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-bonp2-15a
License: GPL
Windows Demo: 2D Nef Polygons
Common Demo Dlls: dlls

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...

Types
enum	CGAL::Nef_polyhedron_2< T >::Boundary { CGAL::Nef_polyhedron_2< T >::EXCLUDED, CGAL::Nef_polyhedron_2< T >::INCLUDED }
	construction selection. More...
enum	CGAL::Nef_polyhedron_2< T >::Content { CGAL::Nef_polyhedron_2< T >::EMPTY, CGAL::Nef_polyhedron_2< T >::COMPLETE }
	construction selection More...
enum	CGAL::Nef_polyhedron_2< T >::Location_mode { CGAL::Nef_polyhedron_2< T >::DEFAULT, CGAL::Nef_polyhedron_2< T >::NAIVE, CGAL::Nef_polyhedron_2< T >::LMWT }
	selectionflag for the point location mode. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Line
	the oriented lines modeling halfplanes. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Point
	the affine points of the plane. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Direction
	directions in our plane. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Polygons_tag
	tag for calling polygon constructor. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Polylines_tag
	tag for calling polyline constructor. More...
typedef unspecified_type	CGAL::Nef_polyhedron_2< T >::Object_handle
	a generic handle to an object of the underlying plane map. More...

Typedef Documentation

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Direction

directions in our plane.

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Line

the oriented lines modeling halfplanes.

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Object_handle

a generic handle to an object of the underlying plane map.

The kind of object (vertex, halfedge, face) can be determined and the object can be assigned to a corresponding handle by the three functions:

bool assign(Vertex_const_handle& h, Object_handle)

bool assign(Halfedge_const_handle& h, Object_handle)

bool assign(Face_const_handle& h, Object_handle)

where each function returns true iff the assignment to h was done.

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Point

the affine points of the plane.

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Polygons_tag

tag for calling polygon constructor.

template<typename T >

typedef unspecified_type CGAL::Nef_polyhedron_2< T >::Polylines_tag

tag for calling polyline constructor.

Enumeration Type Documentation

template<typename T >

enum CGAL::Nef_polyhedron_2::Boundary

construction selection.

Enumerator
EXCLUDED
INCLUDED

template<typename T >

enum CGAL::Nef_polyhedron_2::Content

construction selection

Enumerator
EMPTY
COMPLETE

template<typename T >

enum CGAL::Nef_polyhedron_2::Location_mode

selectionflag for the point location mode.

LMWT stands for Locally Minimum Weight Triangulation, a locally optimized constrained triangulation where the weight corresponds to the length of the edges of the triangulation.

Enumerator
DEFAULT
NAIVE
LMWT