In computer aided geometric design (CAGD)

the Bernstein-Bézier system for polynomial space including the triangular domain is an important tool for modeling free form shapes. The Bernstein-like bases for other spaces (trigonometric polynomial

hyperbolic polynomial

or blended space) has also been studied. However

none of them was extended to the triangular domain. In this paper

we extend the linear trigonometric polynomial basis to the triangular domain and obtain a new Bernstein-like basis

which is linearly independent and satisfies positivity

partition of unity

symmetry

and boundary representation. We prove some properties of the corresponding surfaces

including differentiation

subdivision

convex hull

and so forth. Some applications are shown.