Modelling of cubic Bézier curves by electronic circuits

Abstract

In this paper, analog techniques have been utilized to translate the mathematical formulation of arbitrary functions into electronic circuits which embody instantaneous DC relationships between sets of voltages having a limited dynamic range of variation. Suitable building blocks and electronic circuits have been designed to implement some of the basic functional operations. These functional operations were used to embody an analog modelling technique for the generation of free-form curves based on Bezier curve generation method. To draw a specified curve, the control parameters represented by a group of variable resistors are set at specified positions. These positions correspond to values of the control polygon vertices coordinates that uniquely define the curve shape. To change curve shape, the only requirement is to vary the control parameters represented by the variable resistors, and therefore, the user can use this electronic generation method as a shape designer. Using this analog modelling technique, one can generate curves at speed much more comparable to the alternative software modelling on a digital computer.