On the smooth convergence of subdivision and degree elevation for Bezier curves

Bezier subdivision and degree elevation algorithms generate piecewise linear approximations of Bezier curves that converge to the original Bezier curve. Discrete derivatives of arbitrary order can be associated with these piecewise linear functions via divided differences. Here we establish the convergence of these discrete derivatives to the corresponding continuous derivatives of the initial Bezier curve. Thus, we show that the control polygons generated by subdivision and degree elevation provide not only an approximation to a Bezier curve, but also approximations of its derivatives of arbitrary order. (C) 2001 Elsevier Science B.V. All rights reserved.