CGAL::Envelope_diagram_2< EnvTraits > Class Template Reference

#include <CGAL/envelope_3.h>

Inherits Arrangement_2< EnvTraits >.

Definition

template<typename EnvTraits>
class CGAL::Envelope_diagram_2< EnvTraits >

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.

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.

Member Typedef Documentation

Base

template<typename EnvTraits >

typedef Arrangement_2<EnvTraits> CGAL::Envelope_diagram_2< EnvTraits >::Base

Self

template<typename EnvTraits >

typedef Envelope_diagram_2<EnvTraits> CGAL::Envelope_diagram_2< EnvTraits >::Self

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.

Constructor & Destructor Documentation

Envelope_diagram_2() [1/3]

template<typename EnvTraits >

CGAL::Envelope_diagram_2< EnvTraits >::Envelope_diagram_2

(

)

constructs an empty diagram containing one unbounded face, which corresponds to the entire plane and has no originators.

Envelope_diagram_2() [2/3]

template<typename EnvTraits >

CGAL::Envelope_diagram_2< EnvTraits >::Envelope_diagram_2

(

const Self &

other

)

copy constructor.

Envelope_diagram_2() [3/3]

template<typename EnvTraits >

CGAL::Envelope_diagram_2< EnvTraits >::Envelope_diagram_2

(

EnvTraits *

traits

)

constructs an empty diagram that uses the given traits instance for performing the geometric predicates.