New and Improved! Now with Tk !!

#!/usr/bin/perl

# http://perlmonks.org/?node_id=1204060

use strict;
use warnings;

my @points = points();

#@points = map [int rand 27, int rand 25 ], 1..700; # random test case

my ($minx, $miny, $maxx, $maxy) = (
  $points[0][0], $points[0][1], $points[0][0], $points[0][1]);

for (@points)
  {
  my ($x, $y) = @$_;
  $minx > $x and $minx = $x;
  $miny > $y and $miny = $y;
  $maxx < $x and $maxx = $x;
  $maxy < $y and $maxy = $y;
  }

my $height = $maxy - $miny + 3;  # some useful stuff
my $width = $maxx - $minx + 3;
my $gw = $width + 1; # grid width (distance to down one row)
my $gwm3 = $gw - 3;
my @letters = ('A' .. 'Z', 'a' .. 'z'); # label points by letter seque
+nce
my @steps = (1, $gw+1, $gw, $gw-1, -1, -$gw-1, -$gw, -$gw+1); # by dir
+ection
my $grid = ( ' ' x $width . "\n" ) x $height;

for (@points) # put points on grid (multiline string :)
  {
  my ($x, $y) = @$_;
  substr $grid, (($y - $miny + 1)) * $gw + ($x - $minx + 1), 1, '#';
  }

while( $^R = 0,                     # reset, find valid starting point
     $grid =~ /(?<=   .{$gwm3} )#(?= .{$gwm3} . )/s # top end - spikes
  or $grid =~ /(?<=   .{$gwm3} )#(?=..{$gwm3}   )/s # left end
  or $grid =~ /(?<=   .{$gwm3}.)#(?= .{$gwm3}   )/s # right end
  or $grid =~ /(?<= . .{$gwm3} )#(?= .{$gwm3}   )/s # bottom end
  or $grid =~ /(?<=   .{$gwm3} )#(?= .{$gwm3}(  #|#  ))/s # ul | ur en
+d
  or $grid =~ /(?<=(#  |  #).{$gwm3} )#(?= .{$gwm3}   )/s # ll | lr en
+d

  or $grid =~ /(?<=   .{$gwm3} )#(?=#.{$gwm3}(.#|  #))/s # top left
  or $grid =~ /(?<=   .{$gwm3}#)#(?= .{$gwm3}(#| #))/s # top right
  or $grid =~ /(?<=(.#.|  #).{$gwm3} )#(?=#.{$gwm3}   )(?{4})/s # bott
+om left
  or $grid =~ /(?<=(.#.|#..).{$gwm3}#)#(?= .{$gwm3}   )(?{4})/s # bott
+om right
  )
  {
  my $direction = $^R; # 0 is east (increases clockwise)
  my @answerpoints; # coordinates around edge
  my $start = my $at = $-[0]; # at topleft

  do # clockwise walk around edge
    {
    push @answerpoints, [ $at % $gw - 1 + $minx, int $at / $gw - 1 + $
+miny ];
    pos($grid) = $at - $gw - 1; # northwest corner neighbor
    $grid =~ /\G(.)(.)(.).{$gwm3}(.).(.).{$gwm3}(.)(.)(.)/s; # all nei
+ghbors
    $at += ("$1$2$3$5$8$7$6$4" x 2) =~ /^.{$direction} *(#)/ # rotate 
+& scan
      ? $steps[ $direction = ( $-[1] - 3 ) % 8 ] # step in new directi
+on
      : $start - $at; # force loop exit because scan failed
    }
  until( $at == $start );

  #use Data::Dump 'pp'; pp \@answerpoints; # the real answer :)

  my $i = 0;
  for (@answerpoints) # add letters for display if wanted
    {
    my ($x, $y) = @$_;
    pos($grid) = $x - $minx + 1 + ($y - $miny + 1) * $gw;
    $grid =~ s/\G#/$letters[$i++ % @letters]/; # label point if not
    }
  print $grid;

  draw(@answerpoints); # for Tk
  }

sub draw
  {
  use Tk;
  my $size = 700;
  my @pts = map { ($_->[0] - $minx + 1) * $size / $gw + 1,
    ($_->[1] - $miny + 1) * $size / ($maxy - $miny + 2) + 1 } @_;
  @pts > 50 or return;
  my $mw = MainWindow->new;
  $mw->geometry('+600+2');
  my $c = $mw->Canvas(-width => $size, -height => $size)->pack;
  $c->createPolygon(@pts, -fill => 'green',
    -width => 7, -outline => 'black');
  $c->createOval($pts[0] - 10, $pts[1] - 10, $pts[0] + 10, $pts[1] + 1
+0);
  $mw->Button(-text => 'Exit', -command => sub {$mw->destroy},
    )->pack(-fill => 'x', -expand => 1);
  MainLoop;
  }

sub points
  {
  [527,83],[527,84],[526,84],[525,84],[524,84],[523,84],[522,84],
  ... some points not shown to shorten listing ...
  [534,113],[533,113],[532,113],[531,113],[530,113],
  }
[download]

tybalt89:

Very neat! I'll have to study it and see how it works. I've had to put in a few more bounds-checks in mine to remove some problems, adding even more annoying subscripts...

...roboticus

When your only tool is a hammer, all problems look like your thumb.