B-Spline Surfaces Modified Geometry with Control Vertices of Weighted Constrained Optimization

Abstract

B-spline surfaces are widely suitable for the computer-aided geometric design (CAGD) and the modified geometry is one of the important technologies in CAGD. According to variations and weighting coefficients of single or multiple control vertices, the control vertices are modified by the method of weighted constrained optimization, the method of least squares was used for the optimal positions of control vertices on surfaces, and finally the modified B-spline surfaces are worked out by use of the variations of control vertices which had been calculated. The proposed approach not only can realize several modified geometry and deformation, but also is convenient for interaction design. The efficiency of the proposed approaches is illustrated by a practical application.