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Reorder polygon vertex array

Posted on 2008-10-20
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Last Modified: 2010-07-27
I have an array of vertices from a polygon in random order. I need some kind of algorithm to reorder them so that they start from upper left and go clockwise
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Question by:steenpat
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Expert Comment

by:rstaveley
ID: 22758563
Homework?

If (0,0) is the centre and you have (-1,0) and (0,1), which would you say should come first?
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Expert Comment

by:rstaveley
ID: 22758652
Clue: If you want to figure out the neighbours for a vertex, do you simply want to figure out the least acute (i.e. largest) angle that it makes with two other vertices?
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Author Comment

by:steenpat
ID: 22762790
ignore deletion.
no this is not 'homework'.

Clue: If you want to figure out the neighbours for a vertex, do you simply want to figure out the least acute (i.e. largest) angle that it makes with two other vertices?

This won't work all the time if you have a concave or convex object for instance.
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Author Comment

by:steenpat
ID: 22762799
ignore deletion.
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Author Comment

by:steenpat
ID: 22762802
ignore deletion.
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Expert Comment

by:ozo
ID: 22762953
If you have
(0,0) (1,1) (1,-1) (-1,1) (-1,-1)
what order would you want the vertices to be in?
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Author Comment

by:steenpat
ID: 22763166
ozo:
start from upper left top most and go clockwise.
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Author Comment

by:steenpat
ID: 22763190
so, that would be -1,1. this object will work fine if you use the least acute angle method, if for instance you make a hollow "C" shape object then it doesnt work anymore because you have pts that have lower angles which shouldnt come next in the list.
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Expert Comment

by:ozo
ID: 22763199
so (-1,1)(1,1)(1,-1)(-1,-1)
where do we put (0,0)?
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Expert Comment

by:rstaveley
ID: 22764950
Assuming (0,0) is the origin in the middle, (-1,0) is as "left" as (0,1) is "top", so which do you decide is the most "top left"?
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Author Comment

by:steenpat
ID: 22772590
look I have already have code that will grab the same corner pt every time. so.. dont worry about that.
I just need a way of reordering the pts for objects like described above.i dont really feel like repeating myself several times, so i'll say it again, the least acute angle method will not work for these types of objects.
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Expert Comment

by:ozo
ID: 22772647
please describe where in the order the (0,0) point would belong.
Do you want to maximize the area of the polygon?
Do you want to minimize the perimeter of the polygon?
So you want it to be starshaped from its centroid?
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Expert Comment

by:rstaveley
ID: 22774333
I'm fed up with repeating my question too. <resign>
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Accepted Solution

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ozo earned 250 total points
ID: 22774608
(1,1) (1,-1) (-1,1) (-1,-1)
(2,2) (2,-2) (-2,2) (-2,-2)
could be
(-2,2) (2,2) (1,1) (1,-1) (2,-2) (-2,-2) (-1,-1) (-1,1)
or
(-2,2) (-1,1) (1,1) (2,2) (2,-2) (1,-1) (-1,-1) (-2,-1)
or
(-2,2) (2,2) (2,-2) (-2,2) (-1,-1) (1,-1) (1,1) (-1, 1)
or
(-2,2) (2,2) (2,-2) (1,-1) (1,1) (-1,1) (-1,-1) (-2,-2)
or
(-2,2) (2,2) (1,1) (-1,1) (-1,-1) (1,-1) (2,-2) (-2,-2)
or
(-2,2) (-1,1) (-1,-1) (1,-1) (1,1) (2,2) (2,-2) (-2,-2)
among others
How do you want to decide among them?
One way could be to prefer polygons with a shorter perimeter, which you can do
by solving the Traveling Salesman problem.
This could take a long time if you have a lot of points, but if near-optimal solution is good enough, you might use the
 Christofides heuristic and start with a minimal spanning tree and convert it to a simple polygon by skipping nodes.
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Author Comment

by:steenpat
ID: 22776386
Ozo: I see what you're saying. in my case actually the vertices are in an order, but not in the same starting order everytime. i guess i misphrased this question when i said random order because i was in a hurry. i think all i need to do is to find the topmost, leftmost pt and then shuffle the array so they start with that pt and thats it...
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