On the limits of non-uniform rational B-spline surfaces with varying weights
| Autor: | Yue Zhang, Chun-Gang Zhu, Qing-Jie Guo |
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| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Advances in Mechanical Engineering, Vol 9 (2017) |
| Druh dokumentu: | article |
| ISSN: | 1687-8140 16878140 |
| DOI: | 10.1177/1687814017700547 |
| Popis: | The non-uniform rational B-spline is a mathematical model commonly used in computer-aided design and manufacturing. For a non-uniform rational B-spline surface, when a single weight approaches infinity, the surface tends to the corresponding control point. A natural question is that what happens if all of the weights approach infinity. In this article, we define the regular control surface, which is a kind of control structure of non-uniform rational B-spline surface, and prove that it is exactly the limiting position of the non-uniform rational B-spline surface when all of weights, multiplied by a certain one-parametric function with different values for each control point, go to infinity. It develops the geometric meaning of weights of non-uniform rational B-spline surface. Moreover, some examples are presented to show the application for the surface deformation by this property. |
| Databáze: | Directory of Open Access Journals |
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