Disk Rational Bézier Curves

To address robustness problem of rational Bézier curve in CAD systems,two disk rational Bézier curves are given in this paper.One is defined by a perspective map whose perspective center is the origin;the other one is defined by a parallel projection on the hyperplane ω=1.The properties,such as endpoint interpolation,affine transformation invariance etc.,are discussed.Their error radius are also analyized and discussed by using examples.Degeneracy conditions from degree n to degree m(n>m) are given for two kinds of curves respectively.The example for the degree reduction of disk rational Bézier curve under the parallel projection is also given.The theoretical analysis and experimental results show that the proposed rational Bézier curves have some potential significances in CAD.