CGAL 5.1.2 - 3D Envelopes
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This package consists of functions that compute the lower (or upper) envelope of a set of arbitrary surfaces in 3D. The output is represented as an 2D envelope diagram - a planar subdivision such that the identity of the surfaces that induce the envelope over each diagram cell is unique.
CGAL::lower_envelope_3
CGAL::upper_envelope_3
CGAL::lower_envelope_xy_monotone_3
CGAL::upper_envelope_xy_monotone_3
CGAL::Envelope_diagram_2<EnvTraits>
CGAL::Env_triangle_traits_3<Kernel>
CGAL::Env_sphere_traits_3<ConicTraits>
CGAL::Env_plane_traits_3<Kernel>
CGAL::Env_surface_data_traits_3<Traits,XyData,SData,Cnv>
Modules | |
Concepts | |
Classes | |
class | CGAL::Env_plane_traits_3< Kernel > |
The traits class Env_plane_traits_3 models the EnvelopeTraits_3 concept, and is used for the construction of lower and upper envelopes of planes and half planes in the space. More... | |
class | CGAL::Env_sphere_traits_3< ConicTraits > |
The traits class Env_sphere_traits_3 models the EnvelopeTraits_3 concept, and is used for the construction of lower and upper envelopes of spheres. More... | |
class | CGAL::Env_surface_data_traits_3< Traits, XyData, SData, Cnv > |
The class Env_surface_data_traits_3 is a model of the EnvelopeTraits_3 concept and serves as a decorator class that allows the extension of the surfaces defined by the base traits-class (the Traits parameter), which serves as a geometric traits-class (a model of the EnvelopeTraits_3 concept), with extraneous (non-geometric) data fields. More... | |
class | CGAL::Env_triangle_traits_3< Kernel > |
The traits class Env_triangle_traits_3 models the EnvelopeTraits_3 concept, and is used for the construction of lower and upper envelopes of triangles in the space. More... | |
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. More... | |
Functions | |
template<class InputIterator , class Traits > | |
void | CGAL::lower_envelope_3 (InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag) |
Computes the lower envelope of a set of surfaces in \( \mathbb{R}^3\), as given by the range [begin, end) . More... | |
template<class InputIterator , class Traits > | |
void | CGAL::lower_envelope_xy_monotone_3 (InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag) |
Computes the lower envelope of a set of \( xy\)-monotone surfaces in \( \mathbb{R}^3\), as given by the range [begin, end) . More... | |
template<class InputIterator , class Traits > | |
void | CGAL::upper_envelope_3 (InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag) |
Computes the upper envelope of a set of surfaces in \( \mathbb{R}^3\), as given by the range [begin, end) . More... | |
template<class InputIterator , class Traits > | |
void | CGAL::upper_envelope_xy_monotone_3 (InputIterator begin, InputIterator end, Envelope_diagram_2< Traits > &diag) |
Computes the upper envelope of a set of \( xy\)-monotone surfaces in \( \mathbb{R}^3\), as given by the range [begin, end) . More... | |
void CGAL::lower_envelope_3 | ( | InputIterator | begin, |
InputIterator | end, | ||
Envelope_diagram_2< Traits > & | diag | ||
) |
#include <CGAL/envelope_3.h>
Computes the lower envelope of a set of surfaces in \( \mathbb{R}^3\), as given by the range [begin, end)
.
The lower envelope is represented using the output minimization diagram diag
.
Traits | must be a model of EnvelopeTraits_3 . InputIterator must be an input iterator with value type Traits::Surface_3 . |
void CGAL::lower_envelope_xy_monotone_3 | ( | InputIterator | begin, |
InputIterator | end, | ||
Envelope_diagram_2< Traits > & | diag | ||
) |
#include <CGAL/envelope_3.h>
Computes the lower envelope of a set of \( xy\)-monotone surfaces in \( \mathbb{R}^3\), as given by the range [begin, end)
.
The lower envelope is represented using the output minimization diagram diag
.
Traits | must be a model of EnvelopeTraits_3 . InputIterator must be an input iterator with value type Traits::Xy_monotone_surface_3 . |
void CGAL::upper_envelope_3 | ( | InputIterator | begin, |
InputIterator | end, | ||
Envelope_diagram_2< Traits > & | diag | ||
) |
#include <CGAL/envelope_3.h>
Computes the upper envelope of a set of surfaces in \( \mathbb{R}^3\), as given by the range [begin, end)
.
The upper envelope is represented using the output maximization diagram diag
.
Traits | must be a model of EnvelopeTraits_3 . InputIterator must be an input iterator with value type Traits::Surface_3 . |
void CGAL::upper_envelope_xy_monotone_3 | ( | InputIterator | begin, |
InputIterator | end, | ||
Envelope_diagram_2< Traits > & | diag | ||
) |
#include <CGAL/envelope_3.h>
Computes the upper envelope of a set of \( xy\)-monotone surfaces in \( \mathbb{R}^3\), as given by the range [begin, end)
.
The lower envelope is represented using the output maximization diagram diag
.
Traits | must be a model of EnvelopeTraits_3 . InputIterator must be an input iterator with value type Traits::Xy_monotone_surface_3 . |