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\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
-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 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\n"
- $obj->same(<$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().
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.html