PolygonOffsetBuilderTraits_2 Concept Reference

Definition

The concept PolygonOffsetBuilderTraits_2 describes the requirements for the geometric traits class required by the algorithm class Polygon_offset_builder_2<Ss,Gt,Polygon_2>.

Has Models:

CGAL::Polygon_offset_builder_traits_2

See Also

CGAL::Polygon_offset_builder_2<Ss,Gt,Polygon_2>

CGAL::Polygon_offset_builder_traits_2<K>

Types
typedef unspecified_type	Kernel
	A model of the Kernel concept.
typedef unspecified_type	FT
	A model of the FieldWithSqrt concept provided by the kernel. More...
typedef unspecified_type	Point_2
	A 2D point type.
typedef unspecified_type	Compare_offset_against_event_time_2
	A predicate object type. More...
typedef unspecified_type	Construct_offset_point_2
	A construction object type. More...
typedef unspecified_type	Construct_ss_vertex_2
	A construction object type. More...
typedef unspecified_type	Construct_ss_edge_2
	A construction object type. More...
typedef unspecified_type	Construct_ss_triedge_2
	A construction object type. More...
boost::tuple< FT, FT >	Vertex
	A pair of (x,y) coordinates representing a 2D Cartesian point.
boost::tuple< Vertex, Vertex >	Edge
	A pair of vertices representing an edge.
boost::tuple< Edge, Edge, Edge >	EdgeTriple
	A triple of edges representing an event.

Member Typedef Documentation

typedef unspecified_type PolygonOffsetBuilderTraits_2::Compare_offset_against_event_time_2

A predicate object type.

Must provide Comparison_result operator()( FT d, EdgeTriple const& et) const, which compares the Euclidean distance d with the event time for et. Such event time is the Euclidean distance at which the offset lines intersect in a single point. The source of such offset lines is given by the 3 oriented lines defined by the edge-triple et

Precondition

et must be an edge-triple corresponding to an event that actually exist (that is, there must exist an offset distance t > 0 at which the offset lines do intersect at a single point.

typedef unspecified_type PolygonOffsetBuilderTraits_2::Construct_offset_point_2

A construction object type.

Must provide boost::optional<Point_2> operator()( FT t, Edge const& x, Edge const& y) const, which constructs the point of intersection of the lines obtained by offsetting the oriented lines given by x and y an Euclidean distance t. If the point cannot be computed, not even approximately (because of overflow for instance), an empty optional must be returned.

Precondition

x and y must intersect in a single point

typedef unspecified_type PolygonOffsetBuilderTraits_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.)

typedef unspecified_type PolygonOffsetBuilderTraits_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.

typedef unspecified_type PolygonOffsetBuilderTraits_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.

typedef unspecified_type PolygonOffsetBuilderTraits_2::FT

A model of the FieldWithSqrt concept provided by the kernel.

This type is used to represent the coordinates of the input points and to specify the desired offset distance.