Chi-Han Peng
Michael Barton
Caigui Jiang
Peter Wonka
Abstract
We present a framework for exploring topologically unique quadrangulations of an input shape. First, the input shape is segmented into surface patches. Second, different topologies are enumerated and explored in each patch. This is realized by an efficient subdivision-based quadrangulation algorithm that can exhaustively enumerate all mesh topologies within a patch. To help users navigate the potentially huge collection of variations, we propose tools to preview and arrange the results. Furthermore, the requirement that all patches need to be jointly quadrangulatable is formulated as a linear integer program. Finally, we apply the framework to shape-space exploration, remeshing, and design to underline the importance of topology exploration.
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- P. Alliez, D. Cohen-Steiner, O. Devillers, B. Levy, and M. Desbrun. 2003. Anisotropic polygonal remeshing. ACM Trans. Graph. 22, 3, 485--493. Google Scholar
Digital Library
- M. Berkelaar, K. Eikland, and P. Notebaert. 2004. Ipsolve: Open source (mixed-integer) linear programming system. http://lpsolve.sourceforge.net/5.5/Google Scholar
- M. Bessmeltsev, C. Wang, A. Sheffer, and K. Singh. 2012. Design-driven quadrangulation of closed 3d curves. ACM Trans. Graph. 31, 5. Google ScholarDigital Library
- T. D. Blacker And M. B. Stephenson. 1991. Paving: A new approach to automated quadrilateral mesh generation. Int. J. Numer. Methods Engin. 32, 4, 811--847.Google ScholarCross Ref
- D. Bommes, B. Levy, N. Pietroni, E. Puppo, M. Tarini, and D. Zorin. 2012. State of the art in quad meshing. In EuroGraphics STARS.Google Scholar
- D. Bommes, H. Zimmer, and L. Kobbelt. 2009. Mixed-integer quadrangulation. ACM Trans. Graph. 28, 3, 77. Google ScholarDigital Library
- M. Botsch, L. Kobbelt, M. Pauly, P. Alliez, and B. Levy. 2010. Polygon Mesh Processing. A. K. Peters, Natick, MA.Google Scholar
- D. Cohen-Steiner, P. Alliez, and M. Desbrun. 2004. Variational shape approximation. In Proceedings of the Conference on Computer Graphics and Interactive Techniques (SIGGRAPH'04). ACM Press, New York, 905--914. Google ScholarDigital Library
- J. Daniels, C. T. Silva, J. Shepherd, and E. Cohen. 2008. Quadrilateral mesh simplification. ACM Trans. Graph. 27, 5, 148:1--148:9. Google ScholarDigital Library
- S. Dong, P.-T. Bremer, M. Garland, V. Pascucci, and J. C. Hart. 2006. Spectral surface quadrangulation. ACM Trans. Graph. 25, 3, 1057--1066. Google ScholarDigital Library
- S. Dong, S. Kircher, and M. Garland. 2005. Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Comput.-Aid. Geom. Des. 22, 392--423. Google ScholarDigital Library
- F. Kalberer, M. Nieser, and K. Polthier. 2007. Quadcover -- Surface parameterization using branched coverings. Comput. Graph. Forum 26, 3, 375--384.Google ScholarCross Ref
- B. Levy, S. Petitjean, N. Ray, and J. Maillot. 2002. Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph. 21, 3, 362--371. Google ScholarDigital Library
- Y. Liu, H. Pottmann, J. Wallner, Y.-L. Yang, and W. Wang. 2006. Geometric modeling with conical meshes and developable surfaces. ACM Trans. Graph. 25, 3, 681--689. Google ScholarDigital Library
- M. Marinov and L. Kobbelt. 2004. Direct anisotropic quad-dominant remeshing. In Proceedings of the 12th Pacific Conference on Computer Graphics and Applications (PG'04). 207--216. Google ScholarDigital Library
- M. Marinov and L. Kobbelt. 2006. A robust two-step procedure for quad-dominant remeshing. Comput. Graph. Forum 25, 3, 537--546.Google ScholarCross Ref
- S. Maza, F. Noel, and J. Leon. 1999. Generation of quadrilateral meshes on free-form surfaces. Comput. Struct. 71.Google Scholar
- A. S. M. Nasri and Z. Yasseen. 2009. Filling n-sided regions by quad meshes for subdivision surfaces. Comput. Graph. Forum 28, 1644--1658.Google ScholarCross Ref
- J. Palacios and E. Zhang. 2007. Rotational symmetry field design on surfaces. ACM Trans. Graph. 26, 3, 55. Google ScholarDigital Library
- C. Park, J.-S. Noh, I.-S. Jang, and J. M. Kang. 2007. A new automated scheme of quadrilateral mesh generation for randomly distributed line constraints. Comput.-Aid. Des. 39, 4, 258--267. Google ScholarDigital Library
- C.-H. Peng, E. Zhang, Y. Kobayashi, and P. Wonka. 2011. Connectivity editing for quadrilateral meshes. ACM Trans. Graph. 30, 6, 141. Google ScholarDigital Library
- N. Ray, W. C. Li, B. Levy, A. Sheffer, and P. Alliez. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 4, 1460--1485. Google ScholarDigital Library
- N. Ray, B. Vallet, L. Alsonso, and B. Levy. 2009. Geometry aware direction field design. ACM Trans. Graph. 29, 1, 1:1--1:11. Google ScholarDigital Library
- N. Ray, B. Vallet, W. C. Li, and B. Levy. 2008. N-symmetry direction field design. ACM Trans. Graph. 27, 2, 10:1--10:13. Google ScholarDigital Library
- S. Schaefer, J. Warren, and D. Zorin. 2004. Lofting curve networks using subdivision surfaces. In Proceedings of the 2nd EuroGraphics Symposium on Geometry Processing (SGP'04). 103--114. Google ScholarDigital Library
- Y. Tong, P. Alliez, D. Cohen-Steiner, and M. Desbrun. 2006. Designing quadrangulations with discrete harmonic forms. In Proceedings of the 4th EuroGraphics Symposium on Geometry Processing (SGP'06). 201--210. Google ScholarDigital Library
- D. White and P. Kinney. 1997. Redesign of the paving algorithm: Robustness enhancements through element by element meshing. In Proceedings of the 6th International Meshing Round Table. 323--335.Google Scholar
- Y.-L. Yang, Y.-J. Yang, H. Pottmann, and N. J. Mitra. 2011. Shape space exploration of constrained meshes. ACM Trans. Graph. 30, 6, 124:1--124:12. Google ScholarDigital Library
- E. Zhang, K. Mischaikow, and G. Turk. 2006. Vector field design on surfaces. ACM Trans. Graph. 25, 1294--1326. Google ScholarDigital Library
- M. Zhang, J. Huang, X. Liu, And H. Bao. 2010. A wave-based anisotropic quadrangulation method. ACM Trans. Graph. 29, 4, 118:1--118:8. Google ScholarDigital Library
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- Exploring quadrangulations
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