2D and 3D spline coefficient computation
- From: "Tom" <flurboglarf@xxxxxxxxxxxxxx>
- Date: 29 Nov 2005 11:31:13 -0800
Hi,
I am trying to figure out how to interpolate best in 2D and 3D on
regular grids using splines. My impression from what I read is that the
quick and dirty way is to do successive 1D interpolation in the
different directions, i.e. calculate a spline along the x-axis and then
interpolate in y direction using the interpolated values at the x
position of interest, or vice versa.
However, for my purpose this seems to result in a large overhead, and I
would rather determine the coefficients for an ansatz of the type
S(x,y)=\sum\limits_{k,l=0}^3 a_{ijkl} (x-x_i)^k (y-y_j)^l
and evaluate that with a double Horner scheme.
It seems that Spaeth (1983) gives a description for 2D and even
provides the necessary factor matrices. However, I couldn't figure out
how to extend that to 3D, and I also don't understand why for the 2D
splines only requirements about the mixed 2nd derivatives are made, but
not on the pure 2nd derivatives. Which requirements would have to be
made for the 3D case?
I'm quite lost here, the other books I have looked into treat
multidimensional splines in even less detail (including the de Boor
Practical Guide) or not at all.
Any advice?
Tom
.
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