Subdividing multivariate polynomials over simplices in Bernstein-Bezier form without de Casteljau algorithm

Abstract Some possible alternatives to the “classical” subdivision of Bernstein polynomials (i.e., based on utilizing the well known de Casteljau algorithm), are sketched. Our schemes have “asymptotically” lower computational complexities and can be carried out such that the resulting “control points” take the precise values of the polynomial surface being subdivided. For one particular approach, the so called discrete Bernstein basis polynomials are introduced.