NURBS曲面权因子及其在曲面修形中的应用研究

Research on NURBS Surface Weight and Its Application in Surface Modification

对非均匀有理B样条(NURBS)的权因子作了分析研究。首先,阐述了NURBS曲面权因子的几何意义,说明权因子是有关四点的交比;分析了权因子的极限性质以及零权因子对曲面形状的影响。其次,就曲面上一点在控制顶点方向或任意方向移动的情况,给出了曲面形状调整时权因子的计算公式;最后,给出了曲面权因子调整的应用算例。

In this paper, the weight of the NonUniform Rational BSpline (NURBS) is analyzed and researched.First,the geometric sense of the weight of the NURBS surface weight is represented. It is shown that the weight is crossratios of four related points.The limit nature of weight and the influence of the zero weight on surface shape are analyzed. Secondly,the computation formula of weight in the course of adjusting the surface shape is presented when one point on the surface is moved in the control point direction or random direction.Finally,an application example of changing the weight of surface is shown.