CGAL::Envelope_diagram_2< EnvTraits > Class Template Reference

#include <CGAL/envelope_3.h>

Inherits from

CGAL::Arrangement_2< EnvTraits >.

Definition

The class-template Envelope_diagram_2 represents the minimization diagram that corresponds to the lower envelope of a set of curves, or the maximization diagram that corresponds to their upper envelope.

It is parameterized by a traits class that must be a model of the EnvelopeTraits_3 concept, and is basically a planar arrangement of \( x\)-monotone curves, as defined by this traits class. These \( x\)-monotone curves are the projections of boundary curves of \( xy\)-monotone surfaces, or the intersection curves between such surfaces, onto the \( xy\)-plane. Thus, it is possible to traverse the envelope diagram using the methods inherited from the Arrangement_2 class.

The envelope diagram extends the arrangement features (namely the vertices, halfedges, and faces), such that each feature stores a container of originators - namely, the \( xy\)-monotone surfaces (instances of the type EnvTraits::Xy_monotone_surface_3) that induce the lower envelope (or the upper envelope, in case of a maximization diagram) over this feature. The envelope diagram provides access methods to these originators.

Examples:

Envelope_3/envelope_planes.cpp, Envelope_3/envelope_spheres.cpp, and Envelope_3/envelope_triangles.cpp.

Classes
class	Face
class	Halfedge
class	Vertex

Types
typedef Envelope_diagram_2< EnvTraits >	Self
typedef Arrangement_2< EnvTraits >	Base
typedef unspecified_type	Surface_const_iterator
	an iterator for the \( xy\)-monotone surfaces that induce a diagram feature. More...

Creation
	Envelope_diagram_2 ()
	constructs an empty diagram containing one unbounded face, which corresponds to the entire plane and has no originators.
	Envelope_diagram_2 (const Self &other)
	copy constructor.
	Envelope_diagram_2 (EnvTraits *traits)
	constructs an empty diagram that uses the given traits instance for performing the geometric predicates.

Additional Inherited Members
Public Types inherited from CGAL::Arrangement_2< EnvTraits >
typedef Traits	Geometry_traits
typedef Default_planar_topology< Geometry_traits, Dcel >::Traits	Topology_traits
typedef Arrangement_on_surface_2< Geometry_traits, Topology_traits >	Base
typedef Base::Point_2	Point_2
typedef Base::X_monotone_curve_2	X_monotone_curve_2
typedef Base::Curve_2	Curve_2
typedef Base::Size	Size
typedef Base::Vertex	Vertex
typedef Base::Halfedge	Halfedge
typedef Base::Face	Face
typedef Base::Vertex_handle	Vertex_handle
typedef Base::Halfedge_handle	Halfedge_handle
typedef Base::Face_handle	Face_handle
typedef Base::Vertex_iterator	Vertex_iterator
typedef Base::Halfedge_iterator	Halfedge_iterator
typedef Base::Edge_iterator	Edge_iterator
typedef Base::Face_iterator	Face_iterator
typedef Base::Unbounded_face_iterator	Unbounded_face_iterator
typedef Base::Halfedge_around_vertex_circulator	Halfedge_around_vertex_circulator
typedef Base::Ccb_halfedge_circulator	Ccb_halfedge_circulator
typedef Base::Hole_iterator	Hole_iterator
typedef Base::Isolated_vertex_iterator	Isolated_vertex_iterator
typedef Base::Vertex_handle	Vertex_const_handle
typedef Base::Halfedge_handle	Halfedge_const_handle
typedef Base::Face_handle	Face_const_handle
typedef Base::Vertex_iterator	Vertex_const_iterator
typedef Base::Halfedge_iterator	Halfedge_const_iterator
typedef Base::Edge_iterator	Edge_const_iterator
typedef Base::Face_iterator	Face_const_iterator
typedef Base::Unbounded_face_iterator	Unbounded_face_const_iterator
typedef Base::Halfedge_around_vertex_circulator	Halfedge_around_const_vertex_circulator
typedef Base::Ccb_halfedge_circulator	Ccb_halfedge_const_circulator
typedef Base::Hole_iterator	Hole_const_iterator
typedef Base::Isolated_vertex_iterator	Isolated_vertex_const_iterator
Public Member Functions inherited from CGAL::Arrangement_2< EnvTraits >
	Arrangement_2 ()
	Arrangement_2 (const Arrangement_2< Traits, Dcel > &other)
	Arrangement_2 (const Traits *traits)
Arrangement_2< Traits, Dcel > &	operator= (other)
void	assign (const Arrangement_2< Traits, Dcel > &other)
void	clear ()
Traits *	traits ()

Member Typedef Documentation

Surface_const_iterator

template<typename EnvTraits >

typedef unspecified_type CGAL::Envelope_diagram_2< EnvTraits >::Surface_const_iterator

an iterator for the \( xy\)-monotone surfaces that induce a diagram feature.

Its value-type is EnvTraits::Xy_monotone_surface_3.