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Barycentric coordinates for convex polytopes

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Abstract

An extension of the standard barycentric coordinate functions for simplices to arbitrary convex polytopes is described. The key to this extension is the construction, for a given convex polytope, of a unique polynomial associated with that polytope. This polynomial, theadjoint of the polytope, generalizes a previous two-dimensional construction described by Wachspress. The barycentric coordinate functions for the polytope are rational combinations of adjoints of various dual cones associated with the polytope.

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Communicated by C.A. Micchelli

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Warren, J. Barycentric coordinates for convex polytopes. Adv Comput Math 6, 97–108 (1996). https://doi.org/10.1007/BF02127699

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  • DOI: https://doi.org/10.1007/BF02127699

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