Triangular Bezier sub-surfaces on a triangular Bezier surface

This paper considers the problem of computing the Bezier representation for a triangular sub-patch on a triangular Bezier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bezier patch. Based on de Casteljau recursions and shifting operators, previous methods express the control points of the triangular sub-patch as linear combinations of the construction points that are constructed from the control points of the triangular Bezier surface. The construction points contain too many redundancies. This paper derives a simple explicit formula that computes the composite triangular sub-patch in terms of the blossoming points that correspond to distinct construction points and then an efficient algorithm is presented to calculate the control points of the sub-patch. (C) 2011 Elsevier B.V. All rights reserved.