How to plot closed polygon from set of random points with edges not intersecting?

I have set of random points in 2D plane, and have to make a closed polygon without any intersection between edges. There is a possibility that one or more polygons can be drawn. How do I get all those possible polygons along with their perimeter.

[Guillaume]

Sound to me like you want the convex hull of your set of points but I don't understand why you'd have several polygons. You illustration certainly doesn't explain that.

[akash sonnad]

check this out at 1.11 and 1.16 sec, for the same points, 2 different polygons can be drawn. That's what i mean https://www.youtube.com/watch?v=SC5CX8drAtU

[KSSV]

Yes..... Guillaume suggested convhull shall work.

[akash sonnad]

Does convhull cover all the points? I want every point to be a vertex of polygon.

[KSSV]

Mostly it should..if not you can also have a look on boundary.

[Guillaume]

No, convhull does not include all the points. Matlab does not have any built-in functions for that as far as I know. Your video suggests two different methods for achieving that. You'll have to implement them yourself or see if there's something on the file exchange.

[KSSV]

I have just seen your video.....I think in your case boundary will work.

[akash sonnad]

Boundary doesn't cover all the interior points

[KSSV]

Did you try? Yes, you are right, it will not pick the interior points. Attach your points.....so that we can help you.

[akash sonnad]

The points are random. If i give you certain points, it may work for those. What I need is a generic solution. Can anyone throw some light on polyshape?

[Guillaume]

polyshape does not have any function to do what you want, so it's not clear what light you need. As I said, there's nothing built into matlab to do that search, at least in base matlab. There's an example in the optimisation toolbox for something similar though.

Answer 1

[KSSV]

How about this?

N = 100 ;
x = rand(1,N) ;
y = rand(1,N) ;
P = [x; y]; % coordinates / points 
c = mean(P,2); % mean/ central point 
d = P-c ; % vectors connecting the central point and the given points 
th = atan2(d(2,:),d(1,:)); % angle above x axis
[th, idx] = sort(th);   % sorting the angles 
P = P(:,idx); % sorting the given points

P = [P P(:,1)]; % add the first at the end to close the polygon 
plot( P(1,:), P(2,:), '.-r');

[akash sonnad]

Thanks!

[KSSV]

Thanks is accepting the answer...:)