有理Bézier三角片到退化矩形片的转化

Conversion of a rational triangular Bézier patch to a degenerate rational rectangular Bézier patch

利用齐次坐标给出了n次有理Bézier三角片到n×n次有理Bézier退化矩形片转化的显式表达,它是n次Bézier三角片到n×n次Bézier退化矩形片转化的扩展;与传统的Bézier三角片到Bézier退化矩形片转化相比,可以通过改变权因子的取值,来调整曲面接近控制网格的程度,从而增加了曲面的自由度,使对曲面形状的控制具有更好的灵活性;最后,通过实例加以说明此方法是有效的。

This paper presents an explicit formula of the conversion of a rational triangular Bézier patch of degree n to a degenerate rational rectangularBézier patch of degree n× n by homogeneous coordinates, which is an extension of the conversion of a triangular Bézier patch of degree n to a degenerate rectangular Bézier patch of degree n× n. Unlike the traditional conversion of a triangular Bézier patch of degree n to a degenerate rectangular Bézier patch of degree n × n, the approaching degree of control nets can he adjusted with the presented method by changing the value of the power factor,and then the surface degree of freedom is increased,which enables more flexible control on the surface shape. A few examples illustrate that the method given is effective.