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Math Forum » Discussions » sci.math.* » sci.math.num-analysis.independent

Topic: bicubic spline 3D fitting algorithm
Replies: 2   Last Post: Dec 11, 1996 12:38 PM

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thomas delbert wilkinson

Posts: 5
Registered: 12/15/04
Re: bicubic spline 3D fitting algorithm
Posted: Dec 6, 1996 3:21 AM
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> I'm looking for a routine that can create a cubic spline fit from an
> arbitrary set of points in 3 dimensions, represented by $(x,y,z,v)_i$
> (preferrably in a weighted least squares sense).
>
> For 2 dimensions (i.e. for surfaces with points $(x,y,v)_i$ )these
> routines already exist. For example such a routine is given by NAGs
> E02DAF.


Is it possible that you can call the 2-D function to calculate $(x,y,v)$
and call it again for $(z,0,v)$? Mathematically, it makes sense because
you are dealing with linearly independant functions, ie. the value of
the spline for $(z,0,v)$ should have ZERO effect on the values for
$(x,y,v)$.

The only problems I can see for using this idea is if the functions
require that the known values of $(x,y,v)$ are stored in a
two-dimensional array instead of three one-dimensional array.

A better idea is if there is code to produce a one-dimensional spline
$(x,v)$, call it three times, for $(x,v)$, $(y,v)$, $(z,v)$. This is
also valid because x, y, and z are linearly independant, but it is a
saivngs in work done by the computer because calculating $(z,0,v)$
involves a waste of work because the function will calculate a spline
for $(0, v)$

> Secondly, has anybody experience with these kind of representations.

I've been toying with it, but I don't have any code that works
completely, because I have been trying to code a spline funtion by
myself.

--
_____________________________________________________________________
thomas delbert wilkinson 038 henday lister hall university of alberta
If god were perfect, why did He create discontinuous functions?
http://ugweb.cs.ualberta.ca/~wilkinso/





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