Multi-step Subdivision Algorithm for Chaikin Curves

Abstract

A Chaikin curve is a subdivision curve. Subdivision begins from an initial control polygonal curve. For each subdivision step, all corners of the polygonal curve are cut off, and a new polygonal curve is thus produced as the input of the next subdivision step. In the limit of subdivision, a Chaikin curve is created. In this paper, a multi-step subdivision algorithm for generating Chaikin curves is proposed. For an arbitrary positive integer k, the algorithm builds the resultant polygonal curve of the kth subdivision step directly from the initial polygonal curve. Examples show that the new algorithm speeds up curve generation in several times. © Springer-Verlag 2004.