NURBS曲线形状修改的研究

Modification to NURBS Curve Shape

NURBS曲线是计算机图形学和计算机辅助几何设计中常使用到的一种参数曲线。文章主要在齐次坐标系下对NURBS曲线形状修改进行研究。分别通过修改单个权因子、单个控制点、同时修改单个权因子和控制点等方法对NURBS曲线进行形状的修改。进一步讨论了通过修改多个权因子、多个控制点来修改曲线形状,并给出所满足的公式。文章给出了一些定性结果,并给出了不同情形下的数值模拟。

The paper mainly studies the modification to the shape of NNURBS curves in the homoge- neous coordinate system by respectively varying a single weighting factor and a single control point, and by simultaneously varying the individual weights and control points of NURBS curves. In addi- tion, further discussion on changing multiple weights and multiple control points are presented to modify the shape of the curve, and the eorresponding formulas are also provided.