In that case, you also need to be able to add new points to the beginning of the line: 
#!/usr/bin/perl
use warnings;
use strict;

my @AoA = (
#    [11,29, 10,25],
    [15,35, 11,29],
    [15,15, 11,21],
    [10,25, 11,21],
    [15,35, 21,39],
    [25,40, 21,39],
    [21,11, 25,10],
    [15,15, 21,11],
    [35,35, 29,39],
    [29,39, 25,40],
    [35,15, 29,11],
    [25,10, 29,11],
    [40,25, 39,29],
    [35,35, 39,29],
    [39,21, 40,25],
    [35,15, 39,21],
);

my @line = @{ shift @AoA };
LINE:
while (@AoA) {
    for my $index (0 .. $#AoA) {
        for my $indices ( [0, 1, -2, -1, 0, 0 + @line],
                          [2, 3, -2, -1, 2, 0 + @line],
                          [0, 1,  0,  1, 0, 0],
                          [2, 3,  0,  1, 2, 0],
                        ) {
            if ($AoA[$index][$indices->[0]] == $line[$indices->[2]]
             && $AoA[$index][$indices->[1]] == $line[$indices->[3]]) {

                my $new = splice @AoA, $index, 1;
                splice @$new, $indices->[4], 2;
                splice @line, $indices->[5], 0, @$new;
                next LINE
            }
        }
    }
    die "No solution for @line.\n";
}

print "@line\n";

[download]
لսႽ† ᥲᥒ⚪⟊Ⴙᘓᖇ Ꮅᘓᖇ⎱ Ⴙᥲ𝇋ƙᘓᖇ

In reply to Re^3: Combine line segments to form a single line by choroba
in thread Combine line segments to form a single line by bangor

Title:
Use:  <p> text here (a paragraph) </p>
and:  <code> code here </code>
to format your post, it's "PerlMonks-approved HTML":


  • Posts are HTML formatted. Put <p> </p> tags around your paragraphs. Put <code> </code> tags around your code and data!
  • Titles consisting of a single word are discouraged, and in most cases are disallowed outright.
  • Read Where should I post X? if you're not absolutely sure you're posting in the right place.
  • Please read these before you post! —
  • Posts may use any of the Perl Monks Approved HTML tags:
    a, abbr, b, big, blockquote, br, caption, center, col, colgroup, dd, del, details, div, dl, dt, em, font, h1, h2, h3, h4, h5, h6, hr, i, ins, li, ol, p, pre, readmore, small, span, spoiler, strike, strong, sub, summary, sup, table, tbody, td, tfoot, th, thead, tr, tt, u, ul, wbr
  • You may need to use entities for some characters, as follows. (Exception: Within code tags, you can put the characters literally.)
            For:     Use:
    & &amp;
    < &lt;
    > &gt;
    [ &#91;
    ] &#93;
  • Link using PerlMonks shortcuts! What shortcuts can I use for linking?
  • See Writeup Formatting Tips and other pages linked from there for more info.