基于权因子的NURBS曲线形状调整

利用NURBS曲线的齐次坐标表示，直观地证明了单个权因子变化时，曲线上的点朝向或背离控制点的方向运动．然后推导出两个权因子的变化对曲线形状的影响规律，即曲线上点的位置变化可表示成两种运动的组合：一个是朝向或背离第一个控制点，另一个则朝向或背离第二个控制点．在此基础上，进一步讨论了同时修改三个权因子以实现单点位置和切向约束的问题．最后给出了用该方法对曲线形状做修改的例子．

Weight-Based Shape Modification of NURBS Curves

With the representation of homogeneous coordinates, we prove in the paper that when one weight changes, the points of NURBS curve move toward or away from the control point The effect on the curve by modifying two weights is also discussed in the paper When two weights change simultaneously, the motion of the points on the curve can be regarded as a composite of the two motions: each motion is toward or away from one control point Furthermore, we also discuss a question that single position and tangent constraints could be realized by a modification of three weights simultaneously Finally, examples are given to validate the new method