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.
Similar content being viewed by others
References
G. Farin,Curves and Surfaces for Computer Aided Geometric Design: A Practical Guide (Academic Press, New York, 1988).
W. Fleming,Functions of Several Variables (Springer, 1977).
B. Grunbaum,Convex Polytopes (Wiley, London, 1967).
C. W. Lee, Some recent results on convex polytopes, Manuscript (1989).
C. Loop and T. DeRose, A multisided generalization of Bézier surfaces, ACM Transactions on Graphics 8(3) (1989).
F. Preparata and M. I. Shamos,Computational Geometry: An Introduction (Springer, New York, 1985).
E. Wachspress,A Rational Finite Element Basis (Academic Press, 1975).
Author information
Authors and Affiliations
Additional information
Communicated by C.A. Micchelli
Rights and permissions
About this article
Cite this article
Warren, J. Barycentric coordinates for convex polytopes. Adv Comput Math 6, 97–108 (1996). https://doi.org/10.1007/BF02127699
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02127699