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.
- $obj->points
- In LIST context, the points are returned as list, otherwise
as reference to an ARRAY.
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().
- $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().
- $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().
- $obj->clockwise
- Make sure the points are in clockwise order.
- $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.
- $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.
- $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().
- $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 1.02, built on
September 19, 2011. Website:
http://perl.overmeer.net/geo/
LICENSE¶
Copyrights 2004,2006-2011 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