Constructing Bézier curves with monotone curvature

Abstract

Monotone curvature plays an important role on curve design with aesthetic shapes. In this paper, we analyze the curvature distributions of Bézier curves and show that if three conditions are satisfied, then the curvature of the Bézier curve is monotone. We also give a sufficient geometric condition of Bézier curves with monotone curvature. Furthermore, we present a designing approach of monotone curvature variation (MCV) Bézier curves. Experiments show that curves constructed by the new method perform well not only in terms of aesthetically pleasing shape, but also in monotone curvature distribution. • A sufficient condition of Bézier curves with monotone curvature is given. • A new designing approach of monotone curvature variation Bézier curves is presented. • The effectiveness of the new designing method is verified by some examples.