✍ Scribed by Géraldine Morin; Ron Goldman
No coin nor oath required. For personal study only.
Bézier subdivision and degree elevation algorithms generate piecewise linear approximations of Bézier curves that converge to the original Bézier 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 Bézier curve. Thus, we show that the control polygons generated by subdivision and degree elevation provide not only an approximation to a Bézier curve, but also approximations of its derivatives of arbitrary order.
📜 SIMILAR VOLUMES
In this paper we study the rate of convergence of two Bernstein Be zier type operators B (:) n and L (:) n for bounded variation functions. By means of construction of suitable functions and the method of Bojanic and Vuillemier (J. Approx. Theory 31 (1981), 67 79), using some results of probability