Interpolating a table with missing values

My colleague took experimental velocity data of flow through a rectangular duct in the vertical, horizontal, and a diagonal direction. The velocity data can be seen in the attached excel picture. I need to interpolate this table, so that I can use the data to come up with one function with two inputs (x and y). I'm not too experienced with MatLAB, but I think the scatteredinterpolant function can achieve that. How would I go about interpolating the data since it is nonlinear?

Answer 1

[dpb]

A better experiment design could have been thought out, but...

xx=[0:0.0625:0.625 0.65];
yy=[xx(2:end) 0.675];
x=[zeros(1,12) xx xx(2:end)].';
y=[yy zeros(1,12) yy(2:end)].';
vq=griddata(x,y,v,xq,yq,'cubic');
v=[1 0.997 0.975 0.964 0.9365 0.912 0.866 0.791 0.688 0.427 0.0799 0 0.991 0.987 0.974 0.950 0.912 0.854 0.768 0.646 0.476 0.24 0.123  0 0.990 0.982 0.971 0.954 0.928 0.886 0.816 0.701 0.507 0.180 0].';
[xq,yq]=meshgrid(0:0.025:x(end),0:0.025:y(end));
vq=griddata(x,y,v,xq,yq,'cubic');
figure
plot3(x,y,v,'ok')
hold on 
mesh(xq,yq,vq)
ylim([0 0.7]); xlim([0 0.7]) zlim([0 1])
grid on
xlabel('X')
ylabel('Y')

Seems to not do too badly. It appears I got the data off by one on the x=0.65 slice; there's a hump there that shouldn't be. Having to enter your data by hand, I'm not going to try to sort it out; will leave that to you...the cubic does overshoot just a tad but it's not too, too bad.

You can try the Delauney triangulation; don't know how well it'll work either with the diagonal only...

Answer 2

[Walter Roberson]

Assuming that you have a variable SCFM that is NaN where the cells are empty (as would be the case if you use xlsread), and that your first column and your last row are your X and Y values:

X = SCFM(1:end-1,1);
Y = SCFM(end, 2:end);
Z = SCFM(1:end-1, 2:end);

mask = ~isnan(Z);
[r, c] = find(mask);
scattered_x = X(r);
scattered_y = Y(c);
scattered_z = Z(mask);

F = scatteredInterpolant(scattered_x, scattered_y, scattered_z);

[gX, gY] = ndgrid(X, Y);
reconstructed_Z = F(gX, gY);

surf(gX, gY, reconstructed_Z);