# NAME

Math::Polygon::Calc - Simple polygon calculations

# INHERITANCE

`````` Math::Polygon::Calc
is a Exporter``````

# SYNOPSIS

`````` my @poly = ( [1,2], [2,4], [5,7], [1, 2] );

my (\$xmin, \$ymin, \$xmax, \$ymax) = polygon_bbox @poly;

my \$area = polygon_area @poly;
MY \$L    = polygon_perimeter @poly;
if(polygon_is_clockwise @poly) { ... };

my @rot  = polygon_start_minxy @poly;``````

# DESCRIPTION

This package contains a wide variaty of relatively easy polygon calculations. More complex calculations are put in separate packages.

# FUNCTIONS

polygon_area(@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 * (x1y2-x2y1 + x2y3-x3y2 ...)``
polygon_bbox(@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.

polygon_beautify( [\%options], @points )

Polygons, certainly after some computations, can have a lot of horrible artifacts: points which are double, spikes, etc. The optional HASH contains the %options.

`````` -Option       --Default
remove_spikes  <false>``````
remove_spikes => BOOLEAN

Spikes contain of three successive points, where the first is on the line between the second and the third. The line goes from first to second, but then back to get to the third point.

At the moment, only pure horizontal and pure vertical spikes are removed.

polygon_centroid(@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

polygon_clockwise(@points)

Be sure the polygon points are in clockwise order.

polygon_contains_point(\$point, @points)

Returns true if the point is inside the closed polygon. On an edge will be flagged as 'inside'. But be warned of rounding issues, caused by the floating-point calculations used by this algorithm.

polygon_counter_clockwise(@points)

Be sure the polygon points are in counter-clockwise order.

polygon_distance(\$point, @polygon)

[1.05] calculate the shortest distance between a point and any vertex of a closed polygon.

polygon_equal( \@points1, \@points2, [\$tolerance] )

Compare two polygons, on the level of points. When the polygons are the same but rotated, this will return false. See polygon_same().

polygon_format(\$format, @points)

[1.07] Map the \$format over all @points, both the X and Y coordinate. This is especially useful to reduce the number of digits in the stringification. For instance, when you want reproducible results in regression scripts.

The format is anything supported by printf(), for instance "%5.2f". Or, you can pass a code reference which accepts a single value.

polygon_is_clockwise(@points)
polygon_is_closed(@points)
polygon_perimeter(@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((x1-x0)^2 + (y1-y0)^2) + sqrt((x2-x1)^2+(y2-y1)^2) + ...``
polygon_same( \@points1, \@points2, [\$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.

polygon_start_minxy(@points)

Returns the polygon, where the point which is closest to the left-bottom corner of the bounding box is made first.

polygon_string(@points)