The Kate Edger Department of Mathematics

Bernstein operators on polytopes

In computer graphics (and the finite element method) surfaces are usually described as piecewise polynomial functions on a triangulation.

Each triangle has natural coordinates called barycentric coordinates, and a corresponding (Bernstein) basis of polynomials of degree k. The coordinates of a function in this basis reflect the shape of the function, and function values can be efficiently computed from these coefficients via the de Casteljau algorithm.

Recently, natural coordinates for rectangles, etc have been introduced. We investigate the corresponding Bernstein operators and their approximation properties.

Researcher at The University of Auckland