Parametrização hierárquica de superfícies poligonais construída com triangulação de Delaunay restrita
Resumo
As superfícies triangularizadas podem ser parametrizadas hierarquicamente possibilitando uma representação da superfície, juntamente com o seu domínio paramétrico, por níveis de detalhes e, assim, permitindo um controle melhor da parametrização. Neste artigo apresentamos uma estrutura hierárquica para superfícies triangularizadas, com a topologia de um disco, construída com uma triangulação de Delaunay restrita. Essa construção é livre de possíveis inconsistências topológicas ou na orientação das faces introduzidas na triangulação pelo processo de simplificação. Além disso, utilizamos um processo de otimização na hierarquia para reduzir as distorções causadas pela parametrização.
Palavras-chave:
Hierarquia, parametrização, simplificação, otimização
Referências
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F. Payan, C. Roudet, and B. Sauvage, “Semi-regular triangle remeshing:A comprehensive study,” inComputer Graphics Forum, vol. 34, no. 1.Wiley Online Library, 2015, pp. 86–102. [Online]. :https://doi.org/10.1111/cgf.12461
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K. Hormann and G. Greiner, “Mips: An efficient global parametrizationmethod,”France on 1-7 July 1999. Proceedings, Volume 1. Curve andSurface Design. F61775-99-WF068, p. 153, 2000.
K. Hormann, B. L ́evy, and A. Sheffer, “Mesh parameterization: Theoryand practice,” 2007. DOI=10.1145/1508044.1508091
K. Hormann, G. Greiner, and S. Campagna, “Hierarchical parametriza-tion of triangulated surfaces,” inProceedings of Vision, Modeling, andVisualization, vol. 1999, pp. 219–226, 1999.
M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, and B. L ́evy, Polygon meshprocessing. AK Peters/CRC Press, 2010.
M. Floater, “One-to-one piecewise linear mappings over triangulations, ”Mathematics of Computation, vol. 72, no. 242, pp. 685–696, 2003.
M. P. Do Carmo,Differential Geometry of Curves and Surfaces: Revisedand Updated Second Edition. Courier Dover Publications, 2016.
M. S. Floater and K. Hormann, “Surface parameterization: a tutorialand survey,” inAdvances in multiresolution for geometric modelling.Springer, 2005, pp. 157–186 [Online]. Available:https://doi.org/10.1007/3-540-26808-1_9
M. S. Floater, “Mean value coordinates,”Computer aided geometricdesign, vol. 20, no. 1, pp. 19–27, 2003. [Online]. Available:https://doi.org/10.1016/S0167-8396(03)00002-5
M. S. Floater, “Parametrization and smooth approximation of surfacetriangulations, ”Computer aided geometric design, vol. 14, no. 3, pp.231–250, 1997. [Online]. Available:https://doi.org/10.1016/S0167-8396(96)00031-3
M. Siqueira, D. Xu, J. Gallier, L. G. Nonato, D. M. Morera, andL. Velho, “A new construction of smooth surfaces from triangle meshesusing parametric pseudo-manifolds, ”Computers & Graphics, vol. 33, no. 3, pp. 331–340, 2009. [Online]. https://doi.org/10.1016/j.cag.2009.03.017
O. Devillers, “On deletion in delaunay triangulations,”InternationalJournal of Computational Geometry & Applications, vol. 12, no. 03,pp. 193–205, 2002. DOI=10.1145/304893.304969
P. Degener, J. Meseth, and R. Klein, “An adaptable surface parameteri-zation method.” IMR, vol. 3, pp. 201–213, 2003.
W. T. Tutte, “How to draw a graph,”Proceedings of the LondonMathematical Society, vol. 3, no. 1, pp. 743–767, 1963. [Online]. https://doi.org/10.1112/plms/s3-13.1.743
E. de Medeiros Filho and M. Siqueira, “Good random multi-triangulationof surfaces,”IEEE transactions on visualization and computer graphics, 2017 DOI=10.1109/TVCG.2017.2704078
F. Payan, C. Roudet, and B. Sauvage, “Semi-regular triangle remeshing:A comprehensive study,” inComputer Graphics Forum, vol. 34, no. 1.Wiley Online Library, 2015, pp. 86–102. [Online]. :https://doi.org/10.1111/cgf.12461
H. Hoppe, “Progressive meshes,” inProceedings of the 23rd AnnualConference on Computer Graphics and Interactive Techniques, ser.SIGGRAPH ’96.New York, NY, USA: ACM, 1996, pp. 99–108.[Online]. http://doi.acm.org/10.1145/237170.237216
K. Hormann and G. Greiner, “Mips: An efficient global parametrizationmethod,”France on 1-7 July 1999. Proceedings, Volume 1. Curve andSurface Design. F61775-99-WF068, p. 153, 2000.
K. Hormann, B. L ́evy, and A. Sheffer, “Mesh parameterization: Theoryand practice,” 2007. DOI=10.1145/1508044.1508091
K. Hormann, G. Greiner, and S. Campagna, “Hierarchical parametriza-tion of triangulated surfaces,” inProceedings of Vision, Modeling, andVisualization, vol. 1999, pp. 219–226, 1999.
M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, and B. L ́evy, Polygon meshprocessing. AK Peters/CRC Press, 2010.
M. Floater, “One-to-one piecewise linear mappings over triangulations, ”Mathematics of Computation, vol. 72, no. 242, pp. 685–696, 2003.
M. P. Do Carmo,Differential Geometry of Curves and Surfaces: Revisedand Updated Second Edition. Courier Dover Publications, 2016.
M. S. Floater and K. Hormann, “Surface parameterization: a tutorialand survey,” inAdvances in multiresolution for geometric modelling.Springer, 2005, pp. 157–186 [Online]. Available:https://doi.org/10.1007/3-540-26808-1_9
M. S. Floater, “Mean value coordinates,”Computer aided geometricdesign, vol. 20, no. 1, pp. 19–27, 2003. [Online]. Available:https://doi.org/10.1016/S0167-8396(03)00002-5
M. S. Floater, “Parametrization and smooth approximation of surfacetriangulations, ”Computer aided geometric design, vol. 14, no. 3, pp.231–250, 1997. [Online]. Available:https://doi.org/10.1016/S0167-8396(96)00031-3
M. Siqueira, D. Xu, J. Gallier, L. G. Nonato, D. M. Morera, andL. Velho, “A new construction of smooth surfaces from triangle meshesusing parametric pseudo-manifolds, ”Computers & Graphics, vol. 33, no. 3, pp. 331–340, 2009. [Online]. https://doi.org/10.1016/j.cag.2009.03.017
O. Devillers, “On deletion in delaunay triangulations,”InternationalJournal of Computational Geometry & Applications, vol. 12, no. 03,pp. 193–205, 2002. DOI=10.1145/304893.304969
P. Degener, J. Meseth, and R. Klein, “An adaptable surface parameteri-zation method.” IMR, vol. 3, pp. 201–213, 2003.
W. T. Tutte, “How to draw a graph,”Proceedings of the LondonMathematical Society, vol. 3, no. 1, pp. 743–767, 1963. [Online]. https://doi.org/10.1112/plms/s3-13.1.743
Publicado
28/10/2019
Como Citar
TELLES, Pablo; SILVA, Romildo; MEDEIROS, Esdras; PESCO, Sinesio.
Parametrização hierárquica de superfícies poligonais construída com triangulação de Delaunay restrita. In: WORKSHOP DE TRABALHOS EM ANDAMENTO - CONFERENCE ON GRAPHICS, PATTERNS AND IMAGES (SIBGRAPI), 32. , 2019, Rio de Janeiro.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2019
.
p. 144-147.
DOI: https://doi.org/10.5753/sibgrapi.est.2019.8315.
