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### Re^2: Polygon Creation -- Request for Algorithm Suggestions

by golux (Chaplain)
 on Nov 22, 2017 at 20:33 UTC ( #1204069=note: print w/replies, xml ) Need Help??

I'm not sure what you mean by polyhedron. It's not a 3-dimensional shape, which a polyhedron is by definition.

And no, the points were not ordered to begin with -- they were taken from an image which had no extra information other than (X,Y) pairs of points, and an associated color for each point.

I did look at the module Math::ConvexHull, but determined it didn't do what I needed because if I go with the convex polygon defined for the set of points, it adds more to the shape than necessary, and eats into neighboring shapes to which the algorithm will also eventually be applied.

say  substr+lc crypt(qw \$i3 SI\$),4,5
• Comment on Re^2: Polygon Creation -- Request for Algorithm Suggestions

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Re^3: Polygon Creation -- Request for Algorithm Suggestions
by Anonymous Monk on Nov 22, 2017 at 20:56 UTC

Aye, a polygon, I stand corrected. It looks to me you have a set of pixels (small squares), or a sprite, and you want vector graphics out of it? The shapes are all solid, with no holes?

If you have pixels, they should fall on a grid. You could just walk the outline on the grid and be done with it.

Yes you're correct, it's a set of pixels originally. The shapes are all solid (no holes) and as I mentioned, my pruning algorithm seems to be a plausible first step to narrowing it down to the outline.

But the "walk the outline" step, as you say, is exactly where I'm stuck. I'm searching for an algorithm that will give me the correct order of points that define that outline/perimeter. If there are any points out of order, they will either cut lines across the shape, or (worse) create regions which are outside of the shape.

say  substr+lc crypt(qw \$i3 SI\$),4,5

Here's a "walk the outline" thing. The gist of it is that we have a little state machine that will walk the border for us. The machine wants to follow the border such that it keeps the interior of the polygon on the right hand side. It tracks \$x and \$y as the current border point, and \$in_dir is the direction it came from. Then it looks up the preferred directions to look for the next point.

Other than your starting point list, I ignored your code. (Not that there's anything wrong with your code, but I just wanted to start from scratch.) As such, you'll probably want to rework it a good bit.

Frequently when I get some code together, I'll clean it up before posting, but I'll leave it in it's current form for you, ugly debugging traces and all! (Though I left out your original point data to save 100+ lines.) There are a few things I'd clean up if I felt like looking at it any further, but I'll leave it as an exercise for the reader. Ping me if there are any details you'd like clarified.

```\$ cat pm_1204060.pl
use strict;
use warnings;
use Data::Dump 'pp';

my @pts = (
. . . your original point list elided for brevity . . .
);

# Find bounds of figure
my (\$minX, \$minY) = (999999999,999999999);
my (\$maxX, \$maxY) = (-\$minX, -\$minY);
for my \$ar (@pts) {
my (\$x,\$y) = @\$ar;
\$minX = \$x if \$x < \$minX; \$maxX = \$x if \$x > \$maxX;
\$minY = \$y if \$y < \$minY; \$maxY = \$y if \$y > \$maxY;
}
print "Bounds X:\$minX..\$maxX, Y:\$minY..\$maxY\n";

# Build image
my @img;
push @img, [ (' ') x (\$maxX - \$minX + 1) ] for 0 .. \$maxY-\$minY+1;
for my \$ar (@pts) {
my (\$x, \$y) = @\$ar;
\$x -= \$minX;
\$y -= \$minY;
\$img[\$y][\$x] = '#';
}

print_array(@img);

my @img2 = copy_array(@img);

# Annihilate the interior
for my \$y (1 .. \$#img-1) {
for my \$x (1 .. \$#{\$img[\$y]}-1) {
next unless \$img[\$y][\$x] eq '#';
next if \$img[\$y-1][\$x] ne '#';
next if \$img[\$y+1][\$x] ne '#';
next if \$img[\$y][\$x-1] ne '#';
next if \$img[\$y][\$x+1] ne '#';
\$img2[\$y][\$x] = '.';
}
}

print_array(@img2);

# Find a horizonal bit of edge from the top of the picture
# (so we can ensure that the interior of the image is on the right)
my (\$x, \$y);
OUTER:
for my \$iy (0 .. \$#img2) {
for my \$ix (0 .. \$#{\$img2[0]}) {
if (\$img2[\$iy][\$ix] eq '#'
and \$img2[\$iy][\$ix+1] eq '#'
and \$img2[\$iy+1][\$ix] eq '.') {
\$x = \$ix;
\$y = \$iy;
last OUTER;
}
}
}

print "Found a bit of horizontal top edge at \$x, \$y\n";

# We've found a bit of horizontal edge, and we're proceeding in
# the +X direction, and we know the interior of the polygon is on
# the right hand side.
#
# So we'll build a simple state machine that walks the edge.
#
# \$x, \$y  - current point on the edge
# \$in_dir - the direction we came from
#
# For each incoming direction, build a list of possible 'next points'
# in the preferred order (assuming that interior of polygon is on
# the right-hand side):

my %dirs = (
# IN   [ preferred output directions ]
'1' => [qw( 3 4 5 6 7 8 2 )],
'2' => [qw( 3 4 5 6 7 8 1 )],
'3' => [qw( 4 5 6 7 8 1 2 )],
'4' => [qw( 5 6 7 8 1 2 3 )],
'5' => [qw( 6 7 8 1 2 3 4 )],
'6' => [qw( 7 8 1 2 3 4 5 )],
'7' => [qw( 1 2 3 4 5 6 )],
'8' => [qw( 3 4 5 6 7 )],
);

my %dels = (
# IN   [ dx, dy, new_in_dir ]
'1' => [ -1, -1, '5' ],
'2' => [  0, -1, '6' ],
'3' => [  1, -1, '7' ],
'4' => [  1,  0, '8' ],
'5' => [  1,  1, '1' ],
'6' => [  0,  1, '2' ],
'7' => [ -1,  1, '3' ],
'8' => [ -1,  0, '4' ],
);

# Follow the border
my @points_in_order;

my \$in_dir = '8';
\$img[\$y][\$x] = '*';
push @points_in_order, [\$x, \$y];

my \$cnt = 0;
@img = copy_array(@img2);
OUTER2:
while (1) {
my @dirs = @{\$dirs{\$in_dir}};
for my \$d (@dirs) {
my (\$dx, \$dy, \$new_in_dir) = @{\$dels{\$d}};
print "indir \$in_dir  (\$new_in_dir: \$dx, \$dy)\n";
if (\$img[\$y+\$dy][\$x+\$dx] eq '#') {
++\$cnt;
\$in_dir = \$new_in_dir;
\$y += \$dy;
\$x += \$dx;
\$img[\$y][\$x] = chr(65 + \$cnt%26);
print "  (\$x,\$y) \$img[\$y][\$x]  \$in_dir\n";
push @points_in_order, [ \$x, \$y ];
next OUTER2;
}
}
print "Can't find anywhere to go! ('\$in_dir': \$x, \$y)\n";
last OUTER2;
}

print_array(@img);

print "Points in CW order around the boundary:\n",
pp(\@points_in_order), "\n";

sub print_array {
print "\n";
my @array = @_;
for my \$i (0 .. \$#array) {
print ": ", join("", @{\$array[\$i]}), " : ", sprintf("% 3u",\$i)
+, "\n";
}
print "  ";
print substr("1234567890"x20, 0, scalar(@{\$array[0]})), "\n\n";
}

sub copy_array {
my @array = @_;
my @ret;
for my \$ar (@array) {
push @ret, [ @\$ar ];
}
return @ret;
}

...roboticus

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

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