Smoothing rational B-spline curves using the weights in an optimization procedure

Abstract

Freeform shape design is typically accomplished in an interactive manner and shapes generated by a computer are rarely immediately acceptable. The available techniques for any subsequent modifications depend on the chosen representation for the geometry. In many computer aided styling and design systems which use nonuniform rational B-splines (NURBS) for representation of geometry, the use of the weights as a shape control tool is very inadequately supported. In fact they are often hidden from the user and therefore remain unused. This paper investigates the possibilities of entering the weights in an automatic fairing process. In order to produce a curve with a more gradual change in curvature and the smallest deviation from its initial shape the perturbation of the weights is stated as an optimization problem. Examples of applications to automotive shape design are presented and discussed.