Performance analysis of three curve representation schemes

Abstract

This paper describes the results of an experimental performance comparison of three representation schemes for arbitrary curved shapes: the strip tree [Ballard 1981], a curvefitting approach using Bezier curves [Bezier 1974, Pavlidis 1982], and the arc tree [Günther 1988, Günther and Wong 1989]. Each of these schemes represents a curved shape as a hierarchy of approximations, where higher levels in the hierarchy correspond to coarser approximations of the curve. The schemes are compared on several geometric operations including point inclusion, curve-curve intersection, curve-area intersection, and area-area intersection. It is shown that in most cases the arc tree is the most efficient representation scheme of the three evaluated.