Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-05-12

Journal: ADVANCES IN MECHANICAL ENGINEERING

Included Journals: SCIE

Volume: 9

Issue: 5

ISSN: 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.