# how to get one shape out of multiple shapes

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Asliddin Komilov on 13 Dec 2023
Commented: Asliddin Komilov on 22 Dec 2023
Hi,
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
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.

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.
% 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
plot(X(1),Yh(1),'o')
% 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
plot(Xex,Yex,'--')
plot(Xex(1),Yex(1),'*')
##### 3 CommentsShow 1 older commentHide 1 older comment
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 on 15 Dec 2023
it didn't work korrektly for this set of data

Mathieu NOE on 13 Dec 2023
hello
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 on 15 Dec 2023
thanks, but it didn't work correctly for this set of data.
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 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.
cutxr=X(1:size(X)/2,:);
cutyr=Y(1:size(Y)/2,:);
cutxl=X(size(X)/2:end,:);
cutyl=Y(size(Y)/2:end,:);
% 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
plot(Xhl,Yhl)

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