A class of αβγ-Bernstein-Bézier basis functions over triangular domain

A class of αβγ-Bernstein-Bézier basis functions over triangular domain, which include the cubic Ball basis functions over triangular domain and the cubic Bernstein-Bézier basis functions over triangular domain, is constructed. Based on these new basis functions, a kind of triangular Bernstein-Bézier-type patch with three exponential shape parameters is proposed. The shapes of the triangular Bernstein-Bézier-type patch can be modified intuitively and foreseeable by changing the values of the three exponential shape parameters under the same control net. The conditions for G1 continuous smooth joining two triangular Bernstein-Bézier-type patches are given.