Math::Polygon(3pm)					User Contributed Perl Documentation					Math::Polygon(3pm)

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>

	   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().

       $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().

   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 1.02, 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

perl v5.12.4							    2011-09-19							Math::Polygon(3pm)