\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 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 1 2 3]

CGAL |
Env_plane_traits_3 | 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
Env_sphere_traits_3 | 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
Env_surface_data_traits_3 | 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
Surface_3 | The `Surface_3` class nested within the surface-data traits extends the `Base_traits_3::Surface_3` type with an extra data field
Xy_monotone_surface_3 | The `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
Env_triangle_traits_3 | 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
Envelope_diagram_2 | 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
Face |
Halfedge |
Vertex |
EnvelopeTraits_3 | This 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