圆域有理Bézier曲线

Disk Rational Bézier Curves

针对CAD造型系统中有理Bézier曲线数值运算的鲁棒性问题,首先提出了中心投影变换和平行投影变换下的2种圆域有理Bézier曲线,给出了它们的端点插值、仿射不变性等性质,并通过实例比较了它们的误差半径的异同;其次讨论了这2种圆域有理Bézier曲线的退化条件,给出了平行投影变换下的圆域有理Bézier曲线降阶实例.结果表明,上述2种圆域有理Bézier曲线具有一定的理论意义和应用价值.

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（nm） 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.