Fairing NURBS curve by dual parameter optimization

Abstract

The curve fairing problem has seen many innovations especially in Computer-Aided Design (CAD) applications where product design depend largely on aesthetic, producibility and functional requirements. A major factor for evaluating these requirements is the geometric fairness of the product being modelled. This paper addresses the geometric fairing problem in which we model the shape of the product using Non Uniform Rational B-Splines (NURBS). The concept of curvature plot is used to interrogate the curve for defects and the corresponding knot and weight (at the defective regions) are sequentially modified in a sense that a fair curve ultimately results. Finally, results of our implementation are presented to show the validity of the proposed scheme.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 275-292