Full Text:   <3196>

CLC number: TP391

On-line Access: 2012-08-02

Received: 2012-01-09

Revision Accepted: 2012-05-11

Crosschecked: 2012-07-06

Cited: 1

Clicked: 8277

Citations:  Bibtex RefMan EndNote GB/T7714

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Journal of Zhejiang University SCIENCE C 2012 Vol.13 No.8 P.565-572


Three-dimensional deformation in curl vector field

Author(s):  Dan Zeng, Da-yue Zheng

Affiliation(s):  Key Laboratory of Specialty Fiber Optics and Optical Access Networks, Shanghai University, Shanghai 200072, China; more

Corresponding email(s):   dzeng@shu.edu.cn, iwalu1999@hotmail.com

Key Words:  3D mesh deformation, Curl vector field, Volume preserving, Self-intersection

Dan Zeng, Da-yue Zheng. Three-dimensional deformation in curl vector field[J]. Journal of Zhejiang University Science C, 2012, 13(8): 565-572.

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author="Dan Zeng, Da-yue Zheng",
journal="Journal of Zhejiang University Science C",
publisher="Zhejiang University Press & Springer",

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%T Three-dimensional deformation in curl vector field
%A Dan Zeng
%A Da-yue Zheng
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T1 - Three-dimensional deformation in curl vector field
A1 - Dan Zeng
A1 - Da-yue Zheng
J0 - Journal of Zhejiang University Science C
VL - 13
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SP - 565
EP - 572
%@ 1869-1951
Y1 - 2012
PB - Zhejiang University Press & Springer
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DOI - 10.1631/jzus.C1200004

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.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1]Alexa, M., 2003. Differential coordinates for local mesh morphing and deformation. Vis. Comput., 19(2):105-114.

[2]Angelidis, A., Singh, K., 2007. Kinodynamic Skinning Using Volume-Preserving Deformations. Proc. ACM SIGGRAPH/Eurographics Symp. on Computer Animation, p.129-140.

[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.

[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.

[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.

[6]Botsch, M., Kobbelt, L., 2005. Real-time shape editing using radial basis functions. Comput. Graph. Forum, 24(3):611-621.

[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.

[8]Davis, H., 1967. Introduction to Vector Analysis. Allyn and Bacon Inc., Boston, USA.

[9]Gain, J.E., Dodgson, N.A., 1999. Adaptive Refinement and Decimation under Free-Form Deformation. Proc. 17th Eurographics, p.13-15.

[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.

[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.

[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.

[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.

[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.

[15]Praun, E., Finkelstein, A., Hoppe, H., 2000. Lapped Textures. Proc. 27th Annual Conf. on Computer Graphics and Interactive Techniques, p.465-470.

[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.

[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.

[18]Singh, K., Fiume, E., 1998. Wires: a Geometric Deformation Technique. Proc. 25th Annual Conf. on Computer Graphics and Interactive Techniques, p.405-414.

[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.

[20]Stam, J., 2003. Flows on surfaces of arbitrary topology. ACM Trans. Graph., 22(3):724-731.

[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.

[22]van Wijk, J.J., 2003. Image Based Flow Visualization for Curved Surfaces. Proc. IEEE Visualization, p.123-130.

[23]von Funck, W., Theisel, H., Seidel, H.P., 2006. Vector field based shape deformations. ACM Trans. Graph., 25(3):1118-1125.

[24]Zhang, E., Mischaikow, K., Turk, G., 2006. Vector field design on surfaces. ACM Trans. Graph., 25(4):1294-1326.

[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.

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