Degree reduction of disk Bézier curves

Authors:
Falai Chen;Wu Yang
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China
Venue:
Computer Aided Geometric Design
Year:
2004

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Abstract

A disk Bézier curve is a Bézier curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Bézier curves, that is, bounding disk Bézier curves with lower degree disk Bézier curves. We propose an efficient method to solve this problem. The algorithm starts by finding an optimal approximation to the center curve of the original risk Bézier curve, which is served as the center curve of the degree reduced disk Bézier curve. Then the radius ot the degree reduced disk Bézier curve is computed by solving some linear programming problems, and for which analytic solutions are obtained. Finally, we analyze the bounding errors for the degree reduction algorithm and provide some examples to show the effectiveness of the proposed algorithm.