On the approximation of a smooth surface with a triangulated mesh

Jean-Marie Morvan*, B. Thibert

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

We approximate the normals and the area of a smooth surface with the normals and the area of a triangulated mesh whose vertices belong to the smooth surface. Both approximations only depend on the triangulated mesh (which is supposed to be known), on an upper bound on the smooth surface's curvature, on an upper bound on its reach (which is linked to the local feature size) and on an upper bound on the Hausdorff distance between both surfaces. We show in particular that the upper bound on the error of the normals is better when triangles are right-angled (even if there are small angles). We do not need every angle to be quite large. We just need each triangle of the triangulated mesh to contain at least one angle whose sinus is large enough.

Original languageEnglish (US)
Pages (from-to)337-352
Number of pages16
JournalComputational Geometry: Theory and Applications
Volume23
Issue number3
DOIs
StatePublished - Jan 1 2002

Keywords

  • Approximation
  • Local feature size
  • Medial axis
  • Reach
  • Triangulated mesh

ASJC Scopus subject areas

  • Computer Science Applications
  • Geometry and Topology
  • Control and Optimization
  • Computational Theory and Mathematics
  • Computational Mathematics

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