Article

3D triangular mesh optimization in geometry processing for CAD

Authors:

Guoping WangAuthors Info & Claims

SPM '07: Proceedings of the 2007 ACM symposium on Solid and physical modeling

Pages 23 - 33

https://doi.org/10.1145/1236246.1236253

Published: 04 June 2007 Publication History

Abstract

Geometry processing in CAD proposes rigorous requirements on mesh quality. In this paper an integrated triangular mesh optimization method is proposed. Edge marking function and local edge operations are used to improve the vertex sampling. Modified weighted centroidal Voronoi tessellation is employed to regularize the triangle geometry. A simulated annealing algorithm is proposed for optimizing the vertex connectivity. Finally, a signal processing filter is developed for mesh denoising. In every optimization stage, the shape deviations from original mesh are prevented, and the boundaries and features are well preserved. Since all modifications are performed locally, the error-prone global parameterization is avoided. This technique has been deployed in real-world product design. Its advantage and robustness are verified by many examples implemented in the geometric design software PUM 2.0 developed by Peking University.

References

[1]

Botsch, M., and Kobbelt, L. 2004 A remeshing approach to multiresolution modeling In Proceedings of Eurographics Sympoium on Geometry Processing, 189--196.

Digital Library

[2]

Shewchuk, J. R. 2002. What is a good linear element? interpolation, conditioning, and quality measures. In Proceedings of 11th International Meshing Roundtable.

[3]

Lee, A. W. F., Sweldens, W., Schroder, P., Cowsar, L., and Dobkin, D. 1998. MAPS: Multiresolution adaptive parameterization of surfaces. In Proceedings of ACM SIGGRAPH 1998, 95--104.

Digital Library

[4]

Guskov, I., Vidimce, K., Sweldens, W., and Schroder, P. 2000. Normal meshes. In Proceedings of ACM SIGGRAPH 2000, 95--102.

Digital Library

[5]

Hormann, K., Labsik, U., and Greiner, G. 2001. Remeshing triangulated surfaces with optimal parameterizations. Computer-Aided Design 33, 11, 779--788.

[6]

Vorsatz, J., Rossl, C., Kobbelt, L., and Seidel, H. 2001. Feature sensitive remeshing. Computer Graphics Forum, 393--401.

[7]

Alliez, P., Meyer, M., and Desbrun, M. 2002. Interactive geometry remeshing. In Proceedings of ACM SIGGRAPH 2002, 347--354.

Digital Library

[8]

Gu, X., Gortler, S. J., and Hoppe, H. 2002. Geometry images. In Proceedings of ACM SIGGRAPH 2002, 355--361.

Digital Library

[9]

Alliez, P., Cohen-Steiner, D., Devillers, O., Levy, B., and Desbrun, M. 2003. Anisotropic polygonal remeshing. ACM Transactions on Graphics, 22, 485--493.

Digital Library

[10]

Alliez, P., Verdiere E. C., Devillers, O., and Isenburg, M. 2003. Isotropic surface remeshing. In Proceedings of Shape Modeling International 2003, 49--58.

Digital Library

[11]

Surazhsky, V., and Gotsman, C. 2003. Explicit surface remeshing. In Proceedings of the Eurograhics / ACM SIGGRAPH Symposium on Geometry Processing, 20--30.

Digital Library

[12]

Surazhsky, V., Alliez, P., and Gotsman, C. 2003. Isotropic remeshing of surfaces: a local parameterization approach. In Proceedings of the 12th International meshing Roundtable, 215--224.

[13]

Vorsatz, J., Rossl, C., and Seidel, H. P. 2003. Dynamic remeshing and applications. In Proceedings of the 3th ACM Symposium on Solid Modeling and Applications, 167--175.

Digital Library

[14]

Taubin, G. 1995. A signal processing approach o fair surface design. In Proceedings of ACM SIGGRAPH 1995, 351--358.

Digital Library

[15]

Desbrun, M., Meyer, M., Schroder, P., and Barr, A. H. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In Proceedings of ACM SIGGRAPH 1999, 317--324.

Digital Library

[16]

Fleishman, S., Drori, I., and Cohen, D. 2003. Bilateral meshing denoising. In Proceedings of ACM SIGGRAPH 2003, 950--953.

Digital Library

[17]

Jones, T., Durand, F., and Desbrun, M. 2003. Non-iterative, feature-preserving mesh smoothing. In Proceedings of ACM SIGGRAPH 2003, 943--949.

Digital Library

[18]

Kobbelt, L., Bareuther, T., and Seidel, H.-P. 2000. Multiresolution deformation for meshes with dynamic vertex connectivity. In Proceedings of Eurographics 2000, 249--260.

[19]

Brauwerman, R., Zoll, S. J., Farmer, C. L., and Gunzberger, M. 1999. Centroidal Voronoi tessellations are not good igsaw puzzles. Found at http://www.math.iastate.edu/reu/1999/cvt.pdf.

[20]

Du, Q., Faber, V., and Gunzburger, M. 1999. Centroidal Voronoi tessellations: applications and algorithms. In SIAM Review 41, 4, 637--676.

Digital Library

[21]

Kirkpatrick, S., Gelatt, C., and Vecchi, J. 1983. Optimization by simulated annealings. In Science, 4, 671--680.

[22]

Ohtake, Y., Belyaev, A., and Seidel, H.-P. 2002. Mesh smoothing by adaptive and anisotropic Gaussian filter applied to mesh normal. In Proceedings of the Vision, Modeling and Visualization 2002, 203--210.

[23]

Pinkall, U., and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. In Exp. Math 2, 1, 15--36.

[24]

Floater, M. 2003. Mean value coordinates. In Computer Aided Geometric Design, 20, 19--27.

[25]

Frey, P. J., and Borouchaki, H. 1998. Geometric surface mesh optimization. In Computing and Visualization in Science, 1, 113--121.

[26]

Cignoni, P., Rocchini, C., and Scopigno, R. 1998. Metro: Measuring error on simplified surfaces. In Computer Graphics Forum, 17, 2, 167--174.

Cited By

Liu JYao YFei YZhang GZheng L(2024)Surface remeshing with preservation of sharp features through iterative identification and optimization of sample pointsComputers & Graphics10.1016/j.cag.2024.103949121(103949)Online publication date: Jun-2024
https://doi.org/10.1016/j.cag.2024.103949
Khan DPlopski AFujimoto YKanbara MJabeen GZhang YZhang XKato H(2022)Surface Remeshing: A Systematic Literature Review of Methods and Research DirectionsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.301664528:3(1680-1713)Online publication date: 1-Mar-2022
https://doi.org/10.1109/TVCG.2020.3016645
Rakotosaona MAigerman NMitra NOvsjanikov MGuerrero P(2021)Differentiable surface triangulationACM Transactions on Graphics10.1145/3478513.348055440:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480554
Show More Cited By

Index Terms

3D triangular mesh optimization in geometry processing for CAD
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
      1. Parametric curve and surface models
      2. Volumetric models

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cover image ACM Other conferences

SPM '07: Proceedings of the 2007 ACM symposium on Solid and physical modeling

June 2007

455 pages

ISBN:9781595936660

DOI:10.1145/1236246

Program Chairs:
Bruno Levy
INRIA
,
Dinesh Manocha
University of North Carolina

Copyright © 2007 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Tsinghua University: Tsinghua University

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SIGGRAPH: ACM Special Interest Group on Computer Graphics and Interactive Techniques

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 04 June 2007

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SPM07

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Tsinghua University

SPM07: Symposium on Solid and Physical Modeling

June 4 - 6, 2007

Beijing, China

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Cited By

Liu JYao YFei YZhang GZheng L(2024)Surface remeshing with preservation of sharp features through iterative identification and optimization of sample pointsComputers & Graphics10.1016/j.cag.2024.103949121(103949)Online publication date: Jun-2024
https://doi.org/10.1016/j.cag.2024.103949
Khan DPlopski AFujimoto YKanbara MJabeen GZhang YZhang XKato H(2022)Surface Remeshing: A Systematic Literature Review of Methods and Research DirectionsIEEE Transactions on Visualization and Computer Graphics10.1109/TVCG.2020.301664528:3(1680-1713)Online publication date: 1-Mar-2022
https://doi.org/10.1109/TVCG.2020.3016645
Rakotosaona MAigerman NMitra NOvsjanikov MGuerrero P(2021)Differentiable surface triangulationACM Transactions on Graphics10.1145/3478513.348055440:6(1-13)Online publication date: 10-Dec-2021
https://dl.acm.org/doi/10.1145/3478513.3480554
Gao ZYu ZHolst M(2013)Feature-preserving surface mesh smoothing via suboptimal Delaunay triangulationGraphical Models10.1016/j.gmod.2012.10.00775:1(23-38)Online publication date: 1-Jan-2013
https://dl.acm.org/doi/10.1016/j.gmod.2012.10.007
Chiang CJong BLin T(2011)A robust feature-preserving semi-regular remeshing method for triangular meshesThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-011-0555-127:9(811-825)Online publication date: 1-Sep-2011
https://dl.acm.org/doi/10.1007/s00371-011-0555-1
Jong BChiang CLee PLin T(2010)High quality surface remeshing with equilateral triangle gridThe Visual Computer: International Journal of Computer Graphics10.1007/s00371-009-0392-726:2(121-136)Online publication date: 12-Jan-2010
https://dl.acm.org/doi/10.1007/s00371-009-0392-7
Fu YZhou BHaines EMcGuire M(2008)Direct sampling on surfaces for high quality remeshingProceedings of the 2008 ACM symposium on Solid and physical modeling10.1145/1364901.1364919(115-124)Online publication date: 2-Jun-2008
https://dl.acm.org/doi/10.1145/1364901.1364919
Shi ZLi J(2008)Extract the 3D Facial Region from Point Clouds2008 International Conference on Apperceiving Computing and Intelligence Analysis10.1109/ICACIA.2008.4770011(227-231)Online publication date: Dec-2008
https://doi.org/10.1109/ICACIA.2008.4770011

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