Mesh Data: Interpolating data and swapping axes

Hi

I have a surface plot and would like to swap the axes.

Suppose I have data like this

A = [0 1 2 3 4]; %x-axis
B = [10 11 12]; %y-axis
C = [0 5 3 8 5; 3 4 5 3 1; 6 4 9 2 1]; %z-axis

With surf(A,B,C), I can get a surface plot like this

But now I want to swap the axes for the data, so it would look like this

A = [0 1 2 3 4]; %x-axis (same)
C = [0 1 2 3 4 5 6 7 8 9 10]; %y-axis (new)
B = [??]; %z-axis (new)

How can I compute the new matrix B? I believe I will need to interpolate the data.

[dpb]

"I will need to interpolate the data."

Not interpolate but extrap-olate grossly outside the range of any data. This would be risky at best...

Answer 1

[Philip So]

Thank you for the replies.

Regarding the C data having 3 occurences of '5', sorry, that was a bad example. I was trying to provide a simple example. My actual data set is much larger and is strictly increasing in both axes.

Anyway, I believe I have found a solution. It is a modification of the reverse look-up table discussed here: https://mathworks.com/matlabcentral/answers/12809-reverse-2d-lookup-table

It's modified to loop the reverse look-up table.

Here's the code, and I have provided a better example of the C matrix

A = [20 21 22 23 24]; %x-axis
B = [10 11 12]; %y-axis
C = [0 0.1 0.2 0.3 0.4; 0.1 0.2 0.3 0.4 0.5; 0.2 0.3 0.4 0.5 0.6]; %z-axis

figure(1)
surf(A,B,C)
title('Original Plot')
xlabel('A');
ylabel('B');
zlabel('C');

new_C_range = 0:0.1:0.6;

for j = 1:size(B,2)
    for k = 1:size(new_C_range,2)
        A_new(j,k) = interp1(C(j,:),A,new_C_range(k));
    end
end

figure(3)
surf(new_C_range,B,A_new)
title('Reconstructed A')
xlabel('C');
ylabel('B');
zlabel('A');

Here's the original plot with C as the matrix

and here's the new plot with a reconstructed A matrix (yeah, I realised I reconstructed the wrong axis. In my original question, I wanted to reconstruct the B matrix instead, but the same logic applies.)

I've tried my best to compare the two plots. I believe they are identical and the algorithm is working correctly. Could someone help to double check the two plots and the algorithm? Thank you!

Answer 2

[Walter Roberson]

You cannot do that. Look in your original C data and see that there are three different locations at which C is 5. It is not possible to pick just one of them as being "the" correct place for 5 to occur.