An evaluation algorithm for q-B\'ezier triangular patches formed by convex combinations

Abstract

An extension to triangular domains of the univariate q-Bernstein basis functions is introduced and analyzed. Some recurrence relations and properties such as partition of unity and degree elevation are proved for them. It is also proved that they form a basis for the space of polynomials of total degree less than or equal to n on a triangle. In addition, it is presented a de Casteljau type evaluation algorithm whose steps are all linear convex combinations.