"How to interpolate from a dataset using interp3?"
It is very simple: don't use INTERP3.
"It's completely unlogical"
It is perfectly logical.
It is because users often prefer the array dimensions to correspond to what a matrix/array looks like: the vertical dimension (1) corresponding to the vertical axes (Y), the horizontal dimension (2) corresponding to the horizontal axes (X). But these are swapped around! Yes, they are. And that is exactly how image data are displayed. All image/plotting routines (not just MATLAB) use this interpretation.
Both INTERP2 and INTERP3 use this interpretation of the first two dimensions, because that is what users need.
You can find the TMW attempt at an explanation here:
and here:
Not only MATLAB has to handle this, all applications that process plotted/image data need to consider this. For example, Numpy names these two different interpretations as "ij" and "xy", see the "Notes" here:
Perhaps this could have been avoided if three hundred(?) years ago whoever defined the arbitrary order of matrix/array dimensions had instead specified them as being cols*rows*pages*... , which would probably also have avoided the endless column-major vs row-major flamewars. But too late, we have to work with what we have.
"What can be done to make it logical?"
The very simple solution is to use the correct tool.
For data in ND-grid format (regardless of how many dimensions) like yours you need to use INTERPN:
load('sampleData.mat');
freq1 = 0.01;
freq2 = 0.01;
heading = 0.01;
A = nan(6,1); % better to preallocate
for k = 1:6
A(k,1) = interpn(X, Y, Z, dataset(:,:,:,k), freq1, freq2, heading);
end
disp(A)
Tip for the future: always read the documentation carefully, look at the related functions and topics linked to.
