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Vector field based shape deformations

Published:01 July 2006Publication History
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Abstract

We present an approach to define shape deformations by constructing and interactively modifying C1 continuous time-dependent divergence-free vector fields. The deformation is obtained by a path line integration of the mesh vertices. This way, the deformation is volume-preserving, free of (local and global) self-intersections, feature preserving, smoothness preserving, and local. Different modeling metaphors support the approach which is able to modify the vector field on-the-fly according to the user input. The approach works at interactive frame rates for moderate mesh sizes, and the numerical integration preserves the volume with a high accuracy.

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References

  1. Alexa, M. 2003. Differential coordinates for local mesh morphing and deformation. The Visual Computer 19, 105--114.Google ScholarGoogle ScholarCross RefCross Ref
  2. Alliez, P., Ucelli, G., Gotsman, C., and Attene, M. 2005. Recent Advances in Remeshing of Surfaces. Springer.Google ScholarGoogle Scholar
  3. Angelidis, A., Cani, M.-P., Wyvill, G., and King, S. 2004. Swirling-sweepers: Constant-volume modeling. In Computer Graphics and Applications, 12th Pacific Conference on (PG'04), 10--15. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. Angelidis, A., Wyvill, G., and Cani, M.-P. 2004. Sweepers: Swept user-defined tools for modeling by deformation. In Proceedings of Shape Modeling and Applications, IEEE, 63--73. Google ScholarGoogle ScholarDigital LibraryDigital Library
  5. Aubert, F., and Bechmann, D. 1997. Volume-preserving space deformation. Comput. and Graphics 21, 5, 6125--639. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. Barr, A. 1984. Global and local deformations of solid primitives. In SIGGRAPH'84: Proceedings of the 11th annual conference on Computer graphics and interactive techniques. ACM Press, New York, NY, USA, 21--30. Google ScholarGoogle ScholarDigital LibraryDigital Library
  7. Bendels, G. H., and Klein, R. 2003. Mesh forging: editing of 3d-meshes using implicitly defined occluders. In SGP '03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 207--217. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. Biswas, A., and Shapiro, V. 2004. Approximate distance fields with non-vanishing gradients. Graphical Models 66, 3, 133--159. Google ScholarGoogle ScholarDigital LibraryDigital Library
  9. Botsch, M., and Kobbelt, L. 2003. Multiresolution surface representation based on displacement volumes. Computer Graphics Forum 22, 3, 483--491. (Proceedings Eurographics 2003).Google ScholarGoogle ScholarCross RefCross Ref
  10. Botsch, M., and Kobbelt, L. 2004. An intuitive framework for real-time freeform modeling. ACM Trans. Graph. 23, 3, 630--634. Google ScholarGoogle ScholarDigital LibraryDigital Library
  11. Botsch, M., and Kobbelt, L. 2005. Real-time shape editing using radial basis functions. Computer Graphics Forum 24, 3, 611--621. (Proceedings Eurographics 2005).Google ScholarGoogle ScholarCross RefCross Ref
  12. ColDet. Free 3D collision detection library. http://photoneffect.com/coldet.Google ScholarGoogle Scholar
  13. Coquillart, S. 1990. Extended free-form deformation: a sculpturing tool for 3d geometric modeling. In SIGGRAPH '90: Proceedings of the 17th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 187--196. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. Davis, H. 1967. Introduction to vector analysis. Allyn and Bacon, Inc., Boston.Google ScholarGoogle Scholar
  15. Desbrun, M., and Gascuel, M.-P. 1995. Animating soft substances with implicit surfaces. In SIGGRAPH '95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 287--290. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. Farin, G. 2002. Curves and Surfaces for CAGD, 5th ed. Morgan Kaufmann, San Francisco. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. Foster, N., and Fedkiw, R. 2001. Practical animation of liquids. In SIGGRAPH '01: Proceedings of the 28th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 23--30. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Gain, J. E., and Dodgson, N. A. 1999. Adaptive refinement and decimation under free-form deformation. Eurographics UK '99.Google ScholarGoogle Scholar
  19. Gain, J. E., and Dodgson, N. A. 2001. Preventing self-intersection under free-form deformation. IEEE Transactions on Visualization and Computer Graphics 7, 4, 289--298. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. Guskov, I., Sweldens, W., and Schröder, P. 1999. Multiresolution signal processing for meshes. In SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 325--334. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. Hirota, G., Maheshwari, R., and Lin, M. 1992. Fast volume-preserving free form deformation using multi-level optimization. In Proceedings Solid Modeling and applications, 234--245. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. Hsu, W., Hughes, J., and Kaufman, H. 1992. Direct manipulation of free-form deformations. In SIGGRAPH '92: Proceedings of the 19th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 177--184. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. Kobbelt, L., Campagna, S., Vorsatz, J., and Seidel, H.-P. 1998. Interactive multi-resolution modeling on arbitrary meshes. In SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 105--114. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D., Rössl, C., and Seidel, H.-P. 2004. Differential coordinates for interactive mesh editing. In Proceedings of Shape Modeling International, IEEE Computer Society Press, 181--190. Google ScholarGoogle ScholarDigital LibraryDigital Library
  25. Lipman, Y., Sorkine, O., Levin, D., and Cohen-Or, D. 2005. Linear rotation-invariant coordinates for meshes. ACM Trans. Graph. 24, 3, 479--487. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. Llamas, I., Kim, B., Gargus, J., Rossinac, J., and Shaw, C. 2003. Twister: a space-warp operator for the two-handed editing of 3d shapes. ACM Trans. Graph. 22, 3, 663--668. Google ScholarGoogle ScholarDigital LibraryDigital Library
  27. MacCracken, R., and Joy, K. 1996. Free-form deformations with lattices of arbitrary topology. In SIGGRAPH '96: Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 181--188. Google ScholarGoogle ScholarDigital LibraryDigital Library
  28. Mason, D., and Wyvill, G. 2001. Blendeforming: Ray traceable localized foldover-free space deformation. In CGI '01: Proceedings of the International Conference on Computer Graphics, IEEE Computer Society, Washington, DC, USA, 183. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. Nielson, G., Hagen, H., and Müller, H. 1997, Scientific Visualization. IEEE Computer Society.Google ScholarGoogle Scholar
  30. Pauly, M., Keiser, R., Kobbelt, L., and Gross, M. 2003. Shape modeling with point-sampled geometry. ACM Trans. Graph. 22, 3, 641--650. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. Rappoport, A., Sheffer, A., and Bercovier, M. 1996. Volume-preserving free-form solids. IEEE Transactions on Visualization and Computer Graphics 2, 1, 19--27. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. Sederberg, T., and Parry, S. 1986. Free-form deformation of solid geometric models. In SIGGRAPH '86: Proceedings of the 13th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 151--160. Google ScholarGoogle ScholarDigital LibraryDigital Library
  33. Singh, K., and Fiume, E. 1998. Wires: a geometric deformation technique. In SIGGRAPH '98: Proceedings of the 25th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 405--414. Google ScholarGoogle ScholarDigital LibraryDigital Library
  34. Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rössl, C., and Seidel, H.-P. 2004. Laplacian surface editing. In Proceedings of the Eurographics/ACM SIGGRAPH symposium on Geometry processing, Eurographics Association, 179--188. Google ScholarGoogle ScholarDigital LibraryDigital Library
  35. Taubin, G. 1995. A signal processing approach to fair surface design. In SIGGRAPH '95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 351--358. Google ScholarGoogle ScholarDigital LibraryDigital Library
  36. Theisel, H., Weinkauf, T., Hege, H.-C., and Seidel, H.-P. 2005. Topological methods for 2D time-dependent vector fields based on stream lines and path lines. IEEE Transactions on Visualization and Computer Graphics 11, 4, 383--394. Google ScholarGoogle ScholarDigital LibraryDigital Library
  37. Welch, W., and Witkin, A. 1992. Variational surface modeling. In. SIGGRAPH '92: Proceedings of the 19th annual conference on Computer graphics and interactive techniques, ACM Press, New York, NY, USA, 157--166. Google ScholarGoogle ScholarDigital LibraryDigital Library
  38. Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., and Shum, H.-Y. 2004. Mesh editing with poisson-based gradient field manipulation. ACM Trans. Graph. 23, 3, 644--651. Google ScholarGoogle ScholarDigital LibraryDigital Library
  39. Zayer, R., Rössl, C., Karni, Z., and Seidel, H.-P. 2005. Harmonic guidance for surface deformation. In Computer Graphics Forum, Proceedings of Eurographics 2005, Blackwell, Dublin, Ireland, vol. 24, Eurographics, 601--609.Google ScholarGoogle Scholar
  40. Zhou, K., Huang, J., Snyder, J., Liu, X., Bao, H., Guo, B., and Shum, H.-Y. 2005. Large mesh deformation using the volumetric graph laplacian. ACM Trans. Graph. 24, 3, 496--503. Google ScholarGoogle ScholarDigital LibraryDigital Library
  41. Zorin, D., Schröder, P., and Sweldens, W. 1997. Interactive multiresolution mesh editing. In SIGGRAPH '97: Proceedings of the 24th annual conference on Computer graphics and interactive techniques, ACM Press/Addison-Wesley Publishing Co., New York, NY, USA, 259--268. Google ScholarGoogle ScholarDigital LibraryDigital Library

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        cover image ACM Transactions on Graphics
        ACM Transactions on Graphics  Volume 25, Issue 3
        July 2006
        742 pages
        ISSN:0730-0301
        EISSN:1557-7368
        DOI:10.1145/1141911
        Issue’s Table of Contents

        Copyright © 2006 ACM

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        Publication History

        • Published: 1 July 2006
        Published in tog Volume 25, Issue 3

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