Mesh Editing Based on Discrete Laplace and Poisson Models

  • Marc Alexa
  • Andrew Nealen
Part of the Communications in Computer and Information Science book series (CCIS, volume 4)

Abstract

Surface editing operations commonly require geometric details of the surface to be preserved as much as possible. We argue that geometric detail is an intrinsic property of a surface and that, consequently, surface editing is best performed by operating over an intrinsic surface representation. This intrinsic representation could be derived from differential properties of the mesh, i.e. its Laplacian. The modeling process poses nonzero boundary constraints so that this idea results in a Poisson model. Different ways of representing the intrinsic geometry and the boundary constraints result in alternatives for the properties of the modeling system. In particular, the Laplacian is not invariant to scaling and rotations. Either the intrinsic representation is enhanced to be invariant to (linearized) transformations, or scaling and rotation are computed in a preprocess and are modeled as boundary constraints. Based on this representation, useful editing operations can be developed: Interactive free-form deformation in a region of interest based on the transformation of a handle, transfer and mixing of geometric detail between two surfaces, and transplanting of a partial surface mesh into another surface. The main computation involved in all operations is the solution of a sparse linear system, which can be done at interactive rates. We demonstrate the effectiveness of this approach in several examples, showing that the editing operations change the shape while respecting the structural geometric detail.

Keywords

Mesh editing detail preservation 

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References

  1. Alexa, M.: Differential coordinates for local mesh morphing and deformation. The Visual Computer 19(2), 105–114 (2003a)MATHGoogle Scholar
  2. Alexa, M.: Differential coordinates for local mesh morphing and deformation. The Visual Computer 19(2), 105–114 (2003b)MATHGoogle Scholar
  3. Bendels, G.H., Klein, R.: Mesh forging: editing of 3d-meshes using implicitly defined occluders. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, pp. 207–217. ACM Press, New York (2003)Google Scholar
  4. Biermann, H., Martin, I., Bernardini, F., Zorin, D.: Cut-and-paste editing of multiresolution surfaces. In: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, pp. 312–321 (2002)Google Scholar
  5. Botsch, M., Kobbelt, L.: An intuitive framework for real-time freeform modeling. ACM Trans. Graph 23(3), 630–634 (2004)CrossRefGoogle Scholar
  6. Coquillart, S.: Extended free-form deformation: A sculpturing tool for 3D geometric modeling. In: Proceedings of SIGGRAPH 1990, pp. 187–196 (1990)Google Scholar
  7. DeCarlo, D., Finkelstein, A., Rusinkiewicz, S., Santella, A.: Suggestive contours for conveying shape. ACM Trans. Graph 22(3), 848–855 (2003)CrossRefGoogle Scholar
  8. Desbrun, M., Meyer, M., Schröder, P., Barr, A.H.: Implicit fairing of irregular meshes using diffusion and curvature flow. In: Proceedings of ACM SIGGRAPH 1999, pp. 317–324. ACM Press, New York (1999)Google Scholar
  9. Fattal, R., Lischinski, D., Werman, M.: Gradient domain high dynamic range compression. In: Proceedings of ACM SIGGRAPH 2002, pp. 249–256. ACM Press, New York (2002)Google Scholar
  10. Fleishman, S., Drori, I., Cohen-Or, D.: Bilateral mesh denoising. In: Proceedings of ACM SIGGRAPH 2003, pp. 950–953. ACM Press, New York (2003)CrossRefGoogle Scholar
  11. Floater, M.S.: Mean-value coordinates. Computer Aided Geometric Design 20, 19–27 (2003)MathSciNetCrossRefMATHGoogle Scholar
  12. Forsey, D., Bartels, R.: Hierarchical b-spline refinement. In: Proceedings of ACM SIGGRAPH 1988, pp. 205–212. ACM Press, New York (1988)Google Scholar
  13. Gooch, B., Gooch, A.: Non-Photorealistic Rendering. A.K. Peters (2001)Google Scholar
  14. Guskov, I., Sweldens, W., Schröder, P.: Multiresolution signal processing for meshes. In: Proceedings of ACM SIGGRAPH 1999, pp. 325–334. ACM Press, New York (1999)Google Scholar
  15. Hertzmann, A.: Introduction to 3D non-photorealistic rendering: Silhouettes and outlines. In: Green, S. (ed.) Non-Photorealistic Rendering. SIGGRAPH 1999 Course Notes (1999)Google Scholar
  16. Hertzmann, A., Zorin, D.: Illustrating smooth surfaces. In: Proceedings of the 27th annual conference on Computer graphics and interactive techniques, pp. 517–526 (2000)Google Scholar
  17. Hoffman, D.D., Singh, M.: Salience of visual parts. Cognition 63(1), 29–78 (1997)CrossRefGoogle Scholar
  18. Igarashi, T., Matsuoka, S., Tanaka, H.: Teddy: A sketching interface for 3D freeform design. In: Proceedings of SIGGRAPH 1999, Computer Graphics Proceedings, Annual Conference Series, pp. 409–416 (1999)Google Scholar
  19. Kanai, T., Suzuki, H., Mitani, J., Kimura, F.: Interactive mesh fusion based on local 3D metamorphosis. In: Graphics Interface 1999, pp. 148–156 (1999)Google Scholar
  20. Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.-P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proceedings of ACM SIGGRAPH 1998, pp. 105–114. ACM Press, New York (1998)Google Scholar
  21. Kobbelt, L., Vorsatz, J., Seidel, H.-P.: Multiresolution hierarchies on unstructured triangle meshes. Computational Geometry: Theory and Applications 14, 5–24 (1999)MathSciNetCrossRefMATHGoogle Scholar
  22. Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D.: Differential coordinates for interactive mesh editing. In: SMI 2004. International Conference on Shape Modeling and Applications 2004, pp. 181–190 (2004)Google Scholar
  23. Meyer, M., Desbrun, M., Schröder, P., Barr, A.H.: Discrete differential-geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, pp. 35–57 (2003)Google Scholar
  24. Pérez, P., Gangnet, M., Blake, A.: Poisson image editing. In: Proceedings of ACM SIGGRAPH 2003, pp. 313–318. ACM Press, New York (2003)CrossRefGoogle Scholar
  25. Ranta, M., Inui, M., Kimura, F., Mäntylä, M.: Cut and paste based modeling with boundary features. In: SMA 1993: Proceedings of the Second Symposium on Solid Modeling and Applications, pp. 303–312 (1993)Google Scholar
  26. Sederberg, T.W., Parry, S.R.: Free-form deformation of solid geometric models. In: Proceedings of SIGGRAPH 1986, pp. 151–160 (1986)Google Scholar
  27. Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rössl, C., Seidel, H.-P.: Laplacian surface editing. In: Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry processing. Eurographics Association, pp. 179–188. ACM Press, New York (2004)Google Scholar
  28. Taubin, G.: A signal processing approach to fair surface design. In: Proceedings of ACM SIGGRAPH 1995, pp. 351–358. ACM Press, New York (1995)Google Scholar
  29. Toledo, S.: Taucs: A Library of Sparse Linear Solvers. Tel. Aviv. University (2003)Google Scholar
  30. Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., Shum, H.-Y.: Mesh editing with poisson-based gradient field manipulation. ACM Trans. Graph 23(3), 644–651 (2004)CrossRefGoogle Scholar
  31. Zeleznik, R.C., Herndon, K.P., Hughes, J.F.: Sketch: An interface for sketching 3D scenes. In: Proceedings of SIGGRAPH 1996. Computer Graphics Proceedings. Annual Conference Series, pp. 163–170 (1996)Google Scholar
  32. Zorin, D., Schröder, P., Sweldens, W.: Interactive multiresolution mesh editing. In: Proceedings of ACM SIGGRAPH 1997, pp. 259–268. ACM Press, New York (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Marc Alexa
    • 1
  • Andrew Nealen
    • 1
  1. 1.Faculty of EE & CS TU BerlinGermany

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