Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 thomas delbert wilkinson Posts: 5 Registered: 12/15/04
Re: bicubic spline 3D fitting algorithm
Posted: Dec 6, 1996 3:21 AM

> 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/

Date Subject Author
12/6/96 thomas delbert wilkinson