=encoding utf8

=head1 NAME

Math::Polygon::Calc - Simple polygon calculations

=head1 INHERITANCE

 Math::Polygon::Calc
   is an Exporter

=head1 SYNOPSIS

 my @poly = ( [1,2], [2,4], [5,7], [1, 2] );

 my ($xmin, $ymin, $xmax, $ymax) = polygon_bbox @poly;

 my $area = polygon_area @poly;
 MY $L    = polygon_perimeter @poly;
 if(polygon_is_clockwise @poly) { ... };
 
 my @rot  = polygon_start_minxy @poly;

=head1 DESCRIPTION

This package contains a wide variaty of relatively easy polygon
calculations.  More complex calculations are put in separate
packages.

=head1 FUNCTIONS

=over 4

=item B<polygon_area>(@points)

Returns the area enclosed by the polygon.  The last point of the list
must be the same as the first to produce a correct result.

The algorithm was found at L<http://mathworld.wolfram.com/PolygonArea.html>,
and sounds:

 A = abs( 1/2 * (x1y2-x2y1 + x2y3-x3y2 ...)

=item B<polygon_bbox>(@points)

Returns a list with four elements: (xmin, ymin, xmax, ymax), which describe
the bounding box of the polygon (all points of the polygon are within that
area.

=item B<polygon_beautify>( [\%options], @points )

Polygons, certainly after some computations, can have a lot of
horrible artifacts: points which are double, spikes, etc.
The optional HASH contains the %options.

 -Option       --Default
  remove_spikes  <false>

=over 2

=item remove_spikes => BOOLEAN

Spikes contain of three successive points, where the first is on the
line between the second and the third.  The line goes from first to
second, but then back to get to the third point.

At the moment, only pure horizontal and pure vertical spikes are
removed.

=back

=item B<polygon_centroid>(@points)

Returns the centroid location of the polygon.

The last point of the list must be the same as the first (must be
'closed') to produce a correct result.  When the polygon is very flat,
it will not produce a stable result: minor changes in single coordinates
will move the centroid too far.

The algorithm was found at
F<http://en.wikipedia.org/wiki/Centroid#Of_a_polygon>

=item B<polygon_clockwise>(@points)

Be sure the polygon points are in clockwise order.

=item B<polygon_contains_point>($point, @points)

Returns true if the point is inside the closed polygon.  On an edge will
be flagged as 'inside'.  But be warned of rounding issues, caused by
the floating-point calculations used by this algorithm.

=item B<polygon_counter_clockwise>(@points)

Be sure the polygon points are in counter-clockwise order.

=item B<polygon_distance>($point, @polygon)

[1.05] calculate the shortest distance between a point and any vertex of
a closed polygon.

=item B<polygon_equal>( \@points1, \@points2, [$tolerance] )

Compare two polygons, on the level of points. When the polygons are
the same but rotated, this will return false. See L<polygon_same()|Math::Polygon::Calc/"FUNCTIONS">.

=item B<polygon_format>($format, @points)

[1.07] Map the $format over all @points, both the X and Y coordinate.  This
is especially useful to reduce the number of digits in the stringification.
For instance, when you want reproducible results in regression scripts.

The format is anything supported by printf(), for instance "%5.2f".  Or,
you can pass a code reference which accepts a single value.

=item B<polygon_is_clockwise>(@points)

=item B<polygon_is_closed>(@points)

=item B<polygon_perimeter>(@points)

The length of the line of the polygon.  This can also be used to compute
the length of any line: of the last point is not equal to the first, then
a line is presumed; for a polygon they must match.

This is simply Pythagoras.

 $l = sqrt((x1-x0)^2 + (y1-y0)^2) + sqrt((x2-x1)^2+(y2-y1)^2) + ...

=item B<polygon_same>( \@points1, \@points2, [$tolerance] )

Compare two polygons, where the polygons may be rotated wrt each
other. This is (much) slower than L<polygon_equal()|Math::Polygon::Calc/"FUNCTIONS">, but some algorithms
will cause un unpredictable rotation in the result.

=item B<polygon_start_minxy>(@points)

Returns the polygon, where the point which is closest to the left-bottom
corner of the bounding box is made first.

=item B<polygon_string>(@points)

=back

=head1 SEE ALSO

This module is part of Math-Polygon distribution version 1.11,
built on May 02, 2025. Website: F<http://perl.overmeer.net/CPAN/>

=head1 LICENSE

Copyrights 2004-2025 by [Mark Overmeer <markov@cpan.org>]. For other contributors see ChangeLog.

This program is free software; you can redistribute it and/or modify it
under the same terms as Perl itself.
See F<http://dev.perl.org/licenses/>

