A Short Note on a Bernstein--Bezier Basis for the Pyramid

Abstract

We introduce a Bernstein--Bezier basis for the pyramid, whose restriction to the face reduces to the Bernstein--Bezier basis on the triangle or quadrilateral. The basis satisfies the standard positivity and partition of unity properties common to Bernstein polynomials and spans the same space as nonpolynomial pyramid bases in the literature. Procedures for differentiation and integration of these basis functions are also discussed.