

<B>polygon_areaB>(LISTof$points) 
Returns the area enclosed by the polygon. The last point of the list
must be the same as the first to produce a correct result.
The algorithm was found at <http://mathworld.wolfram.com/PolygonArea.html>, and sounds:
A = abs( 1/2 * (x1y2x2y1 + x2y3x3y2 ...)  
<B>polygon_bboxB>(LISTof$points)  Returns a list with four elements: (xmin, ymin, xmax, ymax), which describe the bounding box of the polygon (all points of the polygon are within that area.  
<B>polygon_beautifyB>([HASH], LISTof$points) 
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
The optional HASH contains the OPTIONS:
Option Default remove_between <false> remove_spikes <false>
 
<B>polygon_centroidB>(LISTof$points) 
Returns the centroid location of the polygon. The last point of the list
must be the same as the first to produce a correct result.
The algorithm was found at http://en.wikipedia.org/wiki/Centroid#Centroid_of_polygon  
<B>polygon_clockwiseB>(LISTof$points)  Be sure the polygon points are in clockwise order.  
<B>polygon_contains_pointB>($point, LISTof$points)  Returns true if the point is unside the closed polygon.  
<B>polygon_counter_clockwiseB>(LISTof$points)  Be sure the polygon points are in counterclockwise order.  
<B>polygon_equalB>(ARRAYof$points, ARRAYof$points, [$tolerance])  Compare two polygons, on the level of points. When the polygons are the same but rotated, this will return false. See polygon_same().  
<B>polygon_is_clockwiseB>(LISTof$points)  
<B>polygon_is_closedB>($points)  
<B>polygon_perimeterB>(LISTof$points) 
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.
This is simply Pythagoras.
$l = sqrt((x1x0)^2 + (y1y0)^2) + sqrt((x2x1)^2+(y2y1)^2) + ...  
<B>polygon_sameB>(ARRAYof$points, ARRAYof$points, [$tolerance])  Compare two polygons, where the polygons may be rotated wrt each other. This is (much) slower than polygon_equal(), but some algorithms will cause un unpredictable rotation in the result.  
<B>polygon_start_minxyB>(LISTof$points)  Returns the polygon, where the point which is closest to the leftbottom corner of the bounding box is made first.  
<B>polygon_stringB>(LISTof$points)  
This module is part of MathPolygon distribution version 1.03, built on January 21, 2014. Website: http://perl.overmeer.net/geo/
Copyrights 2004,20062014 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 v5.20.3  MATH::POLYGON::CALC (3)  20140121 
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