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RGB Subdivision
March/April 2009 (vol. 15 no. 2)
pp. 295-310
Enrico Puppo, University of Genova, Genova
Daniele Panozzo, University of Genova, Genova
We introduce the RGB Subdivision: an adaptive subdivision scheme for triangle meshes, which is based on the iterative application of local refinement and coarsening operators, and generates the same limit surface of the Loop subdivision, independently on the order of application of local operators. Our scheme supports dynamic selective refinement, as in Continuous Level Of Detail models, and it generates conforming meshes at all intermediate steps. The RGB subdivision is encoded in a standard topological data structure, extended with few attributes, which can be used directly for further processing. We present an interactive tool that permits to start from a base mesh and use RGB subdivision to dynamically adjust its level of detail.

[1] T. DeRose, M. Kass, and T. Truong, “Subdivision Surfaces in Character Animation,” Proc. ACM SIGGRAPH '98, pp. 85-94, 1998.
[2] P.-O. Persson, M. Aftosmis, and R. Haimes, “On the Use of Loop Subdivision Surfaces for Surrogate Geometry,” Proc. 15th Int'l Meshing Roundtable (IMR '06), pp. 375-392, Sept. 2006.
[3] Blender, http:/www.blender.org/, 2008.
[4] Autodesk Maya, http:/usa.autodesk.com/, 2008.
[5] Modo 301, http:/www.luxology.com, 2008.
[6] Silo 2, http:/www.nevercenter.com/, 2008.
[7] A. Lee, H. Moreton, and H. Hoppe, “Displaced Subdivision Surfaces,” Proc. ACM SIGGRAPH '00, pp. 85-94, 2000.
[8] M. Sabin, “Recent Progress in Subdivision: A Survey,” Advances in Multiresolution for Geometric Modelling, N. Dogdson, M. Floater, and M. Sabin, eds., pp. 203-230, Springer-Verlag, 2004.
[9] F. Samavati and R. Bartels, “Multiresolution Curve and Surface Representation by Reversing Subdivision Rules,” Computer Graphics Forum, vol. 18, no. 2, pp. 97-120, 1999.
[10] F. Samavati, N. Mahdavi-Amiri, and R. Bartels, “Multiresolution Surfaces Having Arbitrary Topologies by a Reverse Doo Subdivision Method,” Computer Graphics Forum, vol. 21, no. 2, pp. 121-136, 2002.
[11] D. Zorin, P. Schröder, and W. Sweldens, “Interactive Multiresolution Mesh Editing,” Proc. ACM SIGGRAPH '97, pp. 259-268, , 1997.
[12] Subdivision for Modeling and Animation (SIGGRAPH 2000 Tutorial N.23—Course Notes), D. Zorin and P. Schröder, eds., ACM Press, 2000.
[13] D. Lübke, M. Reddy, J. Cohen, A. Varshney, B. Watson, and R. Hübner, Level of Detail for 3D Graphics. Morgan Kaufmann, 2002.
[14] C. Loop, “Smooth Subdivision Surfaces Based on Triangles,” master thesis, Dept. of Math., Univ. of Utah, 1987.
[15] N. Dyn, D. Levin, and J. Gregory, “A Butterfly Subdivision Scheme for Surface Interpolation with Tension Control,” ACM Trans. Graphics, vol. 9, no. 2, pp. 160-169, Apr. 1990.
[16] J. Warren and H. Weimer, Subdivision Methods for Geometric Design. Morgan Kaufmann, 2002.
[17] R. Bank, A. Sherman, and A. Weiser, “Refinement Algorithms and Data Structures for Regular Local Mesh Refinement,” Scientific Computing, R. Stepleman, ed., pp. 3-17, IMACS/North Holland, 1983.
[18] H. Pakdel and F. Samavati, “Incremental Subdivision for Triangle Meshes,” Int'l J. Computational Science and Eng., vol. 3, no. 1, pp. 80-92, 2007.
[19] D. Forsey and R. Bartels, “Hierarchical B-Spline Refinement,” Computer Graphics, Proc. ACM SIGGRAPH '88, vol. 22, no. 4, pp.205-212, Aug. 1988.
[20] A. Yvart, S. Hahmann, and G.-P. Bonneau, “Hierarchical Triangular Splines,” ACM Trans. Graphics, vol. 24, no. 4, pp.1374-1391, 2005.
[21] S. Seeger, K. Hormann, G. Häusler, and G. Greiner, “A Sub-Atomic Subdivision Approach,” Proc. Vision, Modeling and Visualization (VMV '01), B. Girod, H. Niemann, and H.-P. Seidel, eds., pp. 77-85, 2001.
[22] H. Hoppe, “Progressive Meshes,” Proc. ACM SIGGRAPH '96, pp.99-108, Aug. 1996.
[23] L. Velho, “Stellar Subdivision Grammars,” Proc. First Eurographics Symp. Geometry Processing (SGP), 2003.
[24] L. Kobbelt, “$\sqrt{3}$ Subdivision,” Proc. ACM SIGGRAPH '00, pp.103-112, 2000.
[25] L. Velho and D. Zorin, “4-8 Subdivision,” Computer-Aided Geometric Design, vol. 18, pp. 397-427, 2001.
[26] E. Puppo, “Variable Resolution Triangulations,” Computational Geometry, vol. 11, nos. 3-4, pp. 219-238, 1998.
[27] J. Kim and S. Lee, “Transitive Mesh Space of a Progressive Mesh,” IEEE Trans. Visualization and Computer Graphics, vol. 9, no. 4, pp.463-480, 2003.
[28] M. Duchaineau, M. Wolinsky, D. Sigeti, M. Miller, C. Aldrich, and M. Mineev-Weinstein, “ROAMing Terrain: Real-Time Optimally Adapting Meshes,” Proc. IEEE Visualization Conf. (VIS '97), pp. 81-88, Oct. 1997.
[29] L. Velho and J. Gomes, “Variable Resolution 4-K Meshes: Concepts and Applications,” Computer Graphics Forum, vol. 19, no. 4, pp. 195-214, 2000.
[30] J. Stam, “Evaluation of Loop Subdivision Surfaces,” ACM SIGGRAPH '98 CDROM Proc., 1998.
[31] H. Edelsbrunner, Algorithms in Combinatorial Geometry. Springer-Verlag, 1987.
[32] Meshlab, http://muggy.gg.caltech.edu/~dzorin/multires/ meshed/index.htmlhttp:/meshlab.sourceforge.net , 2008.
[33] VCG Library, http:/vcg.sourceforge.net, 2008.
[34] D. Zorin, P. Schröder, and W. Sweldens, “Interpolating Subdivision for Meshes with Arbitrary Topology,” Proc. ACM SIGGRAPH '96, pp. 189-192, 1996.
[35] E. Puppo, “Dynamic Adaptive Subdivision Meshes,” Proc. Israel-Italy Bi-National Conf. Shape Modeling and Reasoning for Industrial and Biomedical Application, pp. 60-64, May 2007.

Index Terms:
Curve, surface, solid, and object representations, Object hierarchies
Citation:
Enrico Puppo, Daniele Panozzo, "RGB Subdivision," IEEE Transactions on Visualization and Computer Graphics, vol. 15, no. 2, pp. 295-310, March-April 2009, doi:10.1109/TVCG.2008.87
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