"Unfurl" 3D surface to 2D plane (not projection)

I have a cloud of points with (x,y,z) coordinates with a scalar value (velocity) at each point, defining a 3D surface.

This surface consists of a straight rectangular section with constant y-values, followed by a curved section (with vertical sides) and then another straight rectangular section, but this time with constant x-values. The surface thus looks like a bent rectangular ribbon, with straight vertical and horizontal edges.

In Matlab, how do I "unfurl" (not project) the ribbon onto a (x,z) plane, i.e. have on the same (x,z) plane the first straight section, then the curved one and finally the second straight one, in adjacent sections? This of course means the obtained (x,z) area needs to have the same surface as the original (x,y,z) 3D surface.

Thank you in advance

[Matt J]

Your post could benefit from some figure illustrations. For me, at least, it is a bit hard to visualize the original 3D cloud from just the verbal description.

[Hugo Calisto]

Hi Matt

Thanks for the prompt reply

Here is a plot of the 3D cloud

[Mathieu NOE]

hello

can you share the data ?

[Hugo Calisto]

Hi Mathieu

Sure, here it goes

Answer 1

[Mathieu NOE]

hello

after a few trials , this is it !

try this :

data = readmatrix('Test1.xlsx',"NumHeaderLines",1); % x	y	z	v
x = data(:,1);
x = x - min(x); % so it starts at x = 0
y = data(:,2);
y = y - min(y); % so it starts at y = 0
z = data(:,3);
z = z - min(z); % so it starts at z = 0
v = data(:,4);

figure(1)
scatter3(x,y,z,5,v,'filled');
colorbar;

% master curve between distance to origin d and arc length s 
d = sqrt( x.^2 + y.^2 );
[val,ix] = sort(d);
xs = x(ix);
ys = y(ix);

% arc length s computed from sorted x,y values
s = 0.0;
for i = 1:numel(xs)-1
  s(i+1) = s(i) + sqrt( (xs(i+1)-xs(i))^2 + (ys(i+1)-ys(i))^2 );
end

% convert back s with correct indices to match initial x,y data (indexes)
% reverse sort as explained here : https://blogs.mathworks.com/loren/2007/08/21/reversal-of-a-sort/
unsorted = 1:length(s);
newInd(ix) = unsorted;
s = s(newInd);

figure(2)
scatter(s,z,5,v,'filled');
colorbar;

[Mathieu NOE]

if you want to store your original data and the "new" x axis (s) for flat display you can simply add these lines of code at the bottom :

% export all data with s as new x axis 
data_out = [data s(:)]; % original data (x	y	z	v) + new x axis = s (flat plot)
writematrix(data_out, "data_out.txt"); % export to txt or xlsx format as you prefer

[Hugo Calisto]

Hi Mathieu

Thank you so much, problem solved

Take care!

[Mathieu NOE]

thanks !

have a great day