# 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 $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 Defined in 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.

## Simple calculations

$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 Defined in Default
remove_spikes <false>
```

. remove_spikes BOOLEAN

$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->**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.

$obj->**string**

## 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 Defined in 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 Defined in Default
b C<0>
line <undef>
rc C<undef>
x C<undef>
y C<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 Defined in 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 Defined in Default
center C<[0,0]>
scale C<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 Defined in Default
center C<[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 Defined in Default
max_points C<undef>
same C<0.0001>
slope C<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.

$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().

# REFERENCES

See the Math::Polygon website at http://perl.overmeer.net/geo for more details.

# COPYRIGHTS

Module version 0.003. Written by Mark Overmeer (polygon@overmeer.net). See the ChangeLog for other contributors.

Copyright (c) 2004 by the author(s). All rights reserved. This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.