CURVATURES OF THE QUADRATIC RATIONAL BEZIER CURVES

We find necessary and sufficient conditions for the curvature of a qua dratic rational Bezier curve to be monotone in [0, 1], to have a uniqu e local minimum, to have a unique local maximum, and to have both extr ema in (0, 1), and we also visualize them in figures. As an applicatio n, we present a necessary and sufficient condition for the offset curv e to be regular and to have the same tangent direction with the given quadratic rational Bezier curve, and give a simple algorithm to find i t. (C) 1998 Elsevier Science Ltd. All rights reserved.