

 
Math::Polygon(3) 
User Contributed Perl Documentation 
Math::Polygon(3) 
Math::Polygon  Class for maintaining polygon data
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);
This class provides an Object Oriented interface around Math::Polygon::Calc,
Math::Polygon::Clip, and other. Together, these modules provide basic
transformations on 2D polygons in pure perl.
WARNING: these computations may show platform dependent ronding
differences. These may also originate from compilation options of the Perl
version you installed.
 $obj>new(%options, [@points], %options)
 Math::Polygon>new(%options, [@points], %options)
 You may add %options before and/or after the @points. You may also use the
"points" option to set the points. Each point in @points is (a
references) to an ARRAY with two elements: an X and a Y coordinate.
When "new()" is called as instance method, it is believed that the
new polygon is derived from the callee, and therefore some facts (like
clockwise or anticlockwise direction) will get copied unless overruled.
Option Default
bbox undef
clockwise undef
points undef
 bbox => [$xmin,$ymin, $xmax,$ymax]
 Usually computed from the shape automatically, but can also be overruled.
See bbox().
 clockwise => BOOLEAN
 Is not specified, it will be computed by the isClockwise() method
on demand.
 points => \@points
 See points() and nrPoints().
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);
 $obj>nrPoints()
 Returns the number of points,
 $obj>order()
 Returns the number of (unique?) points: one less than
nrPoints().
 $obj>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);
 $obj>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 "printf()" alike string. See
Math::Polygon::Calc::polygon_format().
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");
 $obj>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 Math::Polygon::Calc::polygon_area().
example:
my $area = $poly>area;
print "$area $poly_units ^2\n";
 $obj>bbox()
 Returns a list with four elements: (xmin, ymin, xmax, ymax), which
describe the bounding box of the polygon (all points of the polygon are
inside that area). The computation is expensive, and therefore, the
results are cached. Function Math::Polygon::Calc::polygon_bbox().
example:
my ($xmin, $ymin, $xmax, $ymax) = $poly>bbox;
 $obj>beautify(%options)
 Returns a new, beautified version of this polygon. Function
Math::Polygon::Calc::polygon_beautify().
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>
 $obj>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 Math::Polygon::Calc::polygon_centroid().
example:
my $center = $poly>centroid;
my ($cx, $cy) = @$center;
 $obj>clockwise()
 Make sure the points are in clockwise order.
example:
$poly>clockwise;
 $obj>contains($point)
 Returns a truth value indicating whether the point is inside the polygon
or not. On the edge is inside.
 $obj>counterClockwise()
 Make sure the points are in counterclockwise order.
example:
$poly>counterClockwise
 $obj>distance($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.
 $obj>equal( <$other  \@points,[$tolerance]>  $points
)
 Compare two polygons, on the level of points. When the polygons are the
same but rotated, this will return false. See same(). Function
Math::Polygon::Calc::polygon_equal().
example:
if($poly>equal($other_poly, 0.1)) ...
if($poly>equal(\@points, 0.1)) ...
if($poly>equal(@points)) ...
 $obj>isClockwise()
 The points are (in majority) orded in the direction of the hands of the
clock. This calculation is quite expensive (same effort as calculating the
area of the polygon), and the result is therefore cached.
example:
if($poly>isClockwise) ...
 $obj>isClosed()
 Returns true if the first point of the poly definition is the same as the
last point.
 $obj>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
Math::Polygon::Calc::polygon_perimeter().
example:
my $fence = $poly>perimeter;
print "fence length: $fence $poly_units\n"
 $obj>same( <$other_polygon  \@points, [$tolerance]> 
@points )
 Compare two polygons, where the polygons may be rotated wrt each other.
This is (much) slower than equal(), but some algorithms will cause
un unpredictable rotation in the result. Function
Math::Polygon::Calc::polygon_same().
example:
if($poly>same($other_poly, 0.1)) ...
if($poly>same(\@points, 0.1)) ...
if($poly>same(@points)) ...
 $obj>startMinXY()
 Returns a new polygon object, where the points are rotated in such a way
that the point which is losest to the leftbottom point of the bounding
box has become the first.
Function Math::Polygon::Calc::polygon_start_minxy().
Implemented in Math::Polygon::Transform: changes on the structure of the polygon
except clipping. All functions return a new polygon object or undef.
 $obj>grid(%options)
 Returns a polygon object with the points snapped to grid points. See
Math::Polygon::Transform::polygon_grid().
OptionDefault
raster 1.0
 raster => FLOAT
 The raster size, which determines the points to round to. The origin
"[0,0]" is always on a gridpoint. When the raster value is
zero, no transformation will take place.
 $obj>mirror(%options)
 Mirror the polygon in a line. Only one of the options can be provided.
Some programs call this "flip" or "flop".
OptionDefault
b 0
line <undef>
rc undef
x undef
y undef
 b => FLOAT
 Only used in combination with option "rc" to describe a
line.
 line => [POINT, POINT]
 Alternative way to specify the mirror line. The "rc" and
"b" are computed from the two points of the line.
 rc => FLOAT
 Description of the line which is used to mirror in. The line is "y=
rc*x+b". The "rc" equals "dy/dx", the firing
angle. If "undef" is explicitly specified then "b" is
used as constant x: it's a vertical mirror.
 x => FLOAT
 Mirror in the line "x=value", which means that "y"
stays unchanged.
 y => FLOAT
 Mirror in the line "y=value", which means that "x"
stays unchanged.
 $obj>move(%options)
 Returns a moved polygon object: all point are moved over the indicated
distance. See Math::Polygon::Transform::polygon_move().
OptionDefault
dx 0
dy 0
 dx => FLOAT
 Displacement in the horizontal direction.
 dy => FLOAT
 Displacement in the vertical direction.
 $obj>resize(%options)
 Returns a resized polygon object. See
Math::Polygon::Transform::polygon_resize().
OptionDefault
center [0,0]
scale 1.0
xscale <scale>
yscale <scale>
 center => $point
 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.
 xscale => FLOAT
 Specific scaling factor in the horizontal direction.
 yscale => FLOAT
 Specific scaling factor in the vertical direction.
 $obj>rotate(%options)
 Returns a rotated polygon object: all point are moved over the indicated
distance. See Math::Polygon::Transform::polygon_rotate().
Option Default
center [0,0]
degrees 0
radians 0
 center => POINT
 degrees => FLOAT
 specify rotation angle in degrees (between 180 and 360).
 radians => FLOAT
 specify rotation angle in rads (between pi and 2*pi)
 $obj>simplify(%options)
 Returns a polygon object where points are removed. See
Math::Polygon::Transform::polygon_simplify().
Option Default
max_points undef
same 0.0001
slope undef
 max_points => INTEGER
 First, "same" and "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.
 same => FLOAT
 The distance between two points to be considered "the same"
point. The value is used as radius of the circle.
 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
"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.
 $obj>fillClip1($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 "undef" when no polygon is
outside the $box. Function
Math::Polygon::Clip::polygon_fill_clip1().
 $obj>lineClip($box)
 Returned is a list of ARRAYSOFPOINTS containing line pieces from the
input polygon. Function
Math::Polygon::Clip::polygon_line_clip().
 $obj>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.
This module is part of MathPolygon distribution version 1.10, built on January
03, 2018. Website: http://perl.overmeer.net/CPAN/
Copyrights 20042018 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 http://dev.perl.org/licenses/
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