Chen, W., Yu, R., Zheng, J., Cai, Y. & Au, C.K. (2011). Triangular Bézier sub-surfaces on a triangular Bézier surface. Journal of Computational and Applied Mathematics, available online 4 May 2011.
Permanent Research Commons link: http://hdl.handle.net/10289/5330
This paper considers the problem of computing the Bézier representation for a triangular sub-patch on a triangular Bézier surface. The triangular sub-patch is defined as a composition of the triangular surface and a domain surface that is also a triangular Bézier 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 Bézier 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.
This is an author’s accepted version of an article published in the journal: Journal of Computational and Applied Mathematics. © 2011 Elsevier.