Knot Insertion for Beta-Spline Curves and Surfaces

Abstract

Discrete Beta-splines arise when a Beta-spline curve is subdivided; that is, extra knots are inserted so that the curve is expressed in terms of a larger number of control vertices and Beta-splines. Their properties and an algorithm for their computation are given in “Discrete Beta-Splines” by Joe 1990. We prove a stronger version of one of these properties, from which a new algorithm for computing discrete Beta-splines is obtained. This algorithm can also be used to compute discrete B-splines. We give a comparison of operation counts for this algorithm versus other algorithms, and for two methods to compute the new control vertices of Beta-spline and B-spline curves and surfaces. © 1990, ACM. All rights reserved.