Conversion between triangular Bezier patches and rectangular Bezier patches

In this paper, two explicit conversion formulae between triangular and rectangular Bezier patches are derived. Using the formulae, one triangular Bezier patch of degree n can be converted into one rectangular Bezier patch of degree n x n. And one rectangular Bezier patch of degree m x n can be converted into two triangular Bezier patches of degree m+n. Besides, two stable recursive algorithms corresponding to the two conversion formulae are given. Using the algorithms, when converting triangular Bezier patches to rectangular Bezier patches, we can computer the relations between the control points of the two types of patches for any n >= 2 based on the relationships for n=1. When converting rectangular Bezier patches to triangular Bezier patches, we can computer the relations between the control points of the two types of patches for any m >= 2, n is an element of N+ and n >= 2, m is an element of N- based on the relationships for m=n=1. (C) 2014 Elsevier Inc. All rights reserved.