Seminar "Introduction to the triangular Bernstein-Bezier form and application to splines on triangulations"
Prof. Hendrik Speleers
May 22 h . 11.00 room 14
A bivariate polynomial can be written in an especially convenient form in terms of the barycentric coordinates associated with a triangle, the so-called Bernstein-Bezier form. We discuss some properties, and show how to use it in practice to efficiently evaluate polynomials and their derivatives. A particularity of this form is that one can easily derive smoothness conditions for polynomials on adjoining triangles. That motivates why the Bernstein-Bezier form is the main tool for construction and analysis of smooth spline spaces on triangulations.