Full Text:   <3585>

CLC number: TP391

On-line Access: 2024-08-27

Received: 2023-10-17

Revision Accepted: 2024-05-08

Crosschecked: 2009-06-10

Cited: 3

Clicked: 5571

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2009 Vol.10 No.7 P.1009-1017

http://doi.org/10.1631/jzus.A0820728


A spherical parameterization approach based on symmetry analysis of triangular meshes


Author(s):  Jian-ping HU, Xiu-ping LIU, Zhi-xun SU, Xi-quan SHI, Feng-shan LIU

Affiliation(s):  School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China; more

Corresponding email(s):   xpliu@comgi.com

Key Words:  Triangular mesh, Spherical parameterization, Symmetry analysis


Jian-ping HU, Xiu-ping LIU, Zhi-xun SU, Xi-quan SHI, Feng-shan LIU. A spherical parameterization approach based on symmetry analysis of triangular meshes[J]. Journal of Zhejiang University Science A, 2009, 10(7): 1009-1017.

@article{title="A spherical parameterization approach based on symmetry analysis of triangular meshes",
author="Jian-ping HU, Xiu-ping LIU, Zhi-xun SU, Xi-quan SHI, Feng-shan LIU",
journal="Journal of Zhejiang University Science A",
volume="10",
number="7",
pages="1009-1017",
year="2009",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.A0820728"
}

%0 Journal Article
%T A spherical parameterization approach based on symmetry analysis of triangular meshes
%A Jian-ping HU
%A Xiu-ping LIU
%A Zhi-xun SU
%A Xi-quan SHI
%A Feng-shan LIU
%J Journal of Zhejiang University SCIENCE A
%V 10
%N 7
%P 1009-1017
%@ 1673-565X
%D 2009
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820728

TY - JOUR
T1 - A spherical parameterization approach based on symmetry analysis of triangular meshes
A1 - Jian-ping HU
A1 - Xiu-ping LIU
A1 - Zhi-xun SU
A1 - Xi-quan SHI
A1 - Feng-shan LIU
J0 - Journal of Zhejiang University Science A
VL - 10
IS - 7
SP - 1009
EP - 1017
%@ 1673-565X
Y1 - 2009
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820728


Abstract: 
We present an efficient spherical parameterization approach aimed at simultaneously reducing area and angle distortions. We generate the final spherical mapping by independently establishing two hemisphere parameterizations. The essence of the approach is to reduce spherical parameterization to a planar problem using symmetry analysis of 3D meshes. Experiments and comparisons were undertaken with various non-trivial 3D models, which revealed that our approach is efficient and robust. In particular, our method produces almost isometric parameterizations for the objects close to the sphere.

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

Reference

[1] Alexa, M., 2000. Merging polyhedral shapes with scattered features. The Vis. Comput., 16(1):26-37.

[2] Floater, M.S., 2003. Mean value coordinates. Comput. Aided Geometric Des., 20(1):19-27.

[3] Floater, M.S., Hormann, K., 2005. Surface Parameterization: a Tutorial and Survey. Dodgson, N.A., Floater, M.S., Sabin, M.A. (Eds.), Advances in Multiresolution for Geometric Modeling. Springer-Verlag, Heidelberg, p.157-186.

[4] Friedel, I., Schröder, P., Desbrun, M., 2005. Unconstrained Spherical Parameterization. ACM SIGGRAPH Technical Sketches, ACM, New York, USA.

[5] Gotsman, C., Gu, X., Sheffer, A., 2003. Fundamentals of Spherical Parameterization for 3D Meshes. Computer Graphics Proc., Annual Conf. Series, ACM, New York, USA, p.358-364.

[6] Gu, X., Gortler, S.J., Hoppe, H., 2002. Geometry Images. Proc. 29th Annual Conf. on Computer Graphics and Interactive Techniques, ACM, New York, USA, p.355-361.

[7] Gu, X., Wang, Y., Chan, T.F., Thompson, P.M., Yau, S.T, 2004. Genus zero surface conformal mapping and its application to brain surface mapping. IEEE Trans. Med. Imaging, 23(8):949-958.

[8] Haker, S., Angenent, S., Tannenbaum, S., Kikinis, R., Sapiro, G., Halle, M., 2000. Conformal surface parameterization for texture mapping. IEEE TVCG, 6(2):181-189.

[9] Hu, G., Fang, X., Peng, Q., 2004. Convex combination spherical parameterization. J. Comput. Aided Des. Comput. Graph., 16(5):632-637 (in Chinese).

[10] Isenburg, M., Gumhold, S., Gotsman, C., 2001. Connectivity Shapes. Proc. Conf. on Visualization. IEEE Computer Society, Washington, D.C., USA, p.135-142.

[11] Kazhdan, M., Chazelle, B., Dobkin, D., Funkhouser, T., Rusinkiewicz, S., 2003. A reflective symmetry descriptor for 3D models. Algorithmica: Special Issue, 38(1):201-225.

[12] Kharevych, L., Springborn, B., Schröder, P., 2006. Discrete conformal mappings via circle patterns. ACM Trans. Graph., 25(2):412-438.

[13] Kimmel, R., Sethian, J.A., 1999. Fast Voronoi Diagrams and Offsets on Triangulated Surfaces. Proc. AFA Conf. on Curves and Surfaces. Vanderbilt University Press, Nashville, TN, p.193-202.

[14] Li, L., Zhang, D., Pan, Z., Shi, J., Zhou, K., Ye, K., 2004. Watermarking 3D mesh by spherical parameterization. Comput. Graph., 28(6):981-989.

[15] Li, Y., Yang, Z.W., Deng, J.S., 2006. Spherical parameterization of genus-zero meshes by minimizing discrete harmonic energy. J. Zhejiang Univ. SCI. A, 7(9):1589-1595.

[16] Liu, X., Hu, J., Su, Z., Shi, X., 2008. Uniform quasi-conformal spherical parameterization. J. Comput. Aided Des. Comput. Graph., 20(5):618-624 (in Chinese).

[17] Meijster, A., Roerdink, J.B.T.M., Hesselink, W.H., 2000. A General Algorithm for Computing Distance Transforms in Linear Time. Goutsias, J., Vincent, L., Bloomberg, D.S. (Eds.), Mathematical Morphology and Its Applications to Image and Signal Processing, Kluwer, Boston, p.331-340.

[18] Mitra, N.J., Guibas, L.J., Pauly, M., 2006. Partial and approximate symmetry detection for 3D geometry. ACM Trans. Graph., 25(3):560-568.

[19] Mitra, N.J., Guibas, L.J., Pauly, M., 2007. Symmetrization. ACM Trans. Graph., 26(3), Article No. 63.

[20] Mitsumoto, H., Tamura, S., Okazaki, K., Kajimi, N., Fukui, Y., 1992. 3D Reconstruction using mirror images based on a plane symmetry recovery method. IEEE Trans. Pattern Anal. Mach. Intell., 14(9):941-946.

[21] Pauly, M., Mitra, N.J., Wallner, J., Pottmann, H., Guibas, L.J., 2008. Discovering structural regularity in 3D geometry. ACM Trans. Graph., 27(3), Article No. 43.

[22] Praun, E., Hoppe, H., 2003. Spherical Parameterization and Remeshing. Computer Graphics Proc., Annual Conf., ACM, New York, USA, p.340-350.

[23] Saba, S., Yavneh, I., Gotsman, C., Sheffer, A., 2005. Practical Spherical Embedding of Manifold Triangle Meshes. Proc. Int. Conf. on Shape Modeling and Applications, IEEE Computer Society, Washington, D.C., USA, p.258-267.

[24] Sander, P., Snyder, J., Gortler, S., Hoppe, H., 2001. Texture Mapping Progressive Meshes. ACM SIGGRAPH. New York, USA, p.409-416.

[25] Shapiro, A., Tal, A., 1999. Polyhedron realization for shape transformation. The Vis. Comput., 14(8-9):429-444.

[26] Sheffer, A., Gotsman, C., Dyn, N., 2003. Robust spherical parameterization of triangular meshes. Comput., 72(1-2):185-193.

[27] Sheffer, A., Praun, E., Rose, K., 2006. Mesh parameterization methods and their applications. Comput. Graph. Vision, 2(2):105-171.

[28] Tutte, W.T., 1963. How to draw a graph. London Math. Soc., 13(1):743-768.

[29] Zayer, R., Rössl, C., Seidel, H.P., 2005a. Discrete Tensorial Quasi-harmonic Maps. Shape Modeling Int. Proc., Cambridge, MA, USA, p.276-285.

[30] Zayer, R., Rössl, C., Seidel, H.P., 2005b. Setting the Boundary Free: A Composite Approach to Surface Parameterization. Proc. 3rd Eurographics Symp. on Geometry Processing, Eurographics Association Aire-la-Ville, Switzerland, p.101-110.

[31] Zayer, R., Rössl, C., Seidel, H.P., 2006. Curvilinear Spherical Parameterization. Proc. Shape Modeling and Applications. IEEE Computer Society, Washington, D.C., USA, p.57-64.

[32] Zhou, K., Bao, H., Shi, J., 2002. A unified framework for digital geometry processing. Chin. J. Comput., 25(9):904-909 (in Chinese).

[33] Zhou, K., Bao, H., Shi, J., 2004. 3D surface filtering using spherical harmonics. Computer-Aided Des., 36(4):363-375.

Open peer comments: Debate/Discuss/Question/Opinion

<1>

Please provide your name, email address and a comment





Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE