Generate surface from boundary points

I have thickness measurements of a rectangular test specimen. These measurements can only be taken at the boundary, but I would like to get a rough visualization of what the thickness looks like across the span of the panel using the boundary point measurements. This is a general idea of what data I have now using somewhat random numbers:

Is there any way I can make a surface out of this?

Thanks!

[Dyuman Joshi]

The surface in between can be of any shape and size. You will have to specify more details or impose more restrictions to get a unique (or a set of unique) solution(s).

[Michael]

What sorts of details and restrictions?

Answer 1

[Voss]

x = linspace(0,3,6).';
y = linspace(0,1,6).';

nx = numel(x);
ny = numel(y);

zx = 0.134+0.007*rand(nx,2);
zy = [zx(1,1) zx(end,1); 0.134+0.007*rand(ny-2,2); zx(1,2) zx(end,2)];

figure
hold on
plot3(x,y(1)*ones(nx,1),zx(:,1))
plot3(x,y(end)*ones(nx,1),zx(:,2))
plot3(x(1)*ones(ny,1),y,zy(:,1))
plot3(x(end)*ones(ny,1),y,zy(:,2))
view(3)

[X,Y] = meshgrid(x,y);

XE = [X([1 end],:).'; X(2:end-1,[1 end])];
YE = [Y([1 end],:).'; Y(2:end-1,[1 end])];
ZE = [zx; zy(2:end-1,:)];

SI = scatteredInterpolant(XE(:),YE(:),ZE(:));

Z = SI(X,Y);
figure
surf(X,Y,Z,'FaceColor','interp','EdgeColor','none')