Andrew Nealen
Takeo Igarashi
Olga Sorkine
Marc Alexa
ABSTRACT
We introduce a framework for triangle shape optimization and feature preserving smoothing of triangular meshes that is guided by the vertex Laplacians, specifically, the uniformly weighted Laplacian and the discrete mean curvature normal. Vertices are relocated so that they approximate prescribed Laplacians and positions in a weighted least-squares sense; the resulting linear system leads to an efficient, non-iterative solution. We provide different weighting schemes and demonstrate the effectiveness of the framework on a number of detailed and highly irregular meshes; our technique successfully improves the quality of the triangulation while remaining faithful to the original surface geometry, and it is also capable of smoothing the surface while preserving geometric features.
- Alliez, P., Meyer, M., and Desbrun, M. 2002. Interactive geometry remeshing. In SIGGRAPH '02: Proceedings of the 29th annual conference on Computer graphics and interactive techniques, 347--354. Google Scholar
Digital Library
- Alliez, P., Éric Colin De Verdière, Devillers, O., and Isenburg, M. 2003. Isotropic surface remeshing. In SMI '03: Proceedings of the Shape Modeling International 2003. Google ScholarDigital Library
- Alliez, P., Ucelli, G., Gotsman, C., and Attene, M., 2005. Recent advances in remeshing of surfaces. Part of the state-of-the-art report of the AIM@SHAPE EU network.Google Scholar
- Bobenko, A. I., and Schröder, P. 2005. Discrete willmore flow. In Eurographics Symposium on Geometry Processing, 101--110. Google ScholarDigital Library
- Botsch, M., and Kobbelt, L. 2004. A remeshing approach to multiresolution modeling. In SGP '04: Proceedings of the 2004 Eurographics/ACM SIGGRAPH symposium on Geometry processing, 185--192. Google ScholarDigital Library
- Bouguet, J.-Y., and Perona, P. 1998. 3D photography on your desk. In ICCV'98 proceedings, 43--50. Google ScholarDigital Library
- Chen, C.-Y., and Cheng, K.-Y 2005. A sharpness dependent filter for mesh smoothing. Comput. Aided Geom. Des. 22, 5, 376--391. Google ScholarDigital Library
- Cignoni, P., Rocchini, C., and Scopigno, R. 1998. Metro: Measuring error on simplified surfaces. Computer Graphics Forum 17, 2, 167--174.Google ScholarCross Ref
- Desbrun, M., Meyer, M., Schröder, P., and Barr, A. H. 1999. Implicit fairing of irregular meshes using diffusion and curvature flow. In SIGGRAPH '99: Proceedings of the 26th annual conference on Computer graphics and interactive techniques, 317--324. Google ScholarDigital Library
- Fleishman, S., Drori, I., and Cohen-Or, D. 2003. Bilateral mesh denoising. ACM Trans. Graph. 22, 3, 950--953. Google ScholarDigital Library
- Fujiwara, K. 1995. Eigenvalues of Laplacians on a closed Riemannian manifold and its nets. In Proc. AMS., 2585--2594.Google ScholarCross Ref
- Hildebrandt, K., and Polthier, K. 2005. Anisotropic filtering of non-linear surface features. Computer Graphics Forum (Eurographics Proceedings) 23, 3, 101--110.Google Scholar
- Jones, T. R., Durand, P., and Desbrun, M. 2003. Noniterative, feature-preserving mesh smoothing. ACM Trans. Graph. 22, 3, 943--949. Google ScholarDigital Library
- Lipman, Y., Sorkine, O., Cohen-Or, D., and Levin, D. 2004. Differential coordinates for interactive mesh editing. In International Conference on Shape Modeling and Applications, 181--190. Google ScholarDigital Library
- Meyer, M., Desbrun, M., Schröder, P., and Barr, A. H. 2003. Discrete differential-geometry operators for triangulated 2-manifolds. Visualization and Mathematics III, pages 35--57.Google Scholar
- Nealen, A., Sorkine, O., Alexa, M., and Cohen-Or, D. 2005. A sketch-based interface for detail-preserving mesh editing. ACM Trans. Graph. 24, 3, 1142--1147. Google ScholarDigital Library
- Pébay, P. P., and Baker, T. J. 2003. Analysis of triangle quality measures. Math. Comput. 72, 244, 1817--1839. Google ScholarDigital Library
- Pinkall, U., and Polthier, K. 1993. Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2, 1, 15--36.Google ScholarCross Ref
- Schneider, R., and Kobbelt, L. 2001. Geometric fairing of irregular meshes for freeform surface design. Computer Aided Geometric Design 18, 4, 359--379. Google ScholarDigital Library
- Sorkine, O., and Cohen-Or, D. 2004. Least-squares meshes. In Proceedings of Shape Modeling International, 191--199. Google ScholarDigital Library
- Sorkine, O., and Nealen, A. 2006. A note on Laplacian mesh smoothing. Submitted for publication.Google Scholar
- Sorkine, O., Lipman, Y., Cohen-Or, D., Alexa, M., Rossl, C., and Seidel, H.-P. 2004. Laplacian surface editing. In Proceedings of the Eurographics/ACM SIGGRAPH Symposium on Geometry processing, 179--188. Google ScholarDigital Library
- Sorkine, O., Cohen-Or, D., Irony, D., and Toledo, S. 2005. Geometry-aware bases for shape approximation. IEEE Transactions on Visualization and Computer Graphics 11, 2, 171--180. Google ScholarDigital Library
- Surazhsky, V., and Gotsman, C. 2003. Explicit surface remeshing. In SGP '03: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on Geometry processing, 20--30. Google ScholarDigital Library
- Surazhsky, V., Alliez, P., and Gotsman, C. 2003. Isotropic remeshing of surfaces: a local parameterization approach. In proceedings of 12th International Meshing Roundtable, 215--224.Google Scholar
- Taubin, G. 1995. A signal processing approach to fair surface design. In SIGGRAPH '95: Proceedings of the 22nd annual conference on Computer graphics and interactive techniques, 351--358. Google ScholarDigital Library
- Taubin, G., 2000. Geometric signal processing on polygonal meshes. EUROGRAPHICS state-of-the-art report.Google Scholar
- Toledo, S. 2003. TAUCS: A Library of Sparse Linear Solvers. Tel Aviv University.Google Scholar
- Tukey, J. W. 1977. Exploratory Data Analysis. Addison-Wesley.Google Scholar
- Turk, G. 1992. Re-tiling polygonal surfaces. In SIGGRAPH '92: Proceedings of the 19th annual conference on Computer graphics and interactive techniques, 55--64. Google ScholarDigital Library
- Vorsatz, J., Rössl, C., Kobbelt, L., and Seidel, H.-P. 2001. Feature sensitive remeshing. Computer Graphics Forum 20, 3, 393--01.Google ScholarCross Ref
- Vorsatz, J., Rössl, C., and Seidel, H.-P. 2003. Dynamic remeshing and applications. In SM '03: Proceedings of the eighth ACM symposium on Solid modeling and applications, 167--175. Google ScholarDigital Library
- Yu, Y., Zhou, K., Xu, D., Shi, X., Bao, H., Guo, B., and Shum, H.-Y 2004. Mesh editing with Poisson-based gradient field manipulation. ACM Trans. Graph. 23, 3, 644--651. Google ScholarDigital Library
Index Terms
- Laplacian mesh optimization
Recommendations
LV surface reconstruction from sparse TMRI using Laplacian surface deformation and optimization
ISBI'09: Proceedings of the Sixth IEEE international conference on Symposium on Biomedical Imaging: From Nano to MacroWe propose a novel framework to reconstruct the left ventricle (LV)'s 3D surface from sparse tagged-MRI (tMRI). First we acquire an initial surface mesh from a dense tMRI. Then landmarks are calculated both on contours of a specific new tMRI data and on ...
5-6-7 meshes
GI '12: Proceedings of Graphics Interface 2012We introduce a new type of meshes called 5-6-7 meshes. For many mesh processing tasks, low- or high-valence vertices are undesirable. At the same time, it is not always possible to achieve complete vertex valence regularity, i.e., to only have valence-6 ...
Retiling scheme: a novel approach of direct anisotropic quad-dominant remeshing
Remeshing has been an active research topic in Digital Geometry Processing. In this paper, a novel approach of direct anisotropic quad-dominant remeshing is proposed. We apply the retiling method to the particular problem of quad-dominant remeshing. ...
Comments