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RewindGamez

NURBS basis functions

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RewindGamez    100
Hi everyone, I'm having trouble understanding the basis functions required to calculate a NURBS surface. On wikipedia, the calculation is defined here: http://en.wikipedia.org/wiki/NURBS#Construction_of_the_basis_functions_.5B3.5D as: Ni,n = fi,nNi,n − 1 + gi + 1,nNi + 1,n − 1 However, since the calculation for Ni,n involves seemingly already knowing Ni,n I am confused. It seems like circular logic to me. Could anyone please help me understand the basis function? I understand Ni,n(u) is the value for the basis function for control point i of degree n for time value u. But I do not understand the full calculation: Ni,n = fi,nNi,n − 1 + gi + 1,nNi + 1,n − 1 I'd really appreciate a hint or explanation of how to do this calculation. Specifically given i,n and u, how do I calculate Ni,n(u)? Best Regards, David

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davetyler    168
I've no experience with NURBS in general but noone else has answered so hopefully just looking at this mathematically will help.

They key point is that the equation is Recursive:



is only dependent on and

So since you are given that at n=0 is piecewise constant you can calculate .

Page 4 of
http://libnurbs.sourceforge.net/nurbsintro.pdf
gives a better explanation and more explicit information on what the function N actually is where n=0.

p.s. I am a mathematician by training not a computer scientist so apologies if the explanation is overly mathematical.

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RewindGamez    100
Thanks very much - apologies for the late reply.
But that's exactly what I needed - once I understood the function as recursive it was straightforward.

Thanks again :)

David

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