问题描述
我想知道控制和结上的闭合和开放nurbs之间是否有任何区别.
I am wondering if there is any difference between closed and open nurbs on control and knots.
我检查了许多文档，但找不到确切答案，所以在这里问.
I checked many documents, but cannot find the exact answer, so asked here.
推荐答案
在打开或关闭nurbs曲线的控制点和结序列方面，确实没有区别.它们都遵循数字结数=控制点数+顺序"规则.但是，通过对控制点和结序列进行一些特殊的设置，可以实现闭合的nurbs曲线(或周期性nurbs曲线).例如，具有7个控制点(P1，P2，...至P7)的结序列[0.，0.，0.，0.，0.25，0.5，0.75，1.0，1.0，1.0，1.0]在开放的三次B样条曲线中.如果将结序列更改为[-0.75，-0.5，-0.25，0.，0.25，0.5，0.75，1.0，1.25，1.5，1.75]并使P5 = P1，P6 = P2和P7 = P3，则曲线将变为在关节处具有C2连续性的周期性三次B样条曲线.
There is really no difference in terms of control points and knot sequences for open or closed nurbs curves. They both follow the rule "number_of_knots = number_of_control_points + order". However, closed nurbs curves (or periodic nurbs curves) are achieved by having some special arrangement for the control points and knot sequence. For example, the knot sequence [ 0., 0., 0., 0., 0.25, 0.5, 0.75, 1.0, 1.0, 1.0, 1.0] with 7 control points (P1, P2,...to P7) will result in an open cubic B-spline curve. If we change the knot sequence into [ -0.75, -0.5, -0.25, 0., 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75] and make P5=P1, P6=P2 and P7=P3, then the curve will become a periodic cubic B-spline curve with C2 continuity at the joint.
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