Talk:Non-uniform rational B-spline
Also note that the only significant factor is the ratio of the values to each other: the knot vectors [0 0 1 2 3], [0 0 2 4 6] and [1 1 2 3 4] produce the same curve.
Er, I've got a problem with the ratios (0:1 = 0:2 = 1:2) and (1:2 = 2:4 = 2:3) which is what this states. I can only conclude that the minimum value is also a significant factor. Can anyone help me out on this one?
Parameterisation ratio
The only significant thing is the ratio of neighboring parameter values in their ascending order, therefore the given example is correct. Minimum value has no significance. As long as a multiplier value exists to make ratio between different parameter values the same, the resulting b-spline curve will be the same.
E.g. 0 1 2 3 4 is the same as 0 2 4 6 8 (multiplier being 0.5)
or
0 3 6 9 12 is the same as 0 0.25 0.50 0.75 1.0 (multiplier being 12)
Actually for any uniformly increasing parameter values, curves with same control points position and same number of knot vectors will have the same shape (which means that all four above examples give identical curve shape provided their control points positions are the same).
For non-uniform splines:
0 0 1 3 4 5 is the same as 0 0 0.5 1.5 2.0 2.5 (multiplier is 2)
It is those differences in parameter values that determine chord length and affect the resulting curve shape. Therefore, same ratio between knot parameter values, combined with same control points positions will give the same curve. Think of it as a tension increased in one knot by any factor will not change the curve if the same factor of increased tension is applied to all the other knots.
Uniformed circle?
Can someone explain what a "uniformed circle" is? --P3d0 03:21, 5 February 2006 (UTC)
Picture
This article could do with a picture in as much as NURBS is an adjective to describe a class of shapes, particularly shapes of consumer products of recent years. —BenFrantzDale 16:46, 16 February 2006 (UTC)
Well, its kindoff hard and simple at the same time. See more is about the specifications of the image, i mean you could photograph any mobile telephone, or any western airplane. But more of the trouble here is to make a piucture that is MEANINGFULL for the potential viewer. See when i take a look at my telephone i know what im looking for so i can see how the patch layout is done. But the untrained person will most definetly not see it unless pointed out, and even then if the designer of the phone did a superb job there would be noothing to see. Just imaginary lines. So its definetly going to have to be a rendering.
Now to complicate this a bit, most eingeneering applications make use of as many independent pieces of trimmed nurbs surfaces that most noneingeneers wont believe.
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