Journal of Zhejiang University SCIENCE C

, Volume 13, Issue 8, pp 565–572 | Cite as

Three-dimensional deformation in curl vector field

  • Dan Zeng
  • Da-yue Zheng


Deformation is an important research topic in graphics. There are two key issues in mesh deformation: (1) self-intersection and (2) volume preserving. In this paper, we present a new method to construct a vector field for volume-preserving mesh deformation of free-form objects. Volume-preserving is an inherent feature of a curl vector field. Since the field lines of the curl vector field will never intersect with each other, a mesh deformed under a curl vector field can avoid self-intersection between field lines. Designing the vector field based on curl is useful in preserving graphic features and preventing self-intersection. Our proposed algorithm introduces distance field into vector field construction; as a result, the shape of the curl vector field is closely related to the object shape. We define the construction of the curl vector field for translation and rotation and provide some special effects such as twisting and bending. Taking into account the information of the object, this approach can provide easy and intuitive construction for free-form objects. Experimental results show that the approach works effectively in real-time animation.

Key words

3D mesh deformation Curl vector field Volume preserving Self-intersection 

CLC number



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  1. Alexa, M., 2003. Differential coordinates for local mesh morphing and deformation. Vis. Comput., 19(2):105–114.MATHGoogle Scholar
  2. Angelidis, A., Singh, K., 2007. Kinodynamic Skinning Using Volume-Preserving Deformations. Proc. ACM SIGGRAPH/Eurographics Symp. on Computer Animation, p.129–140.Google Scholar
  3. Angelidis, A., Cani, M.P., Wyvill, G., King, S., 2004. Swirling Sweepers: Constant-Volume Modeling. Proc. 12th Pacific Conf. on Computer Graphics and Applications, p.10–15. [doi:10.1109/PCCGA.2004.1348329]Google Scholar
  4. Barr, A.H., 1984. Global and Local Deformations of Solid Primitives. Proc. 11th Annual Conf. on Computer Graphics and Interactive Techniques, p.21–30. [doi:10.1145/800031.808573]Google Scholar
  5. Botsch, M., Kobbelt, L., 2004. An Intuitive Framework for Real-Time Freeform Modeling. Proc. 31st Int. Conf. on Computer Graphics and Interactive Techniques, p.630–634. [doi:10.1145/1186562.1015772]Google Scholar
  6. Botsch, M., Kobbelt, L., 2005. Real-time shape editing using radial basis functions. Comput. Graph. Forum, 24(3):611–621. [doi:10.1111/j.1467-8659.2005.00886.x]CrossRefGoogle Scholar
  7. Coquillart, S., 1990. Extended Free-Form Deformation: a Sculpturing Tool for 3D Geometric Modeling. Proc. 17th Annual Conf. on Computer Graphics and Interactive Techniques, p.187–196. [doi:10.1145/97879.97900]Google Scholar
  8. Davis, H., 1967. Introduction to Vector Analysis. Allyn and Bacon Inc., Boston, USA.Google Scholar
  9. Gain, J.E., Dodgson, N.A., 1999. Adaptive Refinement and Decimation under Free-Form Deformation. Proc. 17th Eurographics, p.13–15.Google Scholar
  10. Hirota, G., Maheshwari, R., Lin, M.C., 2000. Fast volume-preserving free-form deformation using multi-level optimization. Comput.-Aid. Des., 32(8–9):499–512. [doi:10.1016/S0010-4485(00)00038-5]MATHCrossRefGoogle Scholar
  11. Hsu, W.M., Hughes, J.F., Kaufman, H., 1992. Direct Manipulation of Free-Form Deformations. Proc. 19th Annual Conf. on Computer Graphics and Interactive Techniques, p.177–184. [doi:10.1145/133994.134036]Google Scholar
  12. Lipman, Y., Sorkine, O., Cohen-Or, D., Levin, D., Rossi, C., Seidel, H.P., 2004. Differential Coordinates for Interactive Mesh Editing. Proc. 6th Int. Conf. on Shape Modeling and Applications, p.181–190. [doi:10.1109/SMI.2004.1314505]Google Scholar
  13. Lorensen, W.E., Cline, H.E., 1987. Marching Cubes: a High Resolution 3D Surface Construction Algorithm. Proc. 14th Annual Conf. on Computer Graphics and Interactive Techniques, p.163–169. [doi:10.1145/37401.37422]Google Scholar
  14. Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., Seidel, H.P., 2003. Multi-level partition of unity implicits. ACM Trans. Graph., 22(3):463–470. [doi:10.1145/882262.882293]CrossRefGoogle Scholar
  15. Praun, E., Finkelstein, A., Hoppe, H., 2000. Lapped Textures. Proc. 27th Annual Conf. on Computer Graphics and Interactive Techniques, p.465–470. [doi:10.1145/344779.344987]Google Scholar
  16. Rohmer, D., Hahmann, S., Cani, M.P., 2009. Exact Volume Preserving Skinning with Shape Control. Proc. ACM SIGGRAPH/Eurographics Symp. on Computer Animation, p.83–92. [doi:10.1145/1599470.1599481]Google Scholar
  17. Sederberg, T.W., Parry, S.R., 1986. Free-Form Deformation of Solid Geometric Models. Proc. 13th Annual Conf. on Computer Graphics and Interactive Techniques, p.151–160. [doi:10.1145/15922.15903]Google Scholar
  18. Singh, K., Fiume, E., 1998. Wires: a Geometric Deformation Technique. Proc. 25th Annual Conf. on Computer Graphics and Interactive Techniques, p.405–414. [doi:10.1145/280814.280946]Google Scholar
  19. Sorkine, O., Cohen-Or, D., Lipman, Y., Alexa, M., Rössl, C., Seidel, H.P., 2004. Laplacian Surface Editing. Proc. Eurographics ACM SIGGRAPH Symp. on Geometry Processing, p.175–184. [doi:10.1145/1057432.1057456]Google Scholar
  20. Stam, J., 2003. Flows on surfaces of arbitrary topology. ACM Trans. Graph., 22(3):724–731. [doi:10.1145/882262.882338]CrossRefGoogle Scholar
  21. Theisel, H., Weinkauf, T., Hege, H.C., Seidel, H.P., 2005. Topological methods for 2D time-dependent vector fields based on stream lines and path lines. IEEE Trans. Visual. Comput. Graph., 11(4):383–394. [doi:10.1109/TVCG.2005.68]CrossRefGoogle Scholar
  22. van Wijk, J.J., 2003. Image Based Flow Visualization for Curved Surfaces. Proc. IEEE Visualization, p.123–130. [doi:10.1109/VISUAL.2003.1250363]Google Scholar
  23. von Funck, W., Theisel, H., Seidel, H.P., 2006. Vector field based shape deformations. ACM Trans. Graph., 25(3):1118–1125. [doi:10.1145/1141911.1142002]CrossRefGoogle Scholar
  24. Zhang, E., Mischaikow, K., Turk, G., 2006. Vector field design on surfaces. ACM Trans. Graph., 25(4):1294–1326. [doi:10.1145/1183287.1183290]CrossRefGoogle Scholar
  25. Zhou, K., Huang, J., Snyder, J., Liu, X., Bao, H., Guo, B., Shum, H.Y., 2005. Large mesh deformation using the volumetric graph Laplacian. ACM Trans. Graph., 24(3): 496–503. [doi:10.1145/1073204.1073219]CrossRefGoogle Scholar

Copyright information

© Journal of Zhejiang University Science Editorial Office and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Key Laboratory of Specialty Fiber Optics and Optical Access NetworksShanghai UniversityShanghaiChina
  2. 2.NetEase (Hangzhou) Network Co., Ltd.HangzhouChina

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