```
=encoding utf8
=head1 NAME
Math::Polygon - Class for maintaining polygon data
=head1 SYNOPSIS
my $poly = Math::Polygon->new( [1,2], [2,4], [5,7], [1,2] );
print $poly->nrPoints;
my @p = $poly->points;
my ($xmin, $ymin, $xmax, $ymax) = $poly->bbox;
my $area = $poly->area;
my $l = $poly->perimeter;
if($poly->isClockwise) { ... };
my $rot = $poly->startMinXY;
my $center = $poly->centroid;
if($poly->contains($point)) { ... };
my $boxed = $poly->lineClip($xmin, $xmax, $ymin, $ymax);
=head1 DESCRIPTION
This class provides an Object Oriented interface around
L<Math::Polygon::Calc|Math::Polygon::Calc>, L<Math::Polygon::Clip|Math::Polygon::Clip>, and other. Together,
these modules provide basic transformations on 2D polygons in pure perl.
B<WARNING:> these computations may show platform dependent ronding
differences. These may also originate from compilation options of
the Perl version you installed.
=head1 METHODS
=head2 Constructors
=over 4
=item $obj-E<gt>B<new>(%options, [@points], %options)
=item Math::Polygon-E<gt>B<new>(%options, [@points], %options)
You may add %options before and/or after the @points. You may also use
the "points" option to set the points. Each point in @points is
(a references) to an ARRAY with two elements: an X and a Y coordinate.
When C<new()> is called as instance method, it is believed that the
new polygon is derived from the callee, and therefore some facts
(like clockwise or anti-clockwise direction) will get copied unless
overruled.
-Option --Default
bbox undef
clockwise undef
points undef
=over 2
=item bbox => [$xmin,$ymin, $xmax,$ymax]
Usually computed from the shape automatically, but can also be
overruled. See L<bbox()|Math::Polygon/"Geometry">.
=item clockwise => BOOLEAN
Is not specified, it will be computed by the L<isClockwise()|Math::Polygon/"Geometry"> method
on demand.
=item points => \@points
See L<points()|Math::Polygon/"Attributes"> and L<nrPoints()|Math::Polygon/"Attributes">.
=back
example: creation of new polygon
my $p = Math::Polygon->new([1,0],[1,1],[0,1],[0,0],[1,0]);
my @p = ([1,0],[1,1],[0,1],[0,0],[1,0]);
my $p = Math::Polygon->new(points => \@p);
=back
=head2 Attributes
=over 4
=item $obj-E<gt>B<nrPoints>()
Returns the number of points,
=item $obj-E<gt>B<order>()
Returns the number of (unique?) points: one less than L<nrPoints()|Math::Polygon/"Attributes">.
=item $obj-E<gt>B<point>( $index, [$index,...] )
Returns the point with the specified $index or INDEXES. In SCALAR context,
only the first $index is used.
example:
my $point = $poly->point(2);
my ($first, $last) = $poly->point(0, -1);
=item $obj-E<gt>B<points>( [FORMAT] )
In LIST context, the points are returned as list, otherwise as
reference to an ARRAY of points.
[1.09] When a FORMAT is given, each coordinate will get processed.
This may be useful to hide platform specific rounding errors. FORMAT
may be a CODE reference or a C<printf()> alike string.
See L<Math::Polygon::Calc::polygon_format()|Math::Polygon::Calc/"FUNCTIONS">.
example:
my @points = $poly->points;
my $first = $points[0];
my $x0 = $points[0][0]; # == $first->[0] --> X
my $y0 = $points[0][1]; # == $first->[1] --> Y
my @points = $poly->points("%.2f");
=back
=head2 Geometry
=over 4
=item $obj-E<gt>B<area>()
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 computed
result is cached.
Function L<Math::Polygon::Calc::polygon_area()|Math::Polygon::Calc/"FUNCTIONS">.
example:
my $area = $poly->area;
print "$area $poly_units ^2\n";
=item $obj-E<gt>B<bbox>()
Returns a list with four elements: (xmin, ymin, xmax, ymax), which describe
the bounding box of the polygon (all points of the polygon are inside that
area). The computation is expensive, and therefore, the results are
cached.
Function L<Math::Polygon::Calc::polygon_bbox()|Math::Polygon::Calc/"FUNCTIONS">.
example:
my ($xmin, $ymin, $xmax, $ymax) = $poly->bbox;
=item $obj-E<gt>B<beautify>(%options)
Returns a new, beautified version of this polygon.
Function L<Math::Polygon::Calc::polygon_beautify()|Math::Polygon::Calc/"FUNCTIONS">.
Polygons, certainly after some computations, can have a lot of horrible
artifacts: points which are double, spikes, etc. This functions provided
by this module beautify them. A new polygon is returned.
-Option --Default
remove_spikes <false>
=over 2
=item remove_spikes => BOOLEAN
=back
=item $obj-E<gt>B<centroid>()
Returns the centroid location of the polygon. The last point of the list
must be the same as the first to produce a correct result. The computed
result is cached. Function L<Math::Polygon::Calc::polygon_centroid()|Math::Polygon::Calc/"FUNCTIONS">.
example:
my $center = $poly->centroid;
my ($cx, $cy) = @$center;
=item $obj-E<gt>B<clockwise>()
Make sure the points are in clockwise order.
example:
$poly->clockwise;
=item $obj-E<gt>B<contains>($point)
Returns a truth value indicating whether the point is inside the polygon
or not. On the edge is inside.
=item $obj-E<gt>B<counterClockwise>()
Make sure the points are in counter-clockwise order.
example:
$poly->counterClockwise
=item $obj-E<gt>B<distance>($point)
[1.05] Returns the distance of the point to the closest point on the border of
the polygon, zero if the point is on an edge.
=item $obj-E<gt>B<equal>( <$other | \@points,[$tolerance]> | $points )
Compare two polygons, on the level of points. When the polygons are
the same but rotated, this will return false. See L<same()|Math::Polygon/"Geometry">.
Function L<Math::Polygon::Calc::polygon_equal()|Math::Polygon::Calc/"FUNCTIONS">.
example:
if($poly->equal($other_poly, 0.1)) ...
if($poly->equal(\@points, 0.1)) ...
if($poly->equal(@points)) ...
=item $obj-E<gt>B<isClockwise>()
The points are (in majority) orded in the direction of the hands of the clock.
This calculation is quite expensive (same effort as calculating the area of
the polygon), and the result is therefore cached.
example:
if($poly->isClockwise) ...
=item $obj-E<gt>B<isClosed>()
Returns true if the first point of the poly definition is the same
as the last point.
=item $obj-E<gt>B<perimeter>()
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.
Function L<Math::Polygon::Calc::polygon_perimeter()|Math::Polygon::Calc/"FUNCTIONS">.
example:
my $fence = $poly->perimeter;
print "fence length: $fence $poly_units\n"
=item $obj-E<gt>B<same>( <$other_polygon | \@points, [$tolerance]> | @points )
Compare two polygons, where the polygons may be rotated wrt each
other. This is (much) slower than L<equal()|Math::Polygon/"Geometry">, but some algorithms
will cause un unpredictable rotation in the result.
Function L<Math::Polygon::Calc::polygon_same()|Math::Polygon::Calc/"FUNCTIONS">.
example:
if($poly->same($other_poly, 0.1)) ...
if($poly->same(\@points, 0.1)) ...
if($poly->same(@points)) ...
=item $obj-E<gt>B<startMinXY>()
Returns a new polygon object, where the points are rotated in such a way
that the point which is losest to the left-bottom point of the bounding
box has become the first.
Function L<Math::Polygon::Calc::polygon_start_minxy()|Math::Polygon::Calc/"FUNCTIONS">.
=back
=head2 Transformations
Implemented in L<Math::Polygon::Transform|Math::Polygon::Transform>: changes on the structure of
the polygon except clipping. All functions return a new polygon object
or undef.
=over 4
=item $obj-E<gt>B<grid>(%options)
Returns a polygon object with the points snapped to grid points.
See L<Math::Polygon::Transform::polygon_grid()|Math::Polygon::Transform/"FUNCTIONS">.
-Option--Default
raster 1.0
=over 2
=item raster => FLOAT
The raster size, which determines the points to round to. The origin
C<[0,0]> is always on a grid-point. When the raster value is zero,
no transformation will take place.
=back
=item $obj-E<gt>B<mirror>(%options)
Mirror the polygon in a line. Only one of the options can be provided.
Some programs call this "flip" or "flop".
-Option--Default
b 0
line <undef>
rc undef
x undef
y undef
=over 2
=item b => FLOAT
Only used in combination with option C<rc> to describe a line.
=item line => [POINT, POINT]
Alternative way to specify the mirror line. The C<rc> and C<b> are
computed from the two points of the line.
=item rc => FLOAT
Description of the line which is used to mirror in. The line is
C<y= rc*x+b>. The C<rc> equals C<-dy/dx>, the firing angle. If
C<undef> is explicitly specified then C<b> is used as constant x: it's
a vertical mirror.
=item x => FLOAT
Mirror in the line C<x=value>, which means that C<y> stays unchanged.
=item y => FLOAT
Mirror in the line C<y=value>, which means that C<x> stays unchanged.
=back
=item $obj-E<gt>B<move>(%options)
Returns a moved polygon object: all point are moved over the
indicated distance. See L<Math::Polygon::Transform::polygon_move()|Math::Polygon::Transform/"FUNCTIONS">.
-Option--Default
dx 0
dy 0
=over 2
=item dx => FLOAT
Displacement in the horizontal direction.
=item dy => FLOAT
Displacement in the vertical direction.
=back
=item $obj-E<gt>B<resize>(%options)
Returns a resized polygon object.
See L<Math::Polygon::Transform::polygon_resize()|Math::Polygon::Transform/"FUNCTIONS">.
-Option--Default
center [0,0]
scale 1.0
xscale <scale>
yscale <scale>
=over 2
=item center => $point
=item scale => FLOAT
Resize the polygon with the indicated factor. When the factor is larger
than 1, the resulting polygon with grow, when small it will be reduced in
size. The scale will be respective from the center.
=item xscale => FLOAT
Specific scaling factor in the horizontal direction.
=item yscale => FLOAT
Specific scaling factor in the vertical direction.
=back
=item $obj-E<gt>B<rotate>(%options)
Returns a rotated polygon object: all point are moved over the
indicated distance. See L<Math::Polygon::Transform::polygon_rotate()|Math::Polygon::Transform/"FUNCTIONS">.
-Option --Default
center [0,0]
degrees 0
radians 0
=over 2
=item center => POINT
=item degrees => FLOAT
specify rotation angle in degrees (between -180 and 360).
=item radians => FLOAT
specify rotation angle in rads (between -pi and 2*pi)
=back
=item $obj-E<gt>B<simplify>(%options)
Returns a polygon object where points are removed.
See L<Math::Polygon::Transform::polygon_simplify()|Math::Polygon::Transform/"FUNCTIONS">.
-Option --Default
max_points undef
same 0.0001
slope undef
=over 2
=item max_points => INTEGER
First, C<same> and C<slope> reduce the number of points. Then, if there
are still more than the specified number of points left, the points with
the widest angles will be removed until the specified maximum number is
reached.
=item same => FLOAT
The distance between two points to be considered "the same" point. The value
is used as radius of the circle.
=item slope => FLOAT
With three points X(n),X(n+1),X(n+2), the point X(n+1) will be removed if
the length of the path over all three points is less than C<slope> longer
than the direct path between X(n) and X(n+2).
The slope will not be removed around the starting point of the polygon.
Removing points will change the area of the polygon.
=back
=back
=head2 Clipping
=over 4
=item $obj-E<gt>B<fillClip1>($box)
Clipping a polygon into rectangles can be done in various ways.
With this algorithm, the parts of the polygon which are outside
the $box are mapped on the borders. The polygon stays in one piece,
but may have vertices which are followed in two directions.
Returned is one polygon, which is cleaned from double points,
spikes and superfluous intermediate points, or C<undef> when
no polygon is outside the $box.
Function L<Math::Polygon::Clip::polygon_fill_clip1()|Math::Polygon::Clip/"FUNCTIONS">.
=item $obj-E<gt>B<lineClip>($box)
Returned is a list of ARRAYS-OF-POINTS containing line pieces
from the input polygon.
Function L<Math::Polygon::Clip::polygon_line_clip()|Math::Polygon::Clip/"FUNCTIONS">.
=back
=head2 Display
=over 4
=item $obj-E<gt>B<string>( [FORMAT] )
Print the polygon.
[1.09] When a FORMAT is specified, all coordinates will get formatted
first. This may hide platform dependent rounding differences.
=back
=head1 SEE ALSO
This module is part of Math-Polygon distribution version 1.10,
built on January 03, 2018. Website: F<http://perl.overmeer.net/CPAN/>
=head1 LICENSE
Copyrights 2004-2018 by [Mark Overmeer]. 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/>
```