Bézier Curve with a Minimal Jerk Energy

Abstract

We provide a method in order to determine a Bézier curve with a minimal jerk energy by means of associated matrices. By way of an application, we show that the unknown control points of the Bézier curve having a minimal jerk energy can be written as a linear combination of the known control points. Furthermore, for such a Bézier curve we obtain a general form of its matrix represention.