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Evaluation Algorithm of PHT-Spline Surfaces

Published online by Cambridge University Press:  12 September 2017

Zhihua Wang ,
Falai Chen  and
Jiansong Deng
Zhihua Wang
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China School of Mathematics and Computer Science, Anqing Normal University, Anqing 246011, P. R. China
Falai Chen*
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China
Jiansong Deng
Affiliation:
School of Mathematical Sciences, University of Science and Technology of China, Hefei 230026, P. R. China
*
*Corresponding author. Email address:chenfl@ustc.edu.cn (F. L. Chen)
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Abstract

PHT-splines are a type of polynomial splines over hierarchical T-meshes which posses perfect local refinement property. This property makes PHT-splines useful in geometric modeling and iso-geometric analysis. Current implementation of PHT-splines stores the basis functions in Bézier forms, which saves some computational costs but consumes a lot of memories. In this paper, we propose a de Boor like algorithm to evaluate PHT-splines provided that only the information about the control coefficients and the hierarchical mesh structure is given. The basic idea is to represent a PHT-spline locally in a tensor product B-spline, and then apply the de-Boor algorithm to evaluate the PHT-spline at a certain parameter pair. We perform analysis about computational complexity and memory costs. The results show that our algorithm takes about the same order of computational costs while requires much less amount of memory compared with the Bézier representations. We give an example to illustrate the effectiveness of our algorithm.

Keywords

PHT-splineshierarchical T-meshknot insertevaluation algorithm
Type
Research Article
Information
Numerical Mathematics: Theory, Methods and Applications , Volume 10 , Issue 4 , November 2017 , pp. 760 - 774
Copyright
Copyright © Global-Science Press 2017 

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