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

CGAL 4.3 - 2D Boolean Operations on Nef Polygons

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2D Boolean Operations on Nef Polygons Reference

##

Michael Seel
A Nef polygon is any set that can be obtained from a finite set of open halfspaces by set complement and set intersection operations. Due to the fact that all other binary set operations like union, difference and symmetric difference can be reduced to intersection and complement calculations, Nef polygons are also closed under those operations. Apart from the set complement operation there are more topological unary set operations that are closed in the domain of Nef polygons interior, boundary, and closure.

Introduced in: CGAL 2.3
BibTeX: cgal:s-bonp2-13b
License: GPL
Demo: 2D Nef Polygons

## Classified Reference Pages

## Concepts

- `ExtendedKernelTraits_2`

## Classes

- `CGAL::Extended_cartesian<FT>`
- `CGAL::Extended_homogeneous<RT>`
- `CGAL::Filtered_extended_homogeneous<RT>`
- `CGAL::Nef_polyhedron_2<T>`
- `CGAL::Nef_polyhedron_2<T>::Explorer`
- `CGAL::Nef_polyhedron_2<T>::Topological_explorer`

## Modules
| Concepts

## Classes
class | CGAL::Extended_cartesian< FT >
| The class `Extended_cartesian` serves as a traits class for the class `Nef_polyhedron_2<T>`. More...
class | CGAL::Extended_homogeneous< RT >
| The class `Extended_homogeneous` serves as a traits class for the class `Nef_polyhedron_2<T>`. More...
class | CGAL::Filtered_extended_homogeneous< RT >
| The class `Filtered_extended_homogeneous` serves as a traits class for the class `Nef_polyhedron_2<T>`. More...
class | CGAL::Nef_polyhedron_2< T >
| An instance of data type `Nef_polyhedron_2<T>` is a subset of the plane that is the result of forming complements and intersections starting from a finite set `H` of halfspaces. More...
class | CGAL::Nef_polyhedron_2< T >::Topological_explorer
| An instance `D` of the data type `Topological_explorer` is a decorator for interfacing the topological structure of a plane map `P` (read-only). More...
class | CGAL::Nef_polyhedron_2< T >::Explorer
| a decorator to examine the underlying plane map. More...