Degenerations of NURBS curves while all of weights approaching infinity

摘要

Non-Uniform Rational B-Spline (NURBS) is the multidisciplinary topic in Mathematics, Computer Science, and Engineering. The NURBS curves together with their geometric properties are widely used in Computer Aided Design, Computer Aided Geometric Design, and Computational Mathematics. When a single weight approaches infinity, the limit of a NURBS curve tends to the corresponding control point. In this paper, a kind of control structure of a NURBS curve, called regular control curve, is defined. We prove that the limit of the NURBS curve is exactly its regular control curve when all of weights approach infinity, where each weight is multiplied by a certain one-parameter function tending to infinity, different for each control point. Moreover, some representative examples are presented to show this property and indicate its application for shape deformation.