Fundamentals of spherical parameterization for 3D meshes

Craig Gotsman, Xianfeng Gu, Alla Sheffer

Research output: Contribution to journalConference articlepeer-review

147 Scopus citations


Parameterization of 3D mesh data is important for many graphics 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 triangle mesh onto the 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 are not too distorted and do not overlap. Satisfying the non-overlapping requirement is the most difficult and critical component of this process. We describe a generalization of the method of barycentric coordinates for planar parameterization which solves the spherical parameterization problem, prove its correctness by establishing a connection to spectral graph theory and show how to compute these parameterizations.

Original languageEnglish (US)
Pages (from-to)358-363
Number of pages6
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 2003
Externally publishedYes
EventACM SIGGRAPH 2003 - San Diego, CA, United States
Duration: Jul 27 2003Jul 31 2003

All Science Journal Classification (ASJC) codes

  • Computer Graphics and Computer-Aided Design


  • Embedding
  • Parameterization
  • Triangle mesh


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