CGAL 5.1.3  2D Periodic Hyperbolic Triangulations

CGAL traditionally represents a triangulation via its faces and vertices. We represent a triangulation of the Bolza surface via the canonical representatives of its faces in the hyperbolic plane. This package provides the necessary objects and functions to work with Delaunay triangulations of the Bolza surface.
Each vertex gives access to one of its incident faces, and stores an input point. We additionally allow each vertex to store (temporarily) a hyperbolic translation to facilitate the insertion of new points and the removal of existing vertices.
Each face gives access to its three incident vertices and to its three adjacent faces. We enable a face to store additionally three hyperbolic translations. When applied to the three points stored in the vertices of the face, these translations produce the canonical representative of the face in the hyperbolic plane.
The three vertices of a face are indexed with 0, 1, and 2 in positive (counterclockwise) orientation. The orientation of faces on the Bolza surface is defined as the orientation of their canonical representatives in the hyperbolic plane.
Periodic_4HyperbolicTriangulationTraits_2
adds supplementary requirements to the concept HyperbolicDelaunayTriangulationTraits_2
that are necessary for periodic hyperbolic triangulations.Periodic_4HyperbolicDelaunayTriangulationTraits_2
refines the concept Periodic_4HyperbolicTriangulationTraits_2
by adding requirements necessary for the computation of periodic hyperbolic Delaunay triangulations.Periodic_4HyperbolicTriangulationFaceBase_2
describes the requirements for faces to store hyperbolic translations.Periodic_4HyperbolicTriangulationVertexBase_2
describes the requirements for vertices to store hyperbolic translations.CGAL::Periodic_4_hyperbolic_triangulation_2
gives access to the elements of the triangulation (vertices, edges, and faces), and functionality common to triangulations in general, such as point location. This class does not support insertion or removal of points.CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_2
enables the construction and modification of Delaunay triangulations of the Bolza surface.CGAL::Periodic_4_hyperbolic_Delaunay_triangulation_traits_2
is a model for the concept Periodic_4HyperbolicDelaunayTriangulationTraits_2
.CGAL::Periodic_4_hyperbolic_triangulation_face_base_2
is a model of the concept Periodic_4HyperbolicTriangulationFaceBase_2
and represents a face of the triangulation.CGAL::Periodic_4_hyperbolic_triangulation_vertex_base_2
is a model of the concept Periodic_4HyperbolicTriangulationVertexBase_2
and represents a vertex of the triangulation.CGAL::Hyperbolic_octagon_translation
is a class that represent hyperbolic translations of the fundamental group \(\mathcal G\) of the Bolza surface. Modules  
Concepts  
Main Classes  
Traits Classes  
Vertex and Face Base Classes  
Hyperbolic Translations Classes  