论文信息 - Harmonic Coordinates

Harmonic Coordinates

Generalizations of barycentric coordinates in two and higher dimensions have been shown to have a number of applications in recent years, including finite element analysis, the definition of Spatches (n-sided generalizations of Bézier surfaces), free-form deformations, mesh parametrization, and interpolation. In this paper we present a new form of d dimensional generalized barycentric coordinates. The new coordinates are defined as solutions to Laplace’s equation subject to carefully chosen boundary conditions. Since solutions to Laplace’s equation are called harmonic functions, we call the new construction harmonic coordinates. We show that harmonic coordinates possess several properties that make them more attractive than mean value coordinates when used to define two and three dimensional deformations.

Mark Meyer | Tony DeRose | T. DeRose | Mark Meyer

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