Robust spherical parameterization of triangular meshes

A. Sheffer, C. Gotsman, N. Dyn

Research output: Contribution to journalArticlepeer-review

33 Scopus citations

Abstract

Parameterization of 3D mesh data is important for many graphics and mesh processing applications, in particular for texture mapping, remeshing and morphing. Closed, manifold, genus-0 meshes are topologically equivalent to a sphere, hence this is the natural parameter domain for them. Parameterizing a 3D triangle mesh onto the 3D sphere means assigning a 3D position on the unit sphere to each of the mesh vertices, such that the spherical triangles induced by the mesh connectivity do not overlap. This is called a spherical triangulation. In this paper we formulate a set of necessary and sufficient conditions on the spherical angles of the spherical triangles for them to form a spherical triangulation. We formulate and solve an optimization procedure to produce spherical triangulations which reflect the geometric properties of a given 3D mesh in various ways.

Original languageEnglish (US)
Pages (from-to)185-193
Number of pages9
JournalComputing (Vienna/New York)
Volume72
Issue number1-2
DOIs
StatePublished - Jan 1 2004
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Theoretical Computer Science
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Computational Mathematics

Keywords

  • Mesh processing
  • Parameterization
  • Spherical embedding
  • Spherical parametrization

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