An error-bounded approximate method for representing planar curves in B-splines

摘要

This paper addresses the problem of representing a given planar curve in B-splines, where the curve is not so restricted on its initial basis form that it does not have to be compatible with or derivable from B-splines. As B-spline curve approximation is inevitable in this representation process, major concerns are focused both on accuracy control and data reduction to pursue a B-spline curve with fewer control points while keeping the distance between the given curve and the B-spline curve smaller than a specified tolerance. The paper thus presents an error-bounded method for B-spline curve approximation to the given curve within the accuracy. The method adopts an approach of B-spline curve refitting accomplished via polygonal approximation of the given curve and B-spline curve fitting to the polygon. Hausdorff distance is used as a criterion for approximation quality. The offset envelope of a line segment plays an important role in controlling the Hausdorff distance between the line segment and its corresponding curve segment. The method is simple in concept, provides reasonable accuracy control, and realizes efficient data reduction. Some experimental results demonstrate its usefulness and quality.