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how to get one shape out of multiple shapes

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I have multiple shapes I need to merge into a single shape, because I have sets of shapes those I have to merge and compare with each other (put into a one plot).
the set of data is attached and I can plot it like this:
plot(X(:, [1:end 1])', Y(:, [1:end 1])')
let me know, if you know how to do it, thanks.
I got this shape using patch, but it generated a Patch file that I cannot use.
Ideally, I would like my data was interpolated so the final shape will not have sharp edges but be smooth and go down to Y=0.
Help me handle that too if you can. thanks
  1 Comment
Dyuman Joshi
Dyuman Joshi on 13 Dec 2023
"I got this shape using patch, but it generated a Patch file that I cannot use."
You can't use the patch object or you can't use the output generated?
What is the expected output? It will be helpful if you can show an illustration.

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Accepted Answer

DGM on 13 Dec 2023
patch() doesn't create a file. If you created a file somehow, nobody knows how you did it.
I'm not sure where this is going, but here's a guess.
% loads X,Y
load data.mat
% get rid of NaNs
xhasnans = any(isnan(X),2);
yhasnans = any(isnan(Y),2);
goodrows = ~(xhasnans | yhasnans);
X = X(goodrows,:);
Y = Y(goodrows,:);
% find convex hull
K = convhull(double(X),double(Y));
Xh = X(K);
Yh = Y(K);
% plot the convex hull, show the curve endpoint
plot(Xh,Yh); hold on
% get rid of the base of the curve
Xh = Xh(3:end-1);
Yh = Yh(3:end-1);
% extrapolate to Y=0 from last 10 datapoints
Np = 10; % number of points to use
% the right-hand part of the curve
Yhr = Yh(1:Np);
Xhr = Xh(1:Np);
Yexr = [0;Yhr];
Xexr = interp1(Yhr,Xhr,Yexr,'linear','extrap');
% the left-hand part of the curve
Yhl = Yh(end-Np+1:end);
Xhl = Xh(end-Np+1:end);
Yexl = [Yhl;0];
Xexl = interp1(Yhl,Xhl,Yexl,'linear','extrap');
% put them back together
Xex = [Xexr; Xh(Np+1:end-Np); Xexl];
Yex = [Yexr; Yh(Np+1:end-Np); Yexl];
% close the curve (if needed
Xex = Xex([1:end 1]);
Yex = Yex([1:end 1]);
% plot the extraploated curve, show the endpoint
DGM on 14 Dec 2023
I wouldn't call it a guess. I picked it manually based on the given hull. For a different set of polygons, I don't know that it would be consistently correct.
Asliddin Komilov
Asliddin Komilov on 15 Dec 2023
it didn't work korrektly for this set of data

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More Answers (2)

Mathieu NOE
Mathieu NOE on 13 Dec 2023
try this
x = double(X(:));
y = double(Y(:));
% remove nan
id = isnan(x) & isnan(y);
x(id) = [];
y(id) = [];
% k = boundary(___,s) specifies shrink factor s using any of the previous syntaxes.
% s is a scalar between 0 and 1. Setting s to 0 gives the convex hull,
% and setting s to 1 gives a compact boundary that envelops the points.
% The default shrink factor is 0.5.
s = 0.1;
k = boundary(x,y,s);
x_out = x(k);
y_out = y(k);
% find lower left "corner" point to make extrapolation towards Y = 0
[mx,ix1] = min(x_out);
my = y_out(ix1);
ind = find(x_out<(mx+1));
slope = mean(diff(y_out(ind))./diff(x_out(ind)));
x_lower_left = mx - my/slope;
% find lower right "corner" point to make extrapolation towards Y = 0
[mx,ix2] = max(x_out);
my = y_out(ix2);
ind = find(x_out>(mx-1));
slope = mean(diff(y_out(ind))./diff(x_out(ind)));
x_lower_right = mx - my/slope;
% add those two new points to x_out and y_out
x_out2 = [x_out(1:ix2-1); x_lower_right; x_out(ix2:ix1); x_lower_left; x_out(ix1+1:end) ] ;
y_out2 = [y_out(1:ix2-1); 0 ; y_out(ix2:ix1); 0 ; y_out(ix1+1:end) ] ;
plot(x,y, '*', x_out, y_out, '-*r', x_out2, y_out2, '-g')

Asliddin Komilov
Asliddin Komilov on 15 Dec 2023
thanks, but it didn't work correctly for this set of data.
Asliddin Komilov
Asliddin Komilov on 20 Dec 2023
Edited: Asliddin Komilov on 20 Dec 2023
Sorry for the inconvinience, I am myself just recognizing the issues.
Extrapolation is not needed when max([y]) is at max([x]).
Asliddin Komilov
Asliddin Komilov on 22 Dec 2023
I think it will work if the 2 halves of the data are treated separately as follows, but I don't know how to join them together and get read of common point.
% plot(cutxl(:, [1:end 1])', cutyl(:, [1:end 1])'); hold on
% plot(cutxr(:, [1:end 1])', cutyr(:, [1:end 1])')
% find convex hull
Kr = boundary(double(cutxr(:)),double(cutyr(:)),1);
Kl = boundary(double(cutxl(:)),double(cutyl(:)),1);
Xhr = cutxr(Kr);
Yhr = cutyr(Kr);
Xhl = cutxl(Kl);
Yhl = cutyl(Kl);
% plot the convex hull, show the curve endpoint
plot(Xhr,Yhr); hold on

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