Optimization of knots for the multi curve B-spline approximation

This article presents a method for multi curve approximation with B-splines. The approximation is formulated as a constrained optimization problem with the least squares error as the objective function and the knot vector as the variables. The method presented in this article is designed to eliminate the well-known lethargic behaviour and to maintain the accuracy of control points. The method for fitting skeletal curves was tested on a single-section case and a multi-section case. The tests showed that the method reduces the objective function significantly. The proposed method has potential applications in the shape design of wings, turbine blades and automotive body panels.