Recursive algebraic curve fitting and rendering

Abstract

We describe a recursive algorithm that uses quadratic algebraic curve segments to vectorize digital images. The closeness of fitting and the smoothness of connection between curve segments are ensured by a recursive algebraic curve fitting and a subsequent fine-tuning procedure. The idea is to provide an alternative way to vectorize outside parametric schemes, while maintaining the precision of parametric vectorization. We can also have all the new features of algebraic representation; for instance, the implicit forms and unique insights into curve shapes and control point weights. We also present a triangular quadtree rendering scheme for displaying algebraic curves. These algorithms combine features from both parametric and algebraic schemes to meet different requirements for curve fitting.