SPAR/AIModule/BWTA/vendors/CGAL/CGAL/Arr_spherical_gaussian_map_3/Arr_polyhedral_sgm_traits.h File Reference

#include <CGAL/basic.h>
#include <CGAL/Arr_geodesic_arc_on_sphere_traits_2.h>

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Classes
class	Arr_polyhedral_sgm_traits< T_Kernel >

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Detailed Description

A traits class-template for constructing and maintaining Gaussian maps (also known as normal diagrams) of polytopes in 3D. It is parameterized by a (linear) 3D geometry a kernel. It serves two main purposes as follows: 1. It models the concept ArrangementTraits, and as such, it handles arcs, the type of which are present in Gaussian maps of polytopes in 3D, that is, arcs of great circles on 2S, also known as geodesic arcs, and, 2. It provides a type of point in 3D used to represent vertices of polytopes, and an operation that adds two points of this type. This traits is used to instantiate a type that represents an arrangement induced by geodesic arcs embedded on a sphere, where each face of the arrangement stores the corresponding vertex of the polytope. This type, in turn, represents a Gaussian map, which is a unique dual representation of a polytope.