Disk Bézier Curve Approximation of the Offset Curve

To some extent, using a plane curve to approximate an offset curve of the plane Bezier curve is restricted. In this paper, a region approximation idea that means using a “fat curve” with a width to approximate the offset curve is proposed, and a complete set of algorithms to approximate offset curve using disk Bezier curve are given and implemented. In the algorithms, the optimal and uniform approximate curve of the offset curve as the central curve of the Disk Bezier curve 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 curve can be obtained. In the end of this paper, the approximate effect of the Disk Bezier curve is not only analyzed and assessed, but also some specific examples are provided.