Article

An extension of CGAL to the oriented projective plane T² and its dynamic visualization system

Authors:

A. G. Oliveira,

P. J. de Rezende,

F. P. Selmi-DeiAuthors Info & Claims

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

Pages 380 - 381

https://doi.org/10.1145/1064092.1064156

Published: 06 June 2005 Publication History

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Abstract

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 (T² Viewer)built specially for displaying the spherical and planar models of T².

References

[1]

P.J. de Rezende and J.Stolfi. Fundamentos de Geometria Computacional UFPE-DI, IV Escola de Computacao, 1994.

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[2]

P.J. de Rezende and R.B. Westrupp. An Optimal Algorithm to Construct All Voronoi Diagrams for k Nearest Neighbor Search in T2. In Proceedings of the XII SIBGRAPI pages 7--15,1999.

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[3]

CGAL developers' manual, November 2002. http://www.cgal.org

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[4]

C.N. Gon. Computacao Exata em Geometria Projetiva Orientada e Tratamento de Degeneracoes. Master's thesis, UNICAMP, 1996.

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[5]

A.G. Oliveira. Implementacao do Plano Projetivo Orientado na Biblioteca CGAL. Master's thesis, UNICAMP, 2004.

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G.A. Pinto. Generalizacoes do Diagrama de Voronoi construdas atraes de Conicas no Plano Projetivo Orientado. Master's thesis, UNICAMP, 1998.

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[7]

F.P. Selmi-Dei. Um Visualizador para uma Extensao de CGAL ao Plano Projetivo Orientado. Master's thesis, UNICAMP, 2005.

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[8]

J. Stolfi. Oriented Projective Geometry: A Framework for Geometric Computations Acad. Press, Inc., 1991.

Digital Library

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[9]

R.B. Westrupp. Diagramas de Voronoi de Ordem k na Geometria Projetiva Orientada. Master's thesis, UNICAMP, 1999.

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Index Terms

An extension of CGAL to the oriented projective plane T² and its dynamic visualization system
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures

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Information & Contributors

Information

Published In

SCG '05: Proceedings of the twenty-first annual symposium on Computational geometry

June 2005

398 pages

ISBN:1581139918

DOI:10.1145/1064092

Program Chairs:
Joe Mitchell
SUNY Stony Brook
,
Günter Rote
Freie Universität Berlin

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 06 June 2005

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SoCG05

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SoCG05: The 21st Annual ACM Symposium on Computational Geometry 2005

June 6 - 8, 2005

Pisa, Italy

Acceptance Rates

SCG '05 Paper Acceptance Rate 41 of 141 submissions, 29%;

Overall Acceptance Rate 625 of 1,685 submissions, 37%

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Index Terms

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