Volume 10, Issue 4
Evaluation Algorithm of PHT-Spline Surfaces

Zhihua Wang, Falai Chen & Jiansong Deng

Numer. Math. Theor. Meth. Appl., 10 (2017), pp. 760-774.

Published online: 2017-11

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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-splines, hierarchical T-mesh, knot insert, evaluation algorithm.

  • AMS Subject Headings

TP391

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-10-760, author = {}, title = {Evaluation Algorithm of PHT-Spline Surfaces}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2017}, volume = {10}, number = {4}, pages = {760--774}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2017.0003}, url = {http://global-sci.org/intro/article_detail/nmtma/10455.html} }
TY - JOUR T1 - Evaluation Algorithm of PHT-Spline Surfaces JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 760 EP - 774 PY - 2017 DA - 2017/11 SN - 10 DO - http://doi.org/10.4208/nmtma.2017.0003 UR - https://global-sci.org/intro/article_detail/nmtma/10455.html KW - PHT-splines, hierarchical T-mesh, knot insert, evaluation algorithm. AB -

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.

Zhihua Wang, Falai Chen & Jiansong Deng. (2020). Evaluation Algorithm of PHT-Spline Surfaces. Numerical Mathematics: Theory, Methods and Applications. 10 (4). 760-774. doi:10.4208/nmtma.2017.0003
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