Vector field based shape deformations

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.

REFERENCES

• 1: Alexa, M. 2003. Differential coordinates for local mesh morphing and deformation. The Visual Computer 19, 105--114.
• 2: Alliez, P., Ucelli, G., Gotsman, C., and Attene, M. 2005. Recent Advances in Remeshing of Surfaces. Springer.
• 3: Alexis Angelidis , Marie-Paule Cani , Geoff Wyvill , Scott King, Swirling-Sweepers: Constant-Volume Modeling, Proceedings of the Computer Graphics and Applications, 12th Pacific Conference on (PG'04), p.10-15, October 06-08, 2004
• 4: Sweepers: Swept User-Defined Tools for Modeling by Deformation, Proceedings of the Shape Modeling International 2004 (SMI'04), p.63-73, June 07-09, 2004 [doi>10.1109/SMI.2004.62]
• 5: Aubert, F., and Bechmann, D. 1997. Volume-preserving space deformation. Comput. and Graphics 21, 5, 6125--639.
• 6: Alan H. Barr, Global and local deformations of solid primitives, Proceedings of the 11th annual conference on Computer graphics and interactive techniques, p.21-30, January 1984
• 7: G. H. Bendels , R. Klein, Mesh forging: editing of 3D-meshes using implicitly defined occluders, Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, June 23-25, 2003, Aachen, Germany
• 8: Arpan Biswas , Vadim Shapiro, Approximate distance fields with non-vanishing gradients, Graphical Models, v.66 n.3, p.133-159, May 2004 [doi>10.1016/j.gmod.2004.01.003]
• 9: Botsch, M., and Kobbelt, L. 2003. Multiresolution surface representation based on displacement volumes. Computer Graphics Forum 22, 3, 483--491. (Proceedings Eurographics 2003).
• 10: Mario Botsch , Leif Kobbelt, An intuitive framework for real-time freeform modeling, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 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).
• 12: ColDet. Free 3D collision detection library. http://photoneffect.com/coldet.
• 13: Sabine Coquillart, Extended free-form deformation: a sculpturing tool for 3D geometric modeling, Proceedings of the 17th annual conference on Computer graphics and interactive techniques, p.187-196, September 1990, Dallas, TX, USA
• 14: Davis, H. 1967. Introduction to vector analysis. Allyn and Bacon, Inc., Boston.
• 15: Mathieu Desbrun , Marie-Paule Gascuel, Animating soft substances with implicit surfaces, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.287-290, September 1995 [doi>10.1145/218380.218456]
• 16: Gerald Farin, Curves and surfaces for CAGD: a practical guide, Morgan Kaufmann Publishers Inc., San Francisco, CA, 2001
• 17: Nick Foster , Ronald Fedkiw, Practical animation of liquids, Proceedings of the 28th annual conference on Computer graphics and interactive techniques, p.23-30, August 2001 [doi>10.1145/383259.383261]
• 18: Gain, J. E., and Dodgson, N. A. 1999. Adaptive refinement and decimation under free-form deformation. Eurographics UK '99.
• 19: James E. Gain , Neil A. Dodgson, Preventing Self-Intersection under Free-Form Deformation, IEEE Transactions on Visualization and Computer Graphics, v.7 n.4, p.289-298, October 2001 [doi>10.1109/2945.965344]
• 20: Igor Guskov , Wim Sweldens , Peter Schröder, Multiresolution signal processing for meshes, Proceedings of the 26th annual conference on Computer graphics and interactive techniques, p.325-334, July 1999 [doi>10.1145/311535.311577]
• 21: Gentaro Hirota , Renee Maheshwari , Ming C. Lin, Fast volume-preserving free form deformation using multi-level optimization, Proceedings of the fifth ACM symposium on Solid modeling and applications, p.234-245, June 08-11, 1999, Ann Arbor, Michigan, United States [doi>10.1145/304012.304036]
• 22: William M. Hsu , John F. Hughes , Henry Kaufman, Direct manipulation of free-form deformations, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.177-184, July 1992
• 23: Leif Kobbelt , Swen Campagna , Jens Vorsatz , Hans-Peter Seidel, Interactive multi-resolution modeling on arbitrary meshes, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.105-114, July 1998 [doi>10.1145/280814.280831]
• 24: Differential Coordinates for Interactive Mesh Editing, Proceedings of the Shape Modeling International 2004 (SMI'04), p.181-190, June 07-09, 2004 [doi>10.1109/SMI.2004.30]
• 25: Yaron Lipman , Olga Sorkine , David Levin , Daniel Cohen-Or, Linear rotation-invariant coordinates for meshes, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 26: Ignacio Llamas , Byungmoon Kim , Joshua Gargus , Jarek Rossignac , Chris D. Shaw, Twister: a space-warp operator for the two-handed editing of 3D shapes, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 27: Ron MacCracken , Kenneth I. Joy, Free-form deformations with lattices of arbitrary topology, Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, p.181-188, August 1996 [doi>10.1145/237170.237247]
• 28: David Mason , Geoff Wyvill, Blendeforming: Ray Traceable Localized Foldover-Free Space Deformation, Proceedings of the International Conference on Computer Graphics, p.183, July 03-06, 2001
• 29: Nielson, G., Hagen, H., and Müller, H. 1997, Scientific Visualization. IEEE Computer Society.
• 30: Mark Pauly , Richard Keiser , Leif P. Kobbelt , Markus Gross, Shape modeling with point-sampled geometry, ACM Transactions on Graphics (TOG), v.22 n.3, July 2003
• 31: Ari Rappoport , Alla Sheffer , Michel Bercovier, Volume-Preserving Free-Form Solids, IEEE Transactions on Visualization and Computer Graphics, v.2 n.1, p.19-27, March 1996 [doi>10.1109/2945.489383]
• 32: Thomas W. Sederberg , Scott R. Parry, Free-form deformation of solid geometric models, Proceedings of the 13th annual conference on Computer graphics and interactive techniques, p.151-160, August 1986
• 33: Karan Singh , Eugene Fiume, Wires: a geometric deformation technique, Proceedings of the 25th annual conference on Computer graphics and interactive techniques, p.405-414, July 1998 [doi>10.1145/280814.280946]
• 34: O. Sorkine , D. Cohen-Or , Y. Lipman , M. Alexa , C. Rössl , H.-P. Seidel, Laplacian surface editing, Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, July 08-10, 2004, Nice, France [doi>10.1145/1057432.1057456]
• 35: Gabriel Taubin, A signal processing approach to fair surface design, Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, p.351-358, September 1995 [doi>10.1145/218380.218473]
• 36: Holger Theisel , Tino Weinkauf , Hans-Christian Hege , Hans-Peter Seidel, Topological Methods for 2D Time-Dependent Vector Fields Based on Stream Lines and Path Lines, IEEE Transactions on Visualization and Computer Graphics, v.11 n.4, p.383-394, July 2005 [doi>10.1109/TVCG.2005.68]
• 37: William Welch , Andrew Witkin, Variational surface modeling, Proceedings of the 19th annual conference on Computer graphics and interactive techniques, p.157-166, July 1992
• 38: Yizhou Yu , Kun Zhou , Dong Xu , Xiaohan Shi , Hujun Bao , Baining Guo , Heung-Yeung Shum, Mesh editing with poisson-based gradient field manipulation, ACM Transactions on Graphics (TOG), v.23 n.3, August 2004
• 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.
• 40: Kun Zhou , Jin Huang , John Snyder , Xinguo Liu , Hujun Bao , Baining Guo , Heung-Yeung Shum, Large mesh deformation using the volumetric graph Laplacian, ACM Transactions on Graphics (TOG), v.24 n.3, July 2005
• 41: Denis Zorin , Peter Schröder , Wim Sweldens, Interactive multiresolution mesh editing, Proceedings of the 24th annual conference on Computer graphics and interactive techniques, p.259-268, August 1997 [doi>10.1145/258734.258863]

INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.3 COMPUTER GRAPHICS
      I.3.5 Computational Geometry and Object Modeling

Keywords:
shape-deformation, vector fields, volume-preserving