#include <CGAL/envelope_3.h>

Inherits from

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 Arrangement_2 < Traits_2, Dcel >	Self

typedef unspecified_type	Traits_2

typedef Traits_2::Point_2	Point_2

typedef Traits_2::X_monotone_curve_2	X_monotone_curve_2

typedef Dcel::Size	Size

typedef unspecified_type	Vertex_handle

typedef unspecified_type	Halfedge_handle

typedef unspecified_type	Face_handle

typedef unspecified_type	Vertex_iterator

typedef unspecified_type	Halfedge_iterator

typedef unspecified_type	Edge_iterator

typedef unspecified_type	Face_iterator

typedef unspecified_type	Unbounded_face_iterator

typedef unspecified_type	Halfedge_around_vertex_circulator

typedef unspecified_type	Ccb_halfedge_circulator

typedef unspecified_type	Hole_iterator

typedef unspecified_type	Isolated_vertex_iterator

Public Member Functions inherited from CGAL::Arrangement_2< EnvTraits >
	Arrangement_2 ()

	Arrangement_2 (const Self &other)

	Arrangement_2 (const Traits_2 *traits)

Self &	operator= (other)

void	assign (const Self &other)

void	clear ()

Traits_2 *	get_traits ()

bool	is_empty () const

Size	number_of_vertices () const

Size	number_of_isolated_vertices () const

Vertex_iterator	vertices_begin ()

Vertex_iterator	vertices_end ()

Size	number_of_vertices_at_infinity () const

Size	number_of_halfedges () const

Halfedge_iterator	halfedges_begin ()

Halfedge_iterator	halfedges_end ()

Size	number_of_edges () const

Edge_iterator	edges_begin ()

Edge_iterator	edges_end ()

Face_handle	unbounded_face ()

Size	number_of_faces () const

Face_iterator	faces_begin ()

Face_iterator	faces_end ()

Size	number_of_unbounded_faces () const

Unbounded_face_iterator	unbounded_faces_begin ()

Unbounded_face_iterator	unbounded_faces_end ()

Face_handle	fictitious_face ()

Vertex_handle	non_const_handle (Vertex_const_handle v)

Halfedge_handle	non_const_handle (Halfedge_const_handle e)

Face_handle	non_const_handle (Face_const_handle f)

Vertex_handle	insert_in_face_interior (const Point_2 &p, Face_handle f)

Halfedge_handle	insert_in_face_interior (const X_monotone_curve_2 &c, Face_handle f)

Halfedge_handle	insert_in_face_interior (const X_monotone_curve_2 &c, Halfedge_handle fict_pred1, Halfedge_handle fict_pred2=Halfedge_handle())

Halfedge_handle	insert_from_left_vertex (const X_monotone_curve_2 &c, Vertex_handle v)

Halfedge_handle	insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred)

Halfedge_handle	insert_from_left_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred)

Halfedge_handle	insert_from_right_vertex (const X_monotone_curve_2 &c, Vertex_handle v)

Halfedge_handle	insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred)

Halfedge_handle	insert_from_right_vertex (const X_monotone_curve_2 &c, Halfedge_handle pred, Halfedge_handle fict_pred)

Halfedge_handle	insert_at_vertices (const X_monotone_curve_2 &c, Vertex_handle v1, Vertex_handle v2)

Halfedge_handle	insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Vertex_handle v2)

Halfedge_handle	insert_at_vertices (const X_monotone_curve_2 &c, Halfedge_handle pred1, Halfedge_handle pred2)

Vertex_handle	modify_vertex (Vertex_handle v, const Point_2 &p)

Face_handle	remove_isolated_vertex (Vertex_handle v)

Halfedge_handle	modify_edge (Halfedge_handle e, const X_monotone_curve_2 &c)

Halfedge_handle	split_edge (Halfedge_handle e, const X_monotone_curve_2 &c1, const X_monotone_curve_2 &c2)

Halfedge_handle	merge_edge (Halfedge_handle e1, Halfedge_handle e2, const X_monotone_curve_2 &c)

Face_handle	remove_edge (Halfedge_handle e, bool remove_source=true, bool remove_target=true)

bool	is_valid () const

Member Typedef Documentation

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.

Inherits from

Definition

Classes

Types

Creation

Additional Inherited Members

Member Typedef Documentation