Re: 2D interpolation and differentiation problem

On Wed, 03 May 2006 09:55:59 +0000, Peter Spellucci wrote:

linear interpolation will give only very crude approximations to the
derivative which may also behave nonsmooth, hence plotting your
curves will give unsatisfactory results
there are several possibilities, also depending on the nature of your Z
values:
noisy or exact, smooth? I assume the first case. you could define a bicubic
spline on an artificial rectangular grid in the R,Theta plane and fit its
coefficients
against your data in the least squares sense.
most primitive, but simple: you begin with a crude grid,
solve for the spline, evaluate the deviations, if too large (above the noise
level) refine the grid and repeat.

http://www.netlib.org/dierckx
has a least squares fit for spline surfaces which does this even more tricky
using variable nodes (surfit.f)
the spline then allows you to evaluate the derivatives easily.
the directory contains software for this task too.
hth
peter

Thank you very much, this was apparently a very good place to ask my
question!
The dierkx library looks very useful, and would seem to avoid my having to
do a lot of work learning about the splines and coding stuff. Particularly
nice is its ability to fit with the simplest set of splines to a given
accuracy, and to cope with surface irregularities and noise.

Thanks, it certainly does help.

Paul Hilton

.

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