Progressive iterative approximation for triangular Bezier surfaces

摘要

Recently, for the sake of fitting scattered data points, an important method based on the PIA (progressive iterative approximation) property of the univariate NTP (normalized totally positive) bases has been effectively adopted. We extend this property to the bivariate Bernstein basis over a triangle domain for constructing triangular Bezier surfaces, and prove that this good property is satisfied with the triangular Bernstein basis in the case of uniform parameters. Due to the particular advantages of triangular Bezier surfaces or rational triangular Bezier surfaces in CAD (computer aided design), it has wide application prospects in reverse engineering.