Conversion polar to Cartesian by interpolation

Hi every one

I have a strange error in my code

I have convert the data from Cartesian to the polar as bellow:

Error using interp2>makegriddedinterp (line 237)
Input grid is not a valid MESHGRID.

Error in interp2 (line 136)
        F = makegriddedinterp(X, Y, V, method,extrap);

can any body solve this problem?

[Thorsten]

After you define u, what are you trying to achieve?

Answer 1

[Steven Lord]

INTERP2 requires gridded data. The X and Y coordinate data you converted from polar is not gridded.

 theta = (0:1/4:2)*pi;
 rad = 0:5;
 [T, R] = meshgrid(theta, rad);
 [X, Y] = pol2cart(T, R);
 Z = X.^2+Y.^2;
 plot3(X, Y, Z, 'ko');

You may want to rotate that data to convince yourself that it's a bowl shape. To obtain the values of other points on the bowl, you will need to interpolate this using a tool that can interpolate scattered data:

 [x2, y2] = meshgrid(-3:0.25:3);
 S = scatteredInterpolant(X(:), Y(:), Z(:));
 z2 = S(x2, y2);
 hold on
 plot3(x2, y2, z2, 'r+');

You should now see a "mesh" of + signs, like a piece of paper towel resting on the inner surface of the bowl.