运用多项式曲线在多项式曲面上裁剪Bézier曲面

Trimming Bézier surfaces over polynomial surfaces with polynomial curves

在多项式曲面的定义域上,以两多项式曲线及两直线段围成的简单区域作为裁剪区域,运用参数变换将该区域变换到标准正方形区域,以多项式开花为工具,将裁剪区域对应的子曲面片表示成Bézier曲面形式。对于参数平面上的复杂裁剪区域,则分割为若干简单区域来进行。该裁剪算法能处理形状较为复杂的曲面裁剪,方法对任意多项式曲面适用,而且能推广到有理情况。

Over the parametric domain of polynomial surface,trimming subdomain is surrounded with two polynomial curves and two lines,this domain is transformed into standard square by parameter transformation,and Bézier control points of the corresponding subpatch over the surface are evaluated via polonomial’s blossoming.The algorithm makes more choices for the shape of the subdomain and subpatch.And the method works for any polynomial surfaces and rational cases.