An efficient algorithm for the evaluation of B´ezier triangular surfaces

B´ezier triangular patch is well-known and widely used for solving the problem in surface modeling. However, it is based on the Bernstein-B´ezier bivariate basis, which is considered as a time-consuming scheme. Thus, two different generalized Ball bases are acquired to improve the performance in triangular surface construction. This paper proposes a new algorithm to evaluate B´ezier triangular surface by converting a set of control points for a given B´ezier triangular patch into a new set of Hu´s Wang-Ball control points of the same surface. The details of conversion formulae for degree 3 to 7 are described in this paper. Finally, the performance evaluation is also delivered.