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Re: Bivariate Pchip
Posted:
Jan 18, 2013 8:53 AM
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"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <kd8td4$2br$1@newscl01ah.mathworks.com>...
> "Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <kd8ef0$qnh$1@newscl01ah.mathworks.com>...
> > What about perform successively pchip along the first dimension, then along the second dimension.
>
> Just a note that I do not know successive 1D pchip gives the same result when swapping the dimensions. For splines with homogeneous conditions such as natural, not-a-knot, periodic, one can do either way, and it provides the same interpolation results as 2D, just the implementation and work-flow is different.
>
> Bruno
pchip in 2-d as a tensor product form has been shown
NOT to be adequate for the general desired behavior.
(It sometimes will produce an acceptable result, but in
general, it is not adequate.)
My memory tells me that there is a way to correct the
derivatives generated by pchip so that it WILL be
monotone in all desired aspects, and that this was
once implemented as the 2-d version of pchip. Sadly
I no longer have that work in my possession.
Also as you point out, since pchip is a not a linear
procedure, it is potentially not going to produce
the same result as if you do swap the axes.
John
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