An improved computing method for distance between Cubic Bézier curve and corresponding chord

Abstract

Cubic Bezier curve is one of most basic and important drawing objects in computer graphics, and has wide applications in computer aided geometric design. How to draw curves quickly and accurately is a research direction at present. In traditional drawing algorithms, the distance between cubic Bezier curve and corresponding chord can be approximately computed with the maximum value of distance between the middle two control points and corresponding chord. In this paper, an improved computing method based on Cauchy Median Theorem is proposed, by which the accurate value can be worked out and the segmentation count can be reduced. The related experiment is carried out for random generated data, the results show that the improved method can reduce the segmentation count and the computing cost meets the demand of practical application.