An Extension of Chaiken′s Algorithm to B-Spline Curves with Knots in Geometric Progression

Abstract

Chaiken′s algorithm is a procedure for inserting new knots into uniform quadratic B-spline curves by doubling the control points and taking two successive averages. Lane and Riesenfeld showed that Chaiken′s algorithm extends to uniform B-spline curves of arbitrary degree. By generalizing the notion of successive averaging, we further extend Chaiken′s algorithm to B-spline curves of arbitrary degree for knot sequences in geometric and affine progression.