Add "area of polygon"

algorithms/computational-geometry/AreaOfPolygon.pm

@@ -0,0 +1,66 @@
+#!/usr/bin/env perl
+package AreaOfPolygon;
+use strict;
+use Exporter qw< import >;
+our @EXPORT_OK = qw< polygon_area polygon_area_signed >;
+
+=pod
+
+=head1 SYNOPSIS
+
+   use AreaOfPolygon qw< polygon_area polygon_area_signed >;
+
+   my @cw_poly = ( [0, 1], [1, 0], [0, -1], [-1, 0], [0, 1]);
+
+   my $signed_area_cw  = polygon_area_signed(@cw_poly);
+   my $signed_area_ccw = polygon_area_signed(reverse @cw_poly);
+   die unless abs($signed_area_cw + $signed_area_ccw) < 1e-10;
+
+   my $area_cw  = polygon_area(@cw_poly);
+   my $area_ccw = polygon_area(reverse @cw_poly);
+   die unless abs($area_cw - $area_ccw) < 1e-10;
+
+=cut
+
+# Input vertices are supposed to be given in order, with the first one
+# being the same as the last one to close the polygon. Each vertex is
+# provided as a reference to an array of two elements. The result can be
+# positive or negative depending on the ordering of vertices.
+sub polygon_area_signed {
+   my $sum = 0;
+   $sum += $_[$_][0] * $_[$_ + 1][1] - $_[$_ + 1][0] * $_[$_][1]
+      for 0 .. $#_ - 1;
+   return $sum / 2;
+}
+
+# Same as polygon_area_signed
+sub polygon_area { return abs(polygon_area_signed(@_)) }
+
+
+########################################################################
+#
+# What follows is just to show an example usage of the different subs
+# and is ignored if using this implementation as a module.
+#
+########################################################################
+
+sub __MAIN {
+   if (! defined $_[0]) {
+      print {*STDERR} "$0 vertices...\n";
+      return 1;
+   }
+   my @poly = map { [ split m{,}mxs ] } @_;
+   print {*STDOUT} polygon_area_signed(@poly), "\n";
+   return 0;
+}
+
+########################################################################
+#
+# Restrict running MAIN only to when this file is executed, not when
+# it is "use"-d or "require"-d, according to the "Modulino" trick.
+#
+# See https://gitlab.com/polettix/notechs/snippets/1868370
+
+exit sub { return __MAIN(@_) }->(@ARGV) unless caller;
+
+1;