Surface Meshing with Curvature Convergence
Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorit...
| Veröffentlicht in: | IEEE transactions on visualization and computer graphics. - 1996. - 20(2014), 6 vom: 10. Juni, Seite 919-34 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2014
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| Zugriff auf das übergeordnete Werk: | IEEE transactions on visualization and computer graphics |
| Schlagworte: | Journal Article Research Support, U.S. Gov't, Non-P.H.S. |
| Zusammenfassung: | Surface meshing plays a fundamental role in graphics and visualization. Many geometric processing tasks involve solving geometric PDEs on meshes. The numerical stability, convergence rates and approximation errors are largely determined by the mesh qualities. In practice, Delaunay refinement algorithms offer satisfactory solutions to high quality mesh generations. The theoretical proofs for volume based and surface based Delaunay refinement algorithms have been established, but those for conformal parameterization based ones remain wide open. This work focuses on the curvature measure convergence for the conformal parameterization based Delaunay refinement algorithms. Given a metric surface, the proposed approach triangulates its conformal uniformization domain by the planar Delaunay refinement algorithms, and produces a high quality mesh. We give explicit estimates for the Hausdorff distance, the normal deviation, and the differences in curvature measures between the surface and the mesh. In contrast to the conventional results based on volumetric Delaunay refinement, our stronger estimates are independent of the mesh structure and directly guarantee the convergence of curvature measures. Meanwhile, our result on Gaussian curvature measure is intrinsic to the Riemannian metric and independent of the embedding. In practice, our meshing algorithm is much easier to implement and much more efficient. The experimental results verified our theoretical results and demonstrated the efficiency of the meshing algorithm |
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| Beschreibung: | Date Completed 02.12.2015 Date Revised 11.09.2015 published: Print Citation Status PubMed-not-MEDLINE |
| ISSN: | 1941-0506 |
| DOI: | 10.1109/TVCG.2013.253 |