CGAL 4.7 - 2D Regularized Boolean Set-Operations: Concepts

\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.7 - 2D Regularized Boolean Set-Operations

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2D Regularized Boolean Set-Operations Reference

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## Concepts

concept | ArrangementDirectionalXMonotoneTraits_2

This concept refines the basic arrangement \( x\)-monotone traits concept. A model of this concept is able to handle directed \( x\)-monotone curves that intersect in their interior. Namely, an instance of the `X_monotone_curve_2` type defined by a model of the concept `ArrangementXMonotoneTraits_2` is only required to have a left (lexicographically smaller) endpoint and a right endpoint. If the traits class is also a model of `ArrangementDirectionalXMonotoneTraits_2`, the \( x\)-monotone curve is also required to have a direction, namely one of these two endpoint serves as its source and the other as its target. More...

concept | ArrDirectionalTraits::AreMergeable_2
concept | ArrDirectionalTraits::CompareEndpointsXy_2
concept | ArrDirectionalTraits::ConstructOpposite_2
concept | ArrDirectionalTraits::Intersect_2
concept | ArrDirectionalTraits::Merge_2
concept | ArrDirectionalTraits::Split_2
concept | GeneralPolygon_2
concept | GeneralPolygonSetDcel

A doubly-connected edge-list (Dcel for short) data-structure. It consists of three containers of records: vertices \( V\), halfedges \( E\), and faces \( F\). It maintains the incidence relation among them. The halfedges are ordered in pairs sometimes referred to as twins, such that each halfedge pair represent an edge. More...

concept | GeneralPolygonSetDcelFace
| A face record in a Dcel data structure used by the `General_polygon_set_2` and `Polygon_set_2` class-templates to represent the underlying internal `Arrangement_2` data structure. More...
concept | GeneralPolygonSetTraits_2

This concept defines the minimal set of geometric predicates needed to perform the Boolean-set operations. It refines the directional \( x\)-monotone arrangement-traits concept. In addition to the `Point_2` and `X_monotone_curve_2` types defined in the generalized concept, it defines a type that represents a general polygon and another one that represents general polygon with holes. It also requires operations that operate on these types. More...

concept | GeneralPolygonWithHoles_2
concept | GpsTraitsGeneralPolygon_2
| A model of this concept represents a simple general polygon. More...
concept | GpsTraitsGeneralPolygonWithHoles_2
| A model of this concept represents a general polygon with holes. More...