\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)
CGAL 4.6 - 3D Envelopes
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Class and Concept List
Here is the list of all concepts and classes of this package. Classes are inside the namespace CGAL. Concepts are in the global namespace.
[detail level 123]
oNCGAL
|oCEnv_plane_traits_3The 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
|oCEnv_sphere_traits_3The traits class Env_sphere_traits_3 models the EnvelopeTraits_3 concept, and is used for the construction of lower and upper envelopes of spheres
|oCEnv_surface_data_traits_3The 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
||oCSurface_3The Surface_3 class nested within the surface-data traits extends the Base_traits_3::Surface_3 type with an extra data field
||\CXy_monotone_surface_3The Xy_monotone_surface_3 class nested within the surface-data traits extends the Base_traits_3::Xy_monotone_surface_3 type with an extra data field
|oCEnv_triangle_traits_3The 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
|\CEnvelope_diagram_2The 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
| oCFace
| oCHalfedge
| \CVertex
\CEnvelopeTraits_3This concept defines the minimal set of geometric predicates and operations needed to compute the envelope of a set of arbitrary surfaces in \( \mathbb{R}^3\). It refines the ArrangementXMonotoneTraits_2 concept. In addition to the Point_2 and X_monotone_curve_2 types and the Has_boundary_category category tag listed in the base concept, it also lists the Surface_3 and Xy_monotone_surface_3 types, which represent arbitrary surfaces and \( xy\)-monotone surfaces, respectively, and some constructions and predicates on these types. Note however, that these operations usually involve the projection of 3D objects onto the \( xy\)-plane