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http://bura.brunel.ac.uk/handle/2438/2290
Title: | An interpolatory subdivision algorithm for surfaces over arbitrary triangulations |
Authors: | Qu, R |
Issue Date: | 1992 |
Publisher: | Brunel University |
Citation: | Maths Technical Papers (Brunel University). May 1992, pp 1-22 |
Series/Report no.: | TR/04/92 |
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. |
URI: | http://bura.brunel.ac.uk/handle/2438/2290 |
Appears in Collections: | Dept of Mathematics Research Papers Mathematical Sciences |
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TR_04_92.pdf | 478.33 kB | Adobe PDF | View/Open |
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