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论文类型：期刊论文

发表时间：2017-05-12

发表刊物：ADVANCES IN MECHANICAL ENGINEERING

收录刊物：SCIE

卷号：9

期号：5

ISSN号：1687-8140

关键字：Non-uniform rational B-spline surface; weights; regular control surface; toric degenerations; surface deformation

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.