Conversion between triangular and rectangular Bézier patches

This paper presents an explicit formula that converts a triangular Bezier patch of degree n to a degenerate rectangular Bezier patch of degree n × n by reparametrization. Based on this formula, we develop a method for approximating a degenerate rectangular Bezier patch by three nondegenerate Bezier patches; more patches can be introduced by subdivision to meet a user-specified error tolerance.  2001 Elsevier Science B.V. All rights reserved.