Barycentric Algebra Perspective on Partitions of Unity
Recasting the geometric theory of barycentric coordinates and partitions of unity on a convex polytope in the language of barycentric algebras (universal algebra). Shows that the partitions of unity, and those additionally satisfying the Lagrange property, form a chain of subalgebras of a pointwise barycentric algebra of functions, and that Guessab's tautological map sending a partition of unity to the induced point map is a barycentric homomorphism, thereby obtaining the previously geometric relations between subclasses as algebraic consequences.
PARTITIONS OF UNITY AND BARYCENTRIC ALGEBRAS ANNA ZAMOJSKA-DZIENIO Abstract. Barycentric
Barycentric coordinates provide solutions to the problem of expressing an element of a compact convex set as a convex combination of a finite number of extreme points of the set. They have been studi…