On the degree elevation of B-spline curves and corner cutting

In this paper we prove that the degree elevation of B-spline curves can be interpreted as corner cutting process in theory. We also discover the geometric meaning of the auxiliary control points during the corner cutting. Our main idea is to gradually elevate the degree of B-spline curves one knot interval by one knot interval. To this end, a new class of basis functions, to be called bi-degree B-spline basis functions, is constructed and discussed by the integral definition of spline. The transformation formulas between usual and bi-degree B-spline basis functions leads to the corner cutting for degree elevation of B-spline curves. © 2006 Elsevier B.V. All rights reserved.