Barycentric coordinates for polytopes

In Wachspress (1975) [1], theory was developed for constructing rational basis functions for convex polygons and polyhedra. These barycentric coordinates were positive within the elements. Generalization to higher space dimensions is described here. The GADJ algorithm developed by Dasgupta (2003) [5] and in Dasgupta and Wachspress (2008) [6] is crucial for simple construction of rational barycentric basis functions.

[1]  E. Wachspress,et al.  A Rational Finite Element Basis , 1975 .

[2]  Eugene L. Wachspress,et al.  Rational bases for convex polyhedra , 2010, Comput. Math. Appl..

[3]  Mathieu Desbrun,et al.  Barycentric coordinates for convex sets , 2007, Adv. Comput. Math..

[4]  Eugene L. Wachspress,et al.  The adjoint for an algebraic finite element , 2008, Comput. Math. Appl..

[5]  P. Lockhart,et al.  Introduction to Geometry , 1940, The Mathematical Gazette.

[6]  Joe D. Warren,et al.  Barycentric coordinates for convex polytopes , 1996, Adv. Comput. Math..

[7]  Gautam Dasgupta,et al.  Interpolants within Convex Polygons: Wachspress' Shape Functions , 2003 .