StraightSkeletonBuilderTraits_2

Definition

The concept StraightSkeletonBuilderTraits_2 describes the requirements for the geometric traits class required by the algorithm class Straight_skeleton_builder_2<Gt,Ss>.

Types

StraightSkeletonBuilderTraits_2::Equal_2
	A predicate object type being a model of the Kernel::Equal_2 function object concept.
StraightSkeletonBuilderTraits_2::Left_turn_2
	A predicate object type being a model of the Kernel::LeftTurn_2 function object concept.
StraightSkeletonBuilderTraits_2::Collinear_2
	A predicate object type being a model of the Kernel::Collinear_2 function object concept.
StraightSkeletonBuilderTraits_2::Do_ss_event_exist_2
	A predicate object type. Must provide bool operator()( EdgeTriple const& et) const, which determines if, given the 3 oriented lines defined by the 3 input edges (3 pair of points), there exist an Euclidean distance t $$ 0 for which the corresponding 3 offset lines at t (parallel lines at an Euclidean distance of t) intersect in a single point. Precondition:  each edge in the triple must properly define an oriented line, that is, such points cannot be coincident.
StraightSkeletonBuilderTraits_2::Compare_ss_event_times_2
	A predicate object type. Must provide Comparison_result operator()( EdgeTriple const& x, EdgeTriple const& y) const, which compares the times for the events determined by the edge-triples x and y. The time of an event given by an edge triple (which defines 3 oriented lines) is the Euclidean distance t at which the corresponding offset lines at t intersect in a single point. Precondition:  x and y must be edge-triples corresponding to events that actually exist (as determined by the predicate Exist_sls_event_2).
StraightSkeletonBuilderTraits_2::Compare_ss_event_distance_to_seed_2
	A predicate object type. Must provide Comparison_result operator()( Point_2 const& p, EdgeTriple const& x, EdgeTriple const& y), which compares the Euclidean distance of the points of event for x and y to the point p. The point of an event given by an edge triple (which defines 3 oriented lines) is the intersection point of the 3 corresponding offset lines at the time t of the event. It must also provide Comparison_result operator( EdgeTriple const& seed, EdgeTriple const& x, EdgeTriple const& y)() which makes the same comparison as the first overload but where the seed point is given implicitly as the point of event for seed. Precondition:  seed, x and y must be edge-triples corresponding to events that actually exist (as determined by the predicate Exist_sls_event_2).
StraightSkeletonBuilderTraits_2::Is_ss_event_inside_offset_zone_2
	A predicate object type. Must provide bool operator()( EdgeTriple const& e, EdgeTriple const& zone), which determines if the point of event for e is inside the offset zone defined by the 3 oriented lines given by zone. An offset zone given by 3 oriented lines is the intersection of the halfplanes to the left of each oriented line. Precondition:  e must be an edge-triple corresponding to an event that actually exist (as determined by the predicate Exist_sls_event_2), and the 3 oriented lines given by zone must be well defined (no point-pair can have coincident points).
StraightSkeletonBuilderTraits_2::Are_ss_events_simultaneous_2
	A predicate object type. Must provide bool operator()( EdgeTriple const& x, EdgeTriple const& y), which determines if the events given by x and y are coincident in time and space; that is, both triples of offset lines intersect at the same point and at the same Euclidean distance from their sources. Precondition:  x and y must be edge-triples corresponding to events that actually exist (as determined by the predicate Exist_sls_event_2).
StraightSkeletonBuilderTraits_2::Construct_ss_event_time_and_point_2
	A construction object type. Must provide boost::tuple< boost::optional<FT>, boost::optional<Point_2> > operator()( EdgeTriple const& e), which given the 3 oriented lines defined by the 3 input edges (3 pair of points), returns the Euclidean distance t $$ 0 and intersection point at which the corresponding 3 offset lines at t intersect. If the values cannot be computed, not even approximately (because of overflow for instance), an empty optional must be returned. Precondition:  e must be an edge-triple corresponding to an event that actually exist (as determined by the predicate Exist_sls_event_2).
StraightSkeletonBuilderTraits_2::Construct_ss_vertex_2
	A construction object type. Must provide Vertex operator()( Point_2 const& p), which given a Point_2 p returns a Vertex encapsulating the corresponding (x,y) pair of Cartesian coordinates.
StraightSkeletonBuilderTraits_2::Construct_ss_edge_2
	A construction object type. Must provide Edge operator()( Point_2 const& s, Point_2 const& t), which given source and target points s and t returns an Edge encapsulating the corresponding input segment (in Cartesian coordinates.)
StraightSkeletonBuilderTraits_2::Construct_ss_triedge_2
	A construction object type. Must provide Triedge operator()( Edge const& e0, Edge const& e1, Edge const& e2), which given the 3 edges that define an event, e0, e1 and e2, returns a Triedge encapsulating them.

Has Models

CGAL::Straight_skeleton_builder_traits_2<K>.

See Also

CGAL::Straight_skeleton_builder_2<Gt,Ss>
CGAL::Straight_skeleton_builder_traits_2<K>