Hyperbolic Surface Triangulations Reference

Vincent Despré, Loïc Dubois, and Monique Teillaud

This package enables building and handling triangulations of closed orientable hyperbolic surfaces. Functionalities are offered such as the Delaunay flip algorithm, and the construction of a portion of the lift of the triangulation in the Poincaré disk model of the hyperbolic plane. Triangulations can be generated by triangulating a convex fundamental domain in the Poincaré disk model. A method is offered that generates such domains in genus two.

Introduced in: CGAL 6
Depends on: Combinatorial Maps
BibTeX: cgal:y-t2-24b
License: GPL
Windows Demo: Hyperbolic Surface Triangulations

Classified Reference Pages

Concepts

• HyperbolicSurfaceTraits_2 is the concept for the template parameter of most classes of the package.
• ComplexWithoutSqrt describes a complex number type that does not use square root.

Classes

• CGAL::Hyperbolic_surface_triangulation_2 represents a triangulation of a closed orientable hyperbolic surface. It offers facilities such as the generation of the triangulation from a convex fundamental domain, the Delaunay flip algorithm, and the construction of a portion of the lift of the triangulation in the hyperbolic plane.
• CGAL::Hyperbolic_fundamental_domain_2 represents a fundamental domain of a closed orientable hyperbolic surface.
• CGAL::Hyperbolic_fundamental_domain_factory_2 is a factory class, whose purpose is to generate some convex domains of surfaces of genus two.
• CGAL::Hyperbolic_isometry_2 represents an isometry in the Poincaré disk model. Facilities are offered to compose isometries, and apply an isometry to a point.

Models for HyperbolicSurfaceTraits_2 and ComplexWithoutSqrt are provided: CGAL::Hyperbolic_surface_traits_2 and CGAL::Complex_without_sqrt.

Modules
	Concepts
	Main Classes
	Traits Classes