Corner cutting algorithms for the Bézier representation of free form curves

Abstract

We give a general treatment of the problem of converting a curve expressed in a B-spline expansion into its Bézier form. We show that corner cutting of the B-spline control polygon leads to the Bézier points exactly when the Bézier matrix is totally positive. Also, for spline spaces used to model space curves with curvature continuity we give an algorithm for determining the Bézier representation. © 1988.