Provided by: libmath-polygon-perl_1.10-3_all bug

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 Object Oriented interface around Math::Polygon::Calc,
       Math::Polygon::Clip, and other.  Together, these modules provide basic transformations on
       2D polygons in pure perl.

       WARNING: these computations may show platform dependent ronding differences.  These may
       also originate from compilation options of the Perl version you installed.

METHODS

   Constructors
       $obj->new(%options, [@points], %options)
       Math::Polygon->new(%options, [@points], %options)
           You may add %options before and/or after the @points.  You may also use the "points"
           option to set the points.  Each point in @points is (a references) to an ARRAY with
           two elements: an X and a Y coordinate.

           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 => [$xmin,$ymin, $xmax,$ymax]
             Usually computed from the shape automatically, but can also be overruled. See
             bbox().

           clockwise => BOOLEAN
             Is not specified, it will be computed by the isClockwise() method on demand.

           points => \@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 (unique?) 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( [FORMAT] )
           In LIST context, the points are returned as list, otherwise as reference to an ARRAY
           of points.

           [1.09] When a FORMAT is given, each coordinate will get processed.  This may be useful
           to hide platform specific rounding errors.  FORMAT may be a CODE reference or a
           "printf()" alike string.  See Math::Polygon::Calc::polygon_format().

           example:

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

             my @points = $poly->points("%.2f");

   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
           them.  A new polygon is returned.

            -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

       $obj->distance($point)
           [1.05] Returns the distance of the point to the closest point on the border of the
           polygon, zero if the point is on an edge.

       $obj->equal( <$other | \@points,[$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().

           example:

             if($poly->equal($other_poly, 0.1)) ...
             if($poly->equal(\@points, 0.1)) ...
             if($poly->equal(@points)) ...

       $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_polygon | \@points, [$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().

           example:

             if($poly->same($other_poly, 0.1)) ...
             if($poly->same(\@points, 0.1)) ...
             if($poly->same(@points)) ...

       $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 bounding 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( [FORMAT] )
           Print the polygon.

           [1.09] When a FORMAT is specified, all coordinates will get formatted first.  This may
           hide platform dependent rounding differences.

SEE ALSO

       This module is part of Math-Polygon distribution version 1.10, built on January 03, 2018.
       Website: http://perl.overmeer.net/CPAN/

LICENSE

       Copyrights 2004-2018 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://dev.perl.org/licenses/