(f_vector(p[n-1], p[0])));
|
||||
|
||||
return directions;
|
||||
}
|
||||
|
||||
bool is_convex(const Point_2 &prev, const Point_2 &curr,
|
||||
const Point_2 &next) const
|
||||
{
|
||||
return f_orientation(prev, curr, next) == LEFT_TURN;
|
||||
}
|
||||
|
||||
// Returns the point corresponding to a state (i,j).
|
||||
Point_2 get_point(int i1, int i2, const Polygon_2 &pgn1,
|
||||
const Polygon_2 &pgn2) const
|
||||
{
|
||||
|
||||
return f_add(pgn1[i1], Vector_2(Point_2(ORIGIN), pgn2[i2]));
|
||||
}
|
||||
|
||||
// Put the outer loop of the arrangement in 'outer_boundary'
|
||||
void get_outer_loop(Arrangement_history_2 &arr,
|
||||
Polygon_2 &outer_boundary) const
|
||||
{
|
||||
Ccb_halfedge_circulator circ_start = *(arr.unbounded_face()->holes_begin());
|
||||
Ccb_halfedge_circulator circ = circ_start;
|
||||
|
||||
do
|
||||
{
|
||||
outer_boundary.push_back(circ->source()->point());
|
||||
}
|
||||
while (--circ != circ_start);
|
||||
}
|
||||
|
||||
// Check whether the face is on the M-sum's border. Add it to 'holes' if it is.
|
||||
template <class OutputIterator>
|
||||
void handle_face(const Arrangement_history_2 &arr, const Face_handle face,
|
||||
OutputIterator holes, AABB_collision_detector_2<Kernel, Container>
|
||||
&collision_detector) const
|
||||
{
|
||||
|
||||
// If the face contains holes, it can't be on the Minkowski sum's border
|
||||
if (face->holes_begin() != face->holes_end())
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
// Check whether the convolution's original edge(s) had the same direction as the arrangement's half edge
|
||||
bool do_original_edges_have_same_direction(const Arrangement_history_2 &arr, const Halfedge_handle he) const {
|
||||
Originating_curve_iterator segment_itr;
|
||||
Ccb_halfedge_circulator start = face->outer_ccb();
|
||||
Ccb_halfedge_circulator circ = start;
|
||||
|
||||
for (segment_itr = arr.originating_curves_begin(he); segment_itr != arr.originating_curves_end(he); ++segment_itr) {
|
||||
if (f_compare_xy(segment_itr->source(), segment_itr->target()) == (Comparison_result)he->direction()) {
|
||||
return false;
|
||||
}
|
||||
}
|
||||
// The face needs to be orientable
|
||||
do
|
||||
{
|
||||
if (!do_original_edges_have_same_direction(arr, circ))
|
||||
{
|
||||
return;
|
||||
}
|
||||
}
|
||||
while (++circ != start);
|
||||
|
||||
return true;
|
||||
// When the reversed polygon 1, translated by a point inside of this face, collides with polygon 2, this cannot be a hole
|
||||
Point_2 inner_point = get_point_in_face(face);
|
||||
if (collision_detector.check_collision(inner_point))
|
||||
{
|
||||
return;
|
||||
}
|
||||
|
||||
// Return a point in the face's interior by finding a diagonal
|
||||
Point_2 get_point_in_face(const Face_handle face) const {
|
||||
Ccb_halfedge_circulator current_edge = face->outer_ccb();
|
||||
Ccb_halfedge_circulator next_edge = current_edge;
|
||||
next_edge++;
|
||||
// At this point, the face is a real hole, add it to 'holes'
|
||||
Polygon_2 pgn_hole;
|
||||
circ = start;
|
||||
|
||||
Point_2 a, v, b;
|
||||
|
||||
// Move over the face's vertices until a convex corner is encountered:
|
||||
do {
|
||||
a = current_edge->source()->point();
|
||||
v = current_edge->target()->point();
|
||||
b = next_edge->target()->point();
|
||||
|
||||
current_edge++;
|
||||
next_edge++;
|
||||
} while (!is_convex(a, v, b));
|
||||
|
||||
Triangle_2 ear(a, v, b);
|
||||
FT min_distance = -1;
|
||||
Point_2 min_q;
|
||||
|
||||
// Of the remaining vertices, find the one inside of the "ear" with minimal distance to v:
|
||||
while (++next_edge != current_edge) {
|
||||
Point_2 q = next_edge->target()->point();
|
||||
if (ear.has_on_bounded_side(q)) {
|
||||
FT distance = squared_distance(q, v);
|
||||
if (min_distance == -1 || distance < min_distance) {
|
||||
min_distance = distance;
|
||||
min_q = q;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// If there was no vertex inside of the ear, return it's centroid.
|
||||
// Otherwise, return a point between v and min_q.
|
||||
if (min_distance == -1) {
|
||||
return centroid(ear);
|
||||
} else {
|
||||
return midpoint(v, min_q);
|
||||
}
|
||||
do
|
||||
{
|
||||
pgn_hole.push_back(circ->source()->point());
|
||||
}
|
||||
while (--circ != start);
|
||||
|
||||
*holes = pgn_hole;
|
||||
++holes;
|
||||
}
|
||||
|
||||
// Check whether the convolution's original edge(s) had the same direction as the arrangement's half edge
|
||||
bool do_original_edges_have_same_direction(const Arrangement_history_2 &arr,
|
||||
const Halfedge_handle he) const
|
||||
{
|
||||
Originating_curve_iterator segment_itr;
|
||||
|
||||
for (segment_itr = arr.originating_curves_begin(he);
|
||||
segment_itr != arr.originating_curves_end(he); ++segment_itr)
|
||||
{
|
||||
if (f_compare_xy(segment_itr->source(),
|
||||
segment_itr->target()) == (Comparison_result)he->direction())
|
||||
{
|
||||
return false;
|
||||
}
|
||||
}
|
||||
|
||||
return true;
|
||||
}
|
||||
|
||||
// Return a point in the face's interior by finding a diagonal
|
||||
Point_2 get_point_in_face(const Face_handle face) const
|
||||
{
|
||||
Ccb_halfedge_circulator current_edge = face->outer_ccb();
|
||||
Ccb_halfedge_circulator next_edge = current_edge;
|
||||
next_edge++;
|
||||
|
||||
Point_2 a, v, b;
|
||||
|
||||
// Move over the face's vertices until a convex corner is encountered:
|
||||
do
|
||||
{
|
||||
a = current_edge->source()->point();
|
||||
v = current_edge->target()->point();
|
||||
b = next_edge->target()->point();
|
||||
|
||||
current_edge++;
|
||||
next_edge++;
|
||||
}
|
||||
while (!is_convex(a, v, b));
|
||||
|
||||
Triangle_2 ear(a, v, b);
|
||||
FT min_distance = -1;
|
||||
Point_2 min_q;
|
||||
|
||||
// Of the remaining vertices, find the one inside of the "ear" with minimal distance to v:
|
||||
while (++next_edge != current_edge)
|
||||
{
|
||||
Point_2 q = next_edge->target()->point();
|
||||
if (ear.has_on_bounded_side(q))
|
||||
{
|
||||
FT distance = squared_distance(q, v);
|
||||
if (min_distance == -1 || distance < min_distance)
|
||||
{
|
||||
min_distance = distance;
|
||||
min_q = q;
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
// If there was no vertex inside of the ear, return it's centroid.
|
||||
// Otherwise, return a point between v and min_q.
|
||||
if (min_distance == -1)
|
||||
{
|
||||
return centroid(ear);
|
||||
}
|
||||
else
|
||||
{
|
||||
return midpoint(v, min_q);
|
||||
}
|
||||
}
|
||||
};
|
||||
|
||||
} // namespace CGAL
|
||||
|
|
|
|||
Loading…
Reference in New Issue