#### NAME
Math::Polygon - Class for maintaining polygon data
#### 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);
#### DESCRIPTION
This class provides an OO interface around Math::Polygon::Calc and
Math::Polygon::Clip.
#### METHODS
Constructors
$obj->new([%options], [$points], [%options])
Math::Polygon->new([%options], [$points], [%options])
You may add %options after and/or before the $points. You may also
use the "points" options to get the points listed. $points are
references to an ARRAY of X and Y.
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 anti-clockwise direction) will get copied unless
overruled.
-Option --Default
bbox undef
clockwise undef
points undef
bbox => ARRAY
Usually computed from the figure automatically, but can also be
specified as [xmin,ymin,xmax, ymax]. See __bbox()__.
clockwise => BOOLEAN
Is not specified, it will be computed by the __isClockwise()__ method
on demand.
points => ARRAY-of-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);
Attributes
$obj->nrPoints()
Returns the number of points,
$obj->order()
Returns the number of uniqe 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()
In LIST context, the points are returned as list, otherwise as
reference to an ARRAY.
example:
my @points = $poly->points;
my $first = $points[0];
my $x0 = $points[0][0]; # $first->[0]
my $y0 = $points[0][1]; # $first->[1]
Geometry
$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
";
$obj->bbox()
Returns a list with four elements: (xmin, ymin, xmax, ymax), which
describe the bounding box of the polygon (all points of the polygon
are inside that area). The computation is expensive, and
therefore, the results are cached. Function
__Math::Polygon::Calc::polygon_bbox()__.
example:
my ($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
-Option --Default
remove_spikes <false>
remove_spikes => BOOLEAN
$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 counter-clockwise order.
example:
$poly->counterClockwise
$obj->equal(<$other | ARRAY,[$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()__.
$obj->isClockwise()
The points are (in majority) orded in the direction of the hands of
the clock. This calculation is quite expensive (same effort as
calculating the area of the polygon), and the result is therefore
cached.
example:
if($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
"
$obj->same(<$other | ARRAY,[$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()__.
$obj->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 bouding box has become the first.
Function __Math::Polygon::Calc::polygon_start_minxy()__.
Transformations
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()__.
-Option--Default
raster 1.0
raster => FLOAT
The raster size, which determines the points to round to. The
origin "[0,0]" is always on a grid-point. 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".
-Option--Default
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()__.
-Option--Default
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()__.
-Option--Default
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.
Clipping
$obj->fillClip1($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 ARRAYS-OF-POINTS containing line pieces from
the input polygon. Function
__Math::Polygon::Clip::polygon_line_clip()__.
Display
$obj->string()
#### SEE ALSO
This module is part of Math-Polygon distribution version 1.03, built on
January 21, 2014. Website: __http://perl.overmeer.net/geo/__
#### LICENSE
Copyrights 2004,2006-2014 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://www.perl.com/perl/misc/Artistic.php__
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