CLC number: TP391.41
On-line Access: 2024-08-27
Received: 2023-10-17
Revision Accepted: 2024-05-08
Crosschecked: 2009-12-30
Cited: 0
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Jun-jie CAO, Zhi-xun SU, Xiu-ping LIU, Hai-chuan BI. Measured boundary parameterization based on Poisson’s equation[J]. Journal of Zhejiang University Science C, 2010, 11(3): 187-198.
@article{title="Measured boundary parameterization based on Poisson’s equation",
author="Jun-jie CAO, Zhi-xun SU, Xiu-ping LIU, Hai-chuan BI",
journal="Journal of Zhejiang University Science C",
volume="11",
number="3",
pages="187-198",
year="2010",
publisher="Zhejiang University Press & Springer",
doi="10.1631/jzus.C0910460"
}
%0 Journal Article
%T Measured boundary parameterization based on Poisson’s equation
%A Jun-jie CAO
%A Zhi-xun SU
%A Xiu-ping LIU
%A Hai-chuan BI
%J Journal of Zhejiang University SCIENCE C
%V 11
%N 3
%P 187-198
%@ 1869-1951
%D 2010
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.C0910460
TY - JOUR
T1 - Measured boundary parameterization based on Poisson’s equation
A1 - Jun-jie CAO
A1 - Zhi-xun SU
A1 - Xiu-ping LIU
A1 - Hai-chuan BI
J0 - Journal of Zhejiang University Science C
VL - 11
IS - 3
SP - 187
EP - 198
%@ 1869-1951
Y1 - 2010
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.C0910460
Abstract: One major goal of mesh parameterization is to minimize the conformal distortion. measured boundary parameterizations focus on lowering the distortion by setting the boundary free with the help of distance from a center vertex to all the boundary vertices. Hence these parameterizations strongly depend on the determination of the center vertex. In this paper, we introduce two methods to determine the center vertex automatically. Both of them can be used as necessary supplements to the existing measured boundary methods to minimize the common artifacts as a result of the obscure choice of the center vertex. In addition, we propose a simple and fast measured boundary parameterization method based on the poisson’s equation. Our new approach generates less conformal distortion than the fixed boundary methods. It also generates more regular domain boundaries than other measured boundary methods. Moreover, it offers a good tradeoff between computation costs and conformal distortion compared with the fast and robust angle based flattening (ABF++).
[1] Aujay, G., Hétroy, F., Lazarus, F., Depraz, C., 2007. Harmonic Skeleton for Realistic Character Animation. Proc. ACM SIGGRAPH/Eurographics Symp. on Computer Animation, p.151-160.
[2] Ben-Chen, M., Gotsman, C., Bunin, G., 2008. Conformal flattening by curvature prescription and metric scaling. Comput. Graph. Forum, 27(2):449-458.
[3] Chen, Y., Davis, T.A., Hager, W.W., Rajamanickam, S., 2008. Algorithm 887: CHOLMOD, supernodal sparse Cholesky factorization and update/downdate. ACM Trans. Math. Softw., 35(3):1-14.
[4] Desbrun, M., Meyer, M., Alliez, P., 2002. Intrinsic parameterizations of surface meshes. Comput. Graph. Forum, 21(3):209-218.
[5] Dong, S., Garland, M., 2007. Iterative Methods for Improving Mesh Parameterizations. IEEE Int. Conf. on Shape Modeling and Application, p.185-194.
[6] Dong, S., Kircher, S., Garland, M., 2005. Harmonic functions for quadrilateral remeshing of arbitrary manifolds. Comput. Aided Geom. Des., 22(5):392-423.
[7] Fattal, R., Lischinski, D., Werman, M., 2002. Gradient Domain High Dynamic Range Compression. Proc. 29th Annual Conf. on Computer Graphics and Interactive Techniques, p.249-256.
[8] Floater, M.S., 2003. Mean value coordinates. Comput. Aided Geom. Des., 20(1):19-27.
[9] Floater, M.S., Hormann, K., 2005. Surface Parameterization: A Tutorial and Survey. Advances in Multiresolution for Geometric Modelling. Springer Berlin Heidelberg, p.157-186.
[10] Gabriel, P., Laurent, C., 2005. Geodesic Computations for Fast and Accurate Surface Remeshing and Parameterization. In: Brezis, H. (Ed.), Elliptic and Parabolic Problems. Springer-Verlag, p.157-171.
[11] Hormann, K., Greiner, G., 1999. MIPS: An Efficient Global Parameterization Method. Curve and Surface Design. Vanderbilt University Press, Saint-Malo, p.153-162.
[12] Hormann, K., Lévy, B., Sheffer, A., 2007. Mesh Parameterization: Theory and Practice. ACM SIGGRAPH Course Notes, p.1-122.
[13] Karni, Z., Gotsman, C., Gortler, S.J., 2005. Free-Boundary Linear Parameterization of 3D Meshes in the Presence of Constraints. Proc. Int. Conf. on Shape Modeling and Applications, p.268-277.
[14] Kazhdan, M., Bolitho, M., Hoppe, H., 2006. Poisson Surface Reconstruction. Proc. 4th Eurographics Symp. on Geometry Processing, p.61-70.
[15] Kharevych, L., Springborn, B., Schröder, P., 2006. Discrete conformal mappings via circle patterns. ACM Trans. Graph., 25(2):412-438.
[16] Kimmel, R., Sethian, J.A., 1998. Computing geodesic paths on manifolds. PNAS, 95(15):8431-8435.
[17] Lee, H., Tong, Y., Desbrun, M., 2005. Geodesics-based one-to-one parameterization of 3D triangle meshes. IEEE Multim., 12(1):27-33.
[18] Lee, S., Lee, H., 2007. Parameterization of 3D Surface Patches by Straightest Distances. Proc. 7th Int. Conf. on Computational Science: Part II, 4488:73-80.
[19] Lee, S., Han, J., Lee, H., 2006. Straightest paths on meshes by cutting planes. LNCS, 4077:609-615.
[20] Lee, Y., Kim, H.S., Lee, S., 2002. Mesh parameterization with a virtual boundary. Comput. Graph., 26(5):677-686.
[21] Lévy, B., Petitjean, S., Ray, N., Maillot, J., 2002. Least squares conformal maps for automatic texture atlas generation. ACM Trans. Graph., 21(3):362-371.
[22] Liu, L., Zhang, L., Xu, Y., Gotsman, C., Gortler, S.J., 2008. A local/global approach to mesh parameterization. Comput. Graph. Forum, 27(5):1495-1504.
[23] Mitchell, J.S.B., 2000. Geometric Shortest Paths and Network Optimization. Handbook of Computational Geometry. Elsevier Science, Amsterdam, the Netherlands, p.633-701.
[24] Mullen, P., Tong, Y., Alliez, P., Desbrun, M., 2008. Spectral conformal parameterization. Comput. Graph. Forum, 27(5):1487-1494.
[25] Nealen, A., Igarashi, T., Sorkine, O., Alexa, M., 2006. Laplacian Mesh Optimization. Proc. 4th Int. Conf. on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia, p.381-389.
[26] Pérez, P., Gangnet, M., Blake, A., 2003. Poisson image editing. ACM Trans. Graph., 22(3):313-318.
[27] Polthier, K., Schmies, M., 2006. Straightest Geodesics on Polyhedral Surfaces. ACM SIGGRAPH Course, p.30-38.
[28] Sander, P.V., Snyder, J., Gortler, S.J., Hoppe, H., 2001. Texture Mapping Progressive Meshes. Proc. 28th Annual Conf. on Computer Graphics and Interactive Techniques, p.409-416.
[29] Shapira, L., Shamir, A., 2008. Local Geodesic Parameterization: An Ant’s Perspective. Mathematical Foundations of Scientific Visualization, Computer Graphics, and Massive Data Exploration, Mathematics and Visualization. Springer Berlin Heidelberg, p.127-137.
[30] Sheffer, A., de Sturler, E., 2000. Surface Parameterization for Meshing by Triangulation Flattening. Proc. 9th Int. Meshing Roundtable, p.161-172.
[31] Sheffer, A., Hart, J.C., 2002. Seamster: Inconspicuous Low-Distortion Texture Seam Layout. Proc. Conf. on Visualization, p.291-298.
[32] Sheffer, A., Lévy, B., Mogilnitsky, M., Bogomyakov, A., 2005. ABF++: fast and robust angle based flattening. ACM Trans. Graph., 24(2):311-330.
[33] Sheffer, A., Praun, E., Rose, K., 2006. Mesh parameterization methods and their applications. Found. Trends Comput. Graph. Vis., 2(2):105-171.
[34] Sifri, O., Sheffer, A., Gotsman, C., 2003. Geodesic-Based Surface Remeshing. Proc. 12th Int. Meshing Roundtable, p.189-199.
[35] Springborn, B., Schröder, P., Pinkall, U., 2008. Conformal equivalence of triangle meshes. ACM Trans. Graph., 27(3):1-11.
[36] Tierny, J., Vandeborre, J.P., Daoudi, M., 2006. 3D Mesh Skeleton Extraction Using Topological and Geometrical Analyses. Proc. 14th Pacific Conf. on Computer Graphics and Applications, p.85-94.
[37] Wang, C.C.L., Wang, Y., Tang, K., Yuen, M.M.F., 2004. Reduce the stretch in surface flattening by finding cutting paths to the surface boundary. Comput. Aided Des., 36(8):665-677.
[38] Yang, Y.L., Kim, J.H., Luo, F., Hu, S.M., Gu, X.F., 2008. Optimal surface parameterization using inverse curvature map. IEEE Trans. Vis. Comput. Graph., 14(5):1054-1066.
[39] Yu, Y.Z., Zhou, K., Xu, D., Shi, X.H., Bao, H.J., Guo, B.N., Shum, H.Y., 2004. Mesh editing with Poisson-based gradient field manipulation. ACM Trans. Graph., 23(3):644-651.
[40] Zayer, R., Rössl, C., Seidel, H.P., 2005. Setting the Boundary Free: A Composite Approach to Surface Parameterization. Proc. 3rd Eurographics Symp. on Geometry Processing, p.91-100.
[41] Zhou, K., Huang, J., Snyder, J., Liu, X.G., Bao, H.J., Guo, B.N., Shum, H.Y., 2005. Large mesh deformation using the volumetric graph Laplacian. ACM Trans. Graph., 24(3):496-503.
[42] Zhu, X.P., Hu, S.M., Ralph, M., 2003. Skeleton-based seam computation for triangulated surface parameterization. LNCS, 2768:1-13.
Open peer comments: Debate/Discuss/Question/Opinion
<1>
maomao
2010-01-29 10:39:17
This paper is interesting and worth reading very much!Highly recommend!