I seriously doubt that what you want to do is possible, simply because your data do not work that way,
Likely the best you can do is to use the scatteredInterpolant function to interpolate one value as a function of the other two.
That would go something like this —
files = dir('*.txt');
for k = 1:numel(files)
filename = files(k).name
A{k} = readmatrix(filename);
end
V = A{1};
X = A{2};
Y = A{3};
[Vmin,Vmax] = bounds(V,'all')
[Xmin,Xmax] = bounds(X,'all')
[Ymin,Ymax] = bounds(Y,'all')
[A,R,Z] = cart2pol(X, Y, V);
[Amin,Amax] = bounds(A,'all')
[Rmin,Rmax] = bounds(R,'all')
[Vmin,Vmax] = bounds(Z,'all')
Farv = scatteredInterpolant(A(:),R(:),Z(:)); % Velocity As A Function Of Angle & Radius
Favr = scatteredInterpolant(A(:),Z(:),R(:)); % Radius As A Function Of Angle & Velocuty
Frva = scatteredInterpolant(R(:),Z(:),A(:)); % Angle As A Function Of Radius & Velocity
N = 10;
Aq = linspace(Amin, Amax, N).';
Rq = linspace(Rmin, Rmax, N).';
Vi = Farv(Aq, Rq);
ARV_Interpolations = table(Aq, Rq, Vi, 'VariableNames',{'Angle (radians)','Radius','Velocity'})
N = 10;
Aq = linspace(Amin, Amax, N).';
Vq = linspace(Vmin, Vmax, N).';
Ri = Favr(Aq, Vq);
AVR_Interpolations = table(Aq, Vq, Ri, 'VariableNames',{'Angle (radians)','Velocity','Radius'})
N = 10;
Rq = linspace(Rmin, Rmax, N).';
Vq = linspace(Vmin, Vmax, N).';
Ai = Frva(Rq, Vq);
RVA_Interpolations = table(Rq, Vq, Ai, 'VariableNames',{'Radius','Velocity','Angle (radians)'})
figure
hs = surfc(X, Y, V, 'EdgeColor','interp');
colormap(turbo)
xlabel('X')
ylabel('Y')
zlabel('Velocity')
daspect([1 1 0.05])
figure
[c,hc] = contour(X, Y, V, 'ShowText',1);
colormap(turbo)
axis('equal')
This gives an example of thte interpolation approach. The various funcitons created by scatteredInterpolant will return appropriate values for any of the first two arguments that are within their limits, as calculated using the bounds calls.
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