Degree reduction of disk Be'zier curves

A disk Bezier curve is a Bezier 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 Bezier curves, that is, bounding disk Bezier curves with lower degree disk Bezier 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 Bezier curve, which is served as the center curve of the degree reduced disk Bezier curve. Then the radius ot the degree reduced disk Bezier 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.

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