On Mon, 24 Nov 2014 09:35:23 -0500, Hank Grabowski wrote:
I was pleasantly surprised to see that you got the coefficients and
algorithms from that article working. I'm surprised it was a
flipping of
the coefficients. When I re-implemented it in Octave a flipped
coefficient
matrix caused for more havoc than the correctly oriented one. The
"correctly oriented" Octave one was producing the same results as the
Apache Math implementation, the transpose far far worse. Plus there
was a
coefficient flip change in the previous release which addressed the
accuracy issues.
Yes, I'm a bit worried that it looks like reverting to a
previous state, but it is perhaps the second problem (the
"delta" between sample points) that caused a additional bug
to look like an improvement...
It's Ajo's picture case that made me spot where the flip was.
The second problem did not cause a confusion in that case
because the "delta" is 1.
After fixing the two bugs, it took me much more time to figure
out that the points with low accuracy interpolation were all
along the borders of the sample grid. :-/
It would be good to have a way to provide good interpolation
also there, like your implementation does...
Either way it's clear that the new code is working based
on the tight tolerances of the new test, which is great news.
It seems that that algorithm might in some cases produces a
smoother output (cf. link below).
On the question of naming, this doesn't look piecewise to me. Yes,
there
are splines for each region rather trying to create an interpolation
function for the entire region (which of course doesn't work).
However I
look at mine as "piecewise" because I don't calculate two-dimensional
coefficients but rather interpolate in one axis for several lines in
the
second axis and then interpolate those results a second time. Is
there a
common name for the algorithm you implemented, like in the Akima
spline?
Here,
http://www.giassa.net/?page_id=371
they call it "generalized bicubic interpolation".
I'm fine with the existing chosen name for those objects if there
isn't a
specific name. It seems appropriate and descriptive.
I'm fine with the names too, then.
For 3+ dimensional interpolation the good news is that the brute
force
method I used can be extended pretty easily to higher dimensions. It
is
how I was planning on implementing Tricubic when I got time to work
on this
again. It works n-dimensionally because you just repeat that curve
fitting
and sampling for as many dimensions as you like. Rather than coding
up a
Tricubic explicitly maybe we can just code up the n-dimensional
method
instead. The overhead of the generalization to more than three
dimensions
shouldn't be dramatic.
I hope to have more time after the beginning of next month to look at
this
if you would like me to try to take a whack at it.
You are certainly welcome to do it.
Thanks,
Gilles
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