文章基本信息

标题：On the limits of non-uniform rational B-spline surfaces with varying weights
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作者：Yue Zhang ; Chun-Gang Zhu ; Qing-Jie Guo 等
期刊名称：Advances in Mechanical Engineering
印刷版ISSN：1687-8140
电子版ISSN：1687-8140
出版年度：2017
卷号：9
期号：5
DOI：10.1177/1687814017700547
语种：English
出版社：Sage Publications Ltd.
摘要：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.
关键词：Non-uniform rational B-spline surface; weights; regular control surface; toric degenerations; surface deformation