hello,

I'm looking for a fast sorting (or "reordering") algorithm. the situation is as follows: I have a bunch of segments, in the form of 4-elements arrays ( START_X, START_Y, END_X, END_Y ). these segments form a polygon, but unfortunately I don't have them in the right order.

to let you understand the problem, consider this polygon:

   |
 5 +  F-----------E
   |  |           |
 4 +  |           |
   |  |           |
 3 +  |  C--------D
   |  |  |
 2 +  |  |
   |  |  |
 1 +  A--B
   |
   +--+--+--+--+--+--
      1  2  3  4  5
[download]

I could have the segments, for example, in this order (letters are not there, they're just for your reference):

DE = [ 5, 3, 5, 5 ]
AB = [ 1, 1, 2, 1 ]
BC = [ 2, 1, 2, 3 ]
EF = [ 5, 5, 1, 5 ]
FA = [ 1, 5, 1, 1 ]
CD = [ 2, 3, 5, 3 ]
[download]

and I need them in this order:

AB = [ 1, 1, 2, 1 ]
BC = [ 2, 1, 2, 3 ]
CD = [ 2, 3, 5, 3 ]
DE = [ 5, 3, 5, 5 ]
EF = [ 5, 5, 1, 5 ]
FA = [ 1, 5, 1, 1 ]
[download]

in fact, what I need is just the order of the points to build the polygon, which is:

A = [ 1, 1 ]
B = [ 2, 1 ]
C = [ 2, 3 ]
D = [ 5, 3 ]
E = [ 5, 5 ]
F = [ 1, 5 ]
[download]

that said, the algorithm I came up with is:

  # segments are in @seg
  my($start_x, $start_y) = ($seg[0]->[0], $seg[0]->[1]);
  my($end_x, $end_y) = ($seg[0]->[2], $seg[0]->[3]);
  push(@poly, [$start_x, $start_y]);
  push(@poly, [$end_x, $end_y]);
  shift(@seg);    
  while(@seg) {
    for(my $s = 0; $s <= $#seg; $s++) {
      if( $seg[$s]->[0] == $end_x
      and $seg[$s]->[1] == $end_y ) {
        ($end_x, $end_y) = ($seg[$s]->[2], $seg[$s]->[3]);
        push(@poly, [$end_x, $end_y]);
        splice(@seg, $s, 1);
      }
    }
  }
  # polygon points are in @poly
[download]

this actually works, but since I have several hundreds of thousands of points to reorder, I really need something more efficient. I'm pretty sure I have to use a hash somehow, but my brain, or at least part of it, seems to be gone in vacation :-)

well, if your brain is still around, can you help me?

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