Surface meshing with curvature convergence

Huibin Li, Wei Zeng, Jean-Marie Morvan, Liming Chen, Xianfengdavid Gu

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

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. © 2014 IEEE.
Original languageEnglish (US)
Pages (from-to)919-934
Number of pages16
JournalIEEE Transactions on Visualization and Computer Graphics
Volume20
Issue number6
DOIs
StatePublished - Jun 2014

ASJC Scopus subject areas

  • Signal Processing
  • Computer Graphics and Computer-Aided Design
  • Software
  • Computer Vision and Pattern Recognition

Fingerprint

Dive into the research topics of 'Surface meshing with curvature convergence'. Together they form a unique fingerprint.

Cite this