Triangular domain extension of linear Bernstein-like trigonometric polynomial basis

Abstract

In computer aided geometric design (CAGD), the Bernstein-Bezier 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.