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An extension of CGAL to the oriented projective plane T2 and its dynamic visualization system
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Source Annual Symposium on Computational Geometry archive
Proceedings of the twenty-first annual symposium on Computational geometry table of contents
Pisa, Italy
SESSION: Video/multimedia presentations table of contents
Pages: 380 - 381  
Year of Publication: 2005
ISBN:1-58113-991-8
Authors
A. G. Oliveira  Universidade Estadual de Campinas, Campinas, Brazil
P. J. de Rezende  Universidade Estadual de Campinas, Campinas, Brazil
F. P. Selmi-Dei  Universidade Estadual de Campinas, Campinas, Brazil
Sponsors
ACM: Association for Computing Machinery
SIGACT: ACM Special Interest Group on Algorithms and Computation Theory
SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques
Publisher
ACM  New York, NY, USA
Bibliometrics
Downloads (6 Weeks): 3,   Downloads (12 Months): 16,   Citation Count: 0
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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

Note: OCR errors may be found in this Reference List extracted from the full text article. ACM has opted to expose the complete List rather than only correct and linked references.

 
1
P.J. de Rezende and J.Stolfi. Fundamentos de Geometria Computacional UFPE-DI, IV Escola de Computacao, 1994.
 
2
Pedro Jussieu de Rezende , Rodrigo B. Westrupp, An Optimal Algorithm to Construct all Voronoi Diagrams for k Nearest Neighbor Search in T2, Proceedings of the XII Brazilian Symposium on Computer Graphics and Image Processing, p.7-16, October 17-20, 1999
 
3
CGAL developers' manual, November 2002. http://www.cgal.org
 
4
C.N. Gon. Computacao Exata em Geometria Projetiva Orientada e Tratamento de Degeneracoes. Master's thesis, UNICAMP, 1996.
 
5
A.G. Oliveira. Implementacao do Plano Projetivo Orientado na Biblioteca CGAL. Master's thesis, UNICAMP, 2004.
 
6
G.A. Pinto. Generalizacoes do Diagrama de Voronoi construdas atraes de Conicas no Plano Projetivo Orientado. Master's thesis, UNICAMP, 1998.
 
7
F.P. Selmi-Dei. Um Visualizador para uma Extensao de CGAL ao Plano Projetivo Orientado. Master's thesis, UNICAMP, 2005.
 
8
Jorge Stolfi, Oriented projective geometry, Academic Press Professional, Inc., San Diego, CA, 1991
 
9
R.B. Westrupp. Diagramas de Voronoi de Ordem k na Geometria Projetiva Orientada. Master's thesis, UNICAMP, 1999.

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling
          Subjects: Geometric algorithms, languages, and systems


General Terms:
Algorithms


Keywords:
CGAL, algorithm animation, oriented projective plane, visualization

Collaborative Colleagues:
A. G. Oliveira: colleagues
P. J. de Rezende: colleagues
F. P. Selmi-Dei: colleagues

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