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|Title:||An interpolatory subdivision algorithm for surfaces over arbitrary triangulations|
|Citation:||Maths Technical Papers (Brunel University). May 1992, pp 1-22|
|Abstract:||In this paper, an interpolatory subdivision algorithm for surfaces over ar-bitrary triangulations is introduced and its convergence properties over nonuni-form triangulations studied. The so called Butterfly Scheme (interpolatory) is a special case of this algorithm. In our analysis of the algorithm over uniform triangulations, a matrix approach is employed and the idea, of "Cross Differ-ence of Directional Divided Difference" analysis is presented. This method is a generalization of the technique used by Dyn, Gregory and Levin etc. to analyse univariate subdivision algorithms. While for nonuniform data, an extraordi-nary point analysis is introduced and the local subdivision matrix analysis is presented. It is proved that the algorithm produces smooth surfaces over ar-bitrary triangular networks provided the shape parameters are kept within an appropriate range.|
|Appears in Collections:||Dept of Mathematics Research Papers|
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