Least-Squares B-Spline Curve Approximation with Arbitary End Derivatives

Abstract

An algorithm for least-squares approximation of data with end derivative constraints is presented. The approximating curve minimises the error in the least-squares sense, while at the same time assumes the derivatives specified. For degree p approximation, up to p 2 1 derivatives may be specified, resulting in C p−1 continuous curve approximants. The method is useful to piece individual curve segments together, or to create closed curves with various degrees of smoothness.