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Subject: Re: Interpolation with coordinates
Date: Mon, 28 May 2012 14:47:07 +0000 (UTC)
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"Jose Miguel " <josemijauregui@hotmail.com> wrote in message <jpvov1$ae2$1@newscl01ah.mathworks.com>...
> I have four sets of data, (u1,v1), (u2,v2), (u3,v3) and (u4,v4) located at coordinates (x1,y1), (x2,y2), (x3,y3) and (x4,y4). I would like to obtain a new set of data (u0,v0) at given coordinates (x0,y0) using a bilinear interpolation.
- - - - - - - - - -
  As an afterthought, with your general placement of points it would seem much more natural to ask for a six-point interpolation with a general 2D quadratic function involving six coefficients:

 f(x,y) = K1*x^2 + K2*x*y + K3*y^2 + K4*x + K5*y + K6.

After all, when the bilinear form

 K1*x*y + K2*x + K3*y + K4

is subjected to rotation, the result is a 2D quadratic involving terms in x^2 and y^2.  A bilinear surface when rotated is no longer bilinear in the new coordinates, and restriction to bilinearity is therefore somewhat arbitrary.

Roger Stafford