Merging a pair of disk Bézier curves

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 merging a pair of disk Bézier curves, that is, bounding two adjacent disk Bézier curves by a single disk Bézier curve. We propose an efficient method to solve the problem. The basic idea of the method is to merge the center curves of the two original disk Bézier curves and to take the merged curve as the center curve of the merged disk Bézier curve, and then compute the radius by solving some optimization problems. Furthermore, it is shown that degree elevation of original disk Bézier curves will improve the merging effect.

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