Drawing antialiased cubic spline curves

Abstract

Cubic spline curves have many nice properties that make them desirable for use in comptuer graphics, and the advantages of antialiasing have been known for some years. Yet, only recently has there been any attempt at directly antialiasing spline curves. Parametric spline curves have resisted antialiasing in several ways: single segments may cross or become tangent to themselves. Cusps and small loops are easily missed entirely. Thus, short pieces of the curve cannot necessarily be rendered in isolation. Finding the distance from a pixel center to the curve accurately and efficiently—usually an essential part of antialiasing—is an unsolved problem. The method presented by Lien, Shantz, and Pratt [21] is a good start, although it considers pixel-length pieces of the curve in isolation and lacks robustness in the handling of certain curves. This paper provides an improved method that is more robust, and is able to handle intersections and tangency.