[SciPy-user] Bilinear Interpolation
sinclaird at ukzn.ac.za
Wed Sep 27 09:45:43 CDT 2006
Ryan May wrote:
> Ok, if I select the 4 points surrounding the location of interest,
> interp2d gives me the value I get with manually calculating a bilinear
> interpolation. However if I use the whole field (or even 9 points
> instead of 4), I get a different answer. I _know_ I wouldn't expect
> this for bilinear interpolation, and it would seem to imply that even
> _linear_ B-splines uses the information from additional points. Am I
> missing something here, or are the methods just not truly equivalent?
The two are equivalent when there are only 4 surrounding points (as
you've found). Bilinear interpolation is simply linear interpolation,
first in one and then in a second (perpendicular) direction, from what I
understand the method uses 4 known points by definition.
Spline interpolation is a different animal. Here you are trying to find
the "smoothest" (actually minimum bending energy) function that can be
constructed to fit *exactly* through *all* of the known data using a set
of basis functions which may be linear (or cubic etc...). Then you
evaluate the value of that function at your unknown location.
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