Disk Bézier Curve Approximation of the Offset Curve

To some extent, using a plane to approximate an offset of the plane Bezier is restricted. In this paper, a region approximation idea that means using a fat curve with a width to approximate the offset is proposed, and a complete set of algorithms to approximate offset using disk Bezier are given and implemented. In the algorithms, the optimal and uniform approximate of the offset as the central of the Disk Bezier is found by using Remez method, and then the upper optimal and uniform approximation principle is proposed to compute the error radius function of the Disk Bezier curve. Thus, the whole Disk Bezier can be obtained. In the end of this paper, the approximate effect of the Disk Bezier is not only analyzed and assessed, but also some specific examples are provided.