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Multiresolution Methods for Nonmanifold Models
July-September 2001 (vol. 7 no. 3)
pp. 207-221

Abstract—The concept of fairing applied to triangular meshes with irregular connectivity has become more and more important. Previous contributions proposed a variety of fairing operators for manifolds and applied them to design multiresolution representations and editing tools for meshes. In this paper, we generalize these powerful techniques to handle nonmanifold models. We propose a method to construct fairing operators for nonmanifolds which is based on standard operators for the manifold setting. Furthermore, we describe novel approaches to guarantee volume preservation. We introduce various multiresolution techniques that allow us to represent, smooth, and edit nonmanifold models efficiently. Finally, we discuss a semiautomatic feature preservation strategy to retain important model information during the fairing process.

[1] J. Berta, “Integrating VR and CAD,” IEEE Computer Graphics and Applications, vol. 19, no. 6, pp. 14-19, Nov./Dec. 1999.
[2] H. Biermann, A. Levin, and D. Zorin, “Piecewise Smooth Subdivision Surfaces with Normal Control,” Siggraph 2000, Computer Graphics Proc., K. Akeley, ed., pp. 113-120, 2000.
[3] U. Clarenz, U. Diewald, and M. Rumpf, Anisotropic Geometric Diffusion in Surface Processing Proc. IEEE Visualization, pp. 397-405, 2000.
[4] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow,” SIGGRAPH '99 Proc., Computer Graphics Proc., Ann. Conf. Series, Aug. 1999.
[5] T. Dey, H. Edelsbrunner, S. Guha, and D. Nekhayev, “Topology Preserving Edge Contraction,” technical report, Raindrop Geomagic Inc., Research Triangle Park, North Carolina, 1998.
[6] D.R. Forsey and R.H. Bartels, “Hierarchical B-Spline Refinement,” Computer Graphics (SIGGRAPH '88 Proc.), vol. 22, no. 4, pp. 205-212, Aug. 1988.
[7] M. Garland and P.S. Heckbert, "Surface Simplification Using Quadric Error Metrics," Proc. Siggraph 97, ACM Press, New York, 1997, pp. 209-216.
[8] M.H. Gross and A. Hubeli, “Eigenmeshes,” technical report, ETH Zurich, Mar. 2000.
[9] A. Guéziec, “Locally Toleranced Surface Simplification,” technical report, IBM T.J. Watson Research Center, Yorktown Heights, N.Y., 1997.
[10] I. Guskov, W. Sweldens, and P. Schröder, “Multiresolution Signal Processing for Meshes,” SIGGRAPH '99 Proc., Computer Graphics Proc., Ann. Conf. Series, Aug. 1999.
[11] H. Hoppe, “Progressive Meshes,” Proc. SIGGRAPH '96, pp. 99-108, 1996.
[12] H. Hoppe, “Efficient Implementation of Progressive Meshes,” Computers&Graphics, vol. 22, no. 1, pp. 27-36, Feb. 1998.
[13] A. Hubeli and M. Gross, “Fairing of Non-Manifolds for Visualization,” Proc. 11th Ann. IEEE Visualization Conf. (Vis) 2000, 2000.
[14] A. Hubeli and M. Gross, “Multiresolution Feature Extraction from Unstructured Meshes,” Proc. Visualization 2001, to appear.
[15] L. Kobbelt, S. Campagna, J. Vorsatz, and H.P. Seidel, “Interactive Multiresolution Modeling on Arbitrary Meshes,” Proc. ACM SIGGRAPH, pp. 105-114, July 1998.
[16] H. Lu and R. Hammersley, “Adaptive Visualization for Interactive Geometric Modeling in Geoscience,” Proc. Eighth Int'l Conf. in Central Europe on Computer Graphics, Visualization, and Interactive Digital Media 2000, 2000.
[17] W. Massey, A Basic Course in Algebraic Topology. Springer-Verlag, 1991.
[18] J. Popovic and H. Hoppe, “Progressive Simplicial Complexes,” Proc. SIGGRAPH '97, pp. 217-224, 1997.
[19] J. Rossignac and M. O'Connor, “A Dimension-Independent Model for Pointsets with Internal Structures and Incomplete Boundaries,” Geometric Modeling for Product Eng., M.J. Wozny, J.U. Turner, and K. Preiss, eds., North Holland, 1989.
[20] W.J. Schroeder, J.A. Zarge, and W.E. Lorensen, “Decimation of Triangle Meshes,” Proc. SIGGRAPH '92, pp. 65-70, 1992.
[21] O.G. Staadt and M.H. Gross, “Progressive Tetrahedralizations,” Proc. IEEE Visualization '98, pp. 397-402, 1998.
[22] J. Stoer and R. Bulirsch, Introduction to Numerical Analysis. Springer-Verlag, 1993.
[23] G. Taubin, "A Signal Processing Approach to Fair Surface Design," Computer Graphics Proc., Ann. Conf. Series, ACM Siggraph, ACM Press, New York, 1995, pp.351-358.
[24] D. Zorin, P. Schröder, and W. Sweldens, “Interactive Multiresolution Mesh Editing,” Proc. ACM SIGGRAPH, pp. 259-268, Aug. 1997.

Index Terms:
Boundary representations, surface representations, nonmanifold, fairing, geometric modeling, triangle decimation, multiresolution models.
Andreas Hubeli, Markus Gross, "Multiresolution Methods for Nonmanifold Models," IEEE Transactions on Visualization and Computer Graphics, vol. 7, no. 3, pp. 207-221, July-Sept. 2001, doi:10.1109/2945.942689
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