An Extension Of Cgal To The Oriented Projective Plane T2 And Its Dynamic Visualization System

The oriented projective plane T2 is an extension of the Euclidean plane E2 and comprises a number of advantages for algorithm design and implementation. We have extended the Computational Geometry Algorithms Library (CGAL) to allow for the implementation of geometric primitives and algorithms. The present video illustrates both the extension of a few algorithms to T2 under CGAL and a dynamic visualization system (T2Viewer) built specially for displaying the spherical and planar models of T2.380381De Rezende, P.J., Stolfi, J., (1994) Fundamentos de Geometria, Computational, , UFPE-DI, IV Escola de ComputaçãoDe Rezende, P.J., Westrupp, R.B., An optimal algorithm to construct all voronoi diagrams for k nearest neighbor search in T2 (1999) Proceedings of the XII SIBGRAPI, pp. 7-15(2002) CGAL Developers' Manual, , http://www.cgal.org, NovemberGon, C.N., (1996) Computação Exata em Geometria Projetiva Orientada e Tratamento de Degerierações, , Master's thesis, UNICAMPOliveira, A.G., (2004) Implementação Do Piano Projetivo Orientado Na Biblioteca CGAL, , Master's thesis, UNICAMPPinto, G.A., (1998) Generalizações Do Diagrama de Voronoi Construídas Através de Cônicas No Piano Projetivo Orientado, , Master's thesis, UNICAMPSelmi-Dei, F.P., (2005) Um Visualizador Para Uma Extensão de CGAL Ao Piano Projetivo Orientado, , Master's thesis, UNICAMPStolfi, J., (1991) Oriented Projective Geometry: A Framework for Geometric Computations, , Acad. Press, IncWestrupp, R.B., (1999) Diagramas de Voronoi de Ordern K Na Geometria Projetiva Orientada, , Master's thesis, UNICAM