## PolygonOffsetBuilderTraits_2

### 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>.

### Types

 PolygonOffsetBuilderTraits_2::Kernel A model of the Kernel concept. PolygonOffsetBuilderTraits_2::FT A SqrtFieldNumberType provided by the kernel. This type is used to represent the coordinates of the input points and to specify the desired offset distance. PolygonOffsetBuilderTraits_2::Point_2 A 2D point type
 boost::tuple Vertex; A pair of (x,y) coordinates representing a 2D Cartesian point. boost::tuple Edge; A pair of vertices representing an edge boost::tuple EdgeTriple; A triple of edges representing an event

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.

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

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.

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.)

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.