MATLAB: Interpolation between three sets of data

Question

I have three Arrays(Column Vector?) of Speed vs. Position for three different voltages (9V, 13.5V and 16V). Each array contains a speed for every position (2387 values). I would like to make a lookup table with the position and voltage as inputs and the speed value as output. For that, I would like to interpolate the speed vs. position arrays for the voltages in between the three that I already have. That should result in speed vs position arrays for 9v, 10v, 11v – 16v. Is this possible?

The interpolation methods in the help section only show how to interpolate along the x-axis (in this case the Position values) while in my case, I have three sets of data separated by voltage and want to interpolate in between these sets.

Perhaps a multidimensional array could be used?

Any help would be greatly appreciated.

Answer 1

Let your data S (Speed) V (voltages):

V = [9, 13.5, 16];
S = randi(20,10,3);

Solution:

n = 1:size(S,1);
[ii,jj] = ndgrid(n,V);
F = griddedInterpolant(ii,jj,S,'cubic');
[i2,Vnew] = ndgrid(n,[9 10 11 16]);
out = F(i2,Vnew);

or with griddata:

n = 1:size(S,1);
[ii,jj] = ndgrid(n,V);
[i2,Vnew] = ndgrid(n,[9 10 11 16]);
out = griddata(ii,jj,S,i2,Vnew);