Distances with rational triangular Bézier surfaces

摘要

In this paper, we give the matrix form for the degree elevation of rational triangular Bézier surfaces. We use the L2 measure to find a formula for the distance between two rational triangular Bézier surfaces. A polynomial triangular Bézier surface approximation of a rational triangular Bézier surface based on the least-squares method is given. The final formulas contain only Bézier points and matrix of degree elevation.