Triangular domain extension of algebraic trigonometric B,zier-like basis

In computer aided geometric design (CAGD), B,zier-like bases receive more and more considerations as new modeling tools in recent years. But those existing B,zier-like bases are all defined over the rectangular domain. In this paper, we extend the algebraic trigonometric B,zier-like basis of order 4 to the triangular domain. The new basis functions defined over the triangular domain are proved to fulfill non-negativity, partition of unity, symmetry, boundary representation, linear independence and so on. We also prove some properties of the corresponding B,zier-like surfaces. Finally, some applications of the proposed basis are shown.