Degree Reduction of Disk q-Bézier Curves

Disk q-Bézier curve is a special representation form of the parametric curve. Using this representation, the problem of instability due to floating-point arithmetic in all state-of-the-art CAD systems can be largely solved. In this paper, to approximate disk q-Bézier curves with lower degree disk q-Bézier curves, the algorithms for degree reduction of disk q-Bézier curves are proposed. First of all, the degree reduction approximation to the center curves of the original disk q-Bézier curves are found using best uniform approximation methods. The center curves of the degree reduced disk q-Bézier curves are obtained. Then the radius of the degree reduced disk q-Bézier curve is computed by using perturbation method. Finally, the bounding errors for the degree reduction algorithm are analyzed. Some numerical examples demonstrate the effectiveness of the proposed methods.