How do I find values at geographic coordinates in a matrix?

How can I find the values of the matrix R , which geographic coordinates are specified by x and y matrices, at the geographic coordinates specified by Ax and Ay vectors? Exactly matching coordinates of Ax,Ay does not exist in x,y so I guess there is a need to include some interpolation.

Help is much appreciated!

Example:

R = magic(5);
x = [1:5;1:5;1:5;1:5;1:5];
y = x';

Ax = [1,2,3,4,5];
Ay = [3,4,3,4,3];

% for illustration
% I want to find the values of R where the line crosses
hold on
contourf(x,y,R)
plot(Ax,Ay)
hold off

[Amit]

A little more description please. like what is R

Answer 1

[Amit]

I think interpolation will be the route.

You can use interp2. For the example here,

R_int = interp2(X,Y,R,Ax,Ay);

[Pema]

Yes! that's what I was searching for, it works perfectly in my example code but of course (I say a bit ironically) it does not work with my actual data. I get:

Error using interp2/makegriddedinterp (line 223)
Input grid is not a valid MESHGRID.

Error in interp2 (line 133)
       F = makegriddedinterp(X, Y, V, method);

Does the grids/matrices have to be symmetrical to work with interp2? My data is in 23x78..

[Amit]

For the e4xample you gave, it works.

Now, meshgrid is suppose to be the same size as your v. Also, if you know the vectors that make x and y for you: you can create meshgrid using

[X,Y] = meshgrid(x,y);

[Pema]

It turns out, x and y needs to be monotonic for 'interp2', which they are not in my field data. 'griddata' function did the trick.

[Amit]

Good. If it works for you, then you should accept the answer!

Answer 2

[Walter Roberson]

Yes, you would need to do some sort of interpolation.

You have the difficulty that interpolations that depend upon distance from existing elements are not going to work properly for geographic coordinates because of projection issues. The worst location would, I think, be at the centroid of the surrounding coordinates. If your grid is finely enough grained then you might be willing to overlook that. If you do need to take it into account, you would need to project the geographic coordinates onto a flat map before doing the interpolation (using TriScatteredInterp or GriddedInterpolant). That projection is going to lead to trouble by itself near the boundaries of the projection (e.g., the poles).

[Pema]

Thanks! I think I was a bit confusing using the term 'geographic' though, my data does not need to be projected on a sphere. It's in plain 2d already.