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Indexed by:期刊论文

Date of Publication:2017-05-12

Journal:ADVANCES IN MECHANICAL ENGINEERING

Included Journals:SCIE

Volume:9

Issue:5

ISSN No.:1687-8140

Key Words:Non-uniform rational B-spline surface; weights; regular control surface; toric degenerations; surface deformation

Abstract: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.