有理Bézier曲面的标准化

Standardization of Rational Bézier Surfaces

根据Mbius定理给出了有理Bézier曲面通过线性Mbius变换进行标准化的充要条件.为了将任意双三次有理Bézier曲面标准化,提出了一种二次重新参数化算法.该算法通过对4条边界的Mbius变换进行线性插值,将双三次有理Bézier曲面4个角点权因子都变为1.最后通过实例说明了文中算法的有效性.

The sufficient and necessary condition for the existence of linear Mobius transformations that can standardize the rational Bézier surfaces is given based on Mobius reparameterization theorem. To obtain the standard form of an arbitrary cubic rational Bézier surface, we then present a quadratic reparameterization algorithm to reparameterize the surface so that all the corner weights of the surface are equal to one. Examples are included to show the performance of the new method.