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       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 OO interface around Math::Polygon::Calc and


       $obj->new([%options], [$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

            -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);

           Returns the number of points,

           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.


             my $point = $poly->point(2);
             my ($first, $last) = $poly->point(0, -1);

           In LIST context, the points are returned as list, otherwise as
           reference to an ARRAY.


             my @points = $poly->points;
             my $first  = $points[0];
             my $x0 = $points[0][0]; # $first->[0]
             my $y0 = $points[0][1]; # $first->[1]

           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


             my $area = $poly->area;
             print "$area $poly_units ^2

           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


             my ($xmin, $ymin, $xmax, $ymax) = $poly->bbox;

           Returns a new, beautified version of this polygon.  Function

           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
           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


             my $center = $poly->centroid;
             my ($cx, $cy) = @$center;

           Make sure the points are in clockwise order.



           Returns a truth value indicating whether the point is inside the
           polygon or not.  On the edge is inside.

           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

           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


             if($poly->isClockwise) ...

           Returns true if the first point of the poly definition is the same
           as the last point.

           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().


            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

           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.

           Returns a polygon object with the points snapped to grid points.
           See Math::Polygon::Transform::polygon_grid().

             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.

           Mirror the polygon in a line.  Only one of the options can be
           provided.  Some programs call this "flip" or "flop".

             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

           y => FLOAT
             Mirror in the line "y=value", which means that "x" stays

           Returns a moved polygon object: all point are moved over the
           indicated distance.  See Math::Polygon::Transform::polygon_move().

             dx      0
             dy      0

           dx => FLOAT
             Displacement in the horizontal direction.

           dy => FLOAT
             Displacement in the vertical direction.

           Returns a resized polygon object.  See

             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

           xscale => FLOAT
             Specific scaling factor in the horizontal direction.

           yscale => FLOAT
             Specific scaling factor in the vertical direction.

           Returns a rotated polygon object: all point are moved over the
           indicated distance.  See

            -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)

           Returns a polygon object where points are removed.  See

            -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 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

           Returned is a list of ARRAYS-OF-POINTS containing line pieces from
           the input polygon.  Function



       This module is part of Math-Polygon distribution version 1.03, built on
       January 21, 2014. Website:


       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

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