Mean value coordinates for closed triangular meshes

Tao Ju, Scott Schaefer, Joe Warren

Research output: Contribution to journalConference articlepeer-review

514 Scopus citations


Constructing a function that interpolates a set of values defined at vertices of a mesh is a fundamental operation in computer graphics. Such an interpolant has many uses in applications such as shading, parameterization and deformation. For closed polygons, mean value coordinates have been proven to be an excellent method for constructing such an interpolant. In this paper, we generalize mean value coordinates from closed 2D polygons to closed triangular meshes. Given such a mesh P, we show that these coordinates are continuous everywhere and smooth on the interior of P. The coordinates are linear on the triangles of P and can reproduce linear functions on the interior of P. To illustrate their usefulness, we conclude by considering several interesting applications including constructing volumetric textures and surface deformation.

Original languageEnglish
Pages (from-to)561-566
Number of pages6
JournalACM Transactions on Graphics
Issue number3
StatePublished - Jul 2005
EventACM SIGGRAPH 2005 - Los Angeles, CA, United States
Duration: Jul 31 2005Aug 4 2005


  • Barycentric coordinates
  • Mean value coordinates
  • Surface deformation
  • Volumetric textures


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