Abstract:

Because the surface modeling method over the triangular domain can effectively solve the geometric modeling problem of irregular products, it is widely used in practical engineering. However, due to the particularity and complexity of the structure, there are not many studies on the extension of triangular surface at present. In order to enrich the theory of triangular surface, the paper carries out a specialized research on how to enhance the flexibility of shape representation of triangular surface. Firstly, a set of polynomial basis functions of degree four with one parameter over the triangular domain is constructed, which is an extension of the quadratic Bernstein basis function over the triangular domain. Secondly, based on it, the basis functions of degree n+2 with one parameter is defined by a recursive way, which is an extension of the Bernstein basis function of degree n. Thirdly, based on the new basis function of degree n+2, the triangular surface of order n is defined. The properties of the basis functions and the surfaces are analyzed. The new surfaces not only have the basic properties of the BernsteinBézier surfaces, but also enjoy shape adjustable property.

Key words: surface design;shape parameter;triangular domain;Bernstein-Bézier surface