This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Dual Laplacian Editing for Meshes
May/June 2006 (vol. 12 no. 3)
pp. 386-395

Abstract—Recently, differential information as local intrinsic feature descriptors has been used for mesh editing. Given certain user input as constraints, a deformed mesh is reconstructed by minimizing the changes in the differential information. Since the differential information is encoded in a global coordinate system, it must somehow be transformed to fit the orientations of details in the deformed surface, otherwise distortion will appear. We observe that visually pleasing deformed meshes should preserve both local parameterization and geometry details. We propose to encode these two types of information in the dual mesh domain due to the simplicity of the neighborhood structure of dual mesh vertices. Both sets of information are nondirectional and nonlinearly dependent on the vertex positions. Thus, we present a novel editing framework that iteratively updates both the primal vertex positions and the dual Laplacian coordinates to progressively reduce distortion in parametrization and geometry. Unlike previous related work, our method can produce visually pleasing deformations with simple user interaction, requiring only the handle positions, not local frames at the handles.

[1] Y. Lipman, O. Sorkine, D. Cohen-Or, D. Levin, C. Rössl, and H.-P. Seidel, “Differential Coordinates for Interactive Mesh Editing,” Proc. Conf. Shape Modeling Int'l, pp. 181-190, 2004.
[2] O. Sorkine, Y. Lipman, D. Cohen-Or, M. Alexa, C. Rössl, and H.-P. Seidel, “Laplacian Surface Editing,” Proc. Symp. Geometry Processing, pp. 179-188, 2004.
[3] A. Nealen, O. Sorkine, M. Alexa, and D. Cohen-Or, “A Sketch-Based Interface for Detail-Preserving Mesh Editing,” ACM Trans. Graphics, vol. 24, no. 3, 2005.
[4] Y. Yu, K. Zhou, D. Xu, X. Shi, H. Bao, B. Guo, and H.-Y. Shum, “Mesh Editing with Poisson-Based Gradient Field Manipulation,” ACM Trans. Graphics, vol. 23, no. 3, pp. 644-651, 2004.
[5] Y. Lipman, O. Sorkine, D. Levin, and D. Cohen-Or, “Linear Rotation-Invariant Coordinates for Meshes,” ACM Trans. Graphics, vol. 24, 2005.
[6] R. Zayer, C. Rössl, Z. Karni, and H.-P. Seidel, “Harmonic Guidance for Surface Deformation,” Computer Graphics Forum, Proc. Eurographics, 2005.
[7] K. Zhou, J. Huang, J. Snyder, X. Liu, H. Bao, B. Guo, and H.-Y. Shum, “Large Mesh Deformation Using the Volumetric Graph Laplacian,” ACM Trans. Graphics, vol. 24, no. 3, 2005.
[8] D. Forsey and R. Bartels, “Hierarchical B-Spline Refinement,” Proc. ACM SIGGRAPH '88, pp. 205-212, 1988.
[9] D. Zorin, P. Schroder, and W. Sweldens, “Interactive Multiresolution Mesh Editing,” Proc. ACM SIGGRAPH '97, pp. 259-268, 1997.
[10] I. Guskov, W. Sweldens, and P. Schröder, “Multiresolution Signal Processing for Meshes,” Proc. ACM SIGGRAPH '99, pp. 325-334, 1999.
[11] L. Kobbelt, S. Campagna, J. Vorsatz, and H.-P. Seidel, “Interactive Multi-Resolution Modeling on Arbitrary Meshes,” Proc. ACM SIGGRAPH '98, pp. 105-114, 1998.
[12] M. Botsch and L. Kobbelt, “An Intuitive Framework for Real-Time Freeform Modeling,” ACM Trans. Graphics, vol. 23, no. 3, pp. 630-634, 2004.
[13] G. Taubin, “A Signal Processing Approach to Fair Surface Design,” Proc. ACM SIGGRAPH '95, pp. 351-358, 1995.
[14] M. Desbrun, M. Meyer, P. Schröder, and A.H. Barr, “Implicit Fairing of Irregular Meshes Using Diffusion and Curvature Flow,” Proc. ACM SIGGRAPH '99, pp. 317-324, 1999.
[15] A. Sheffer and V. Krayevoy, “Pyramid Coordinates for Morphing and Deformation,” 3D Data Processing, Visualization, and Transmission, pp. 68-75, 2004.
[16] M. Desbrun, M. Meyer, and P. Alliez, “Intrinsic Parameterizations of Surface Meshes,” pp. 209-218, 2002.
[17] M. Eck, T. DeRose, T. Duchamp, H. Hoppe, M. Lounsbery, and W. Stuetzle, “Multiresolution Analysis of Arbitrary Meshes,” Proc. ACM SIGGRAPH, pp. 173-182, 1995.
[18] B. Lévy, S. Petitjean, N. Ray, and J. Maillot, “Least Squares Conformal Maps for Automatic Texture Atlas Generation,” ACM Trans. Graphics, vol. 21, no. 3, pp. 362-371, 2002.
[19] S. Haker, S. Angenent, A. Tannenbaum, R. Kikinis, G. Sapiro, and M. Halle, “Conformal Surface Parameterization for Texture Mapping,” IEEE Trans. Visualization and Computer Graphics, vol. 6, no. 2, pp. 181-189, Apr.-June 2000.
[20] X. Gu and S.-T. Yau, “Global Conformal Surface Parameterization,” Proc. Symp. Geometry Processing, pp. 127-137, 2003.
[21] U. Pinkall and K. Polthier, “Computing Discrete Minimal Surfaces and Their Conjugates,” Experimental Math., vol. 2, no. 1, pp. 15-36, 1993.
[22] G. Taubin, “Dual Mesh Resampling,” Proc. Conf. Pacific Graphics, pp. 94-113, 2001.
[23] S. Toledo, “Taucs: A Library of Sparse Linear Solvers, Version 2.2,” Tel-Aviv Univ., http://www.tau.ac.il/stoledotaucs/, 2003.

Index Terms:
Interaction techniques, surface representations, geometric algorithms.
Citation:
Oscar Kin-Chung Au, Chiew-Lan Tai, Ligang Liu, Hongbo Fu, "Dual Laplacian Editing for Meshes," IEEE Transactions on Visualization and Computer Graphics, vol. 12, no. 3, pp. 386-395, May-June 2006, doi:10.1109/TVCG.2006.47
Usage of this product signifies your acceptance of the Terms of Use.