CGAL 5.5.1 - 2D Straight Skeleton and Polygon Offsetting
PolygonOffsetBuilderTraits_2 Concept Reference

## Definition

Refines:
StraightSkeletonBuilderTraits_2

The concept PolygonOffsetBuilderTraits_2 describes the requirements for the geometric traits class required by the algorithm class CGAL::Polygon_offset_builder_2.

Has Models:
CGAL::Polygon_offset_builder_traits_2
CGAL::Polygon_offset_builder_2<Ss,Traits,Container>

## Types

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...

Compare_offset_against_event_time_2 compare_offset_against_event_time_2_object () const

Construct_offset_point_2 construct_offset_point_2_object () const

## ◆ Compare_offset_against_event_time_2

A predicate object type.

Must provide Comparison_result operator()( FT d, const Trisegment_2_ptr& 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 three 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.

## ◆ Construct_offset_point_2

A construction object type.

Must provide boost::optional<Point_2> operator()(const FT& t, const Segment_2& e0, Segment_2_with_ID const& e1, const Trisegment_2_ptr& et) const, which constructs the point of intersection of the lines obtained by offsetting the oriented lines given by e0 and e0 an Euclidean distance t.

If e0 and e1 are collinear, if seed is not specified (nullptr), then the midpoint should be returned, otherwise, the event point of et should be returned.

If the point cannot be computed, not even approximately (because of overflow for instance), an empty optional must be returned.

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.