Mean value coordinates for closed triangular meshes Conference Paper uri icon

abstract

  • 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. Copyright © 2005 by the Association for Computing Machinery, Inc.

altmetric score

  • 6

author list (cited authors)

  • Ju, T., Schaefer, S., & Warren, J.

citation count

  • 293

publication date

  • July 2005