# Measurement#

area(geometry, **kwargs)#

Computes the area of a (multi)polygon.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import MultiPolygon, Polygon
>>> polygon = Polygon([(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)])
>>> area(polygon)
100.0
>>> area(MultiPolygon([polygon, Polygon([(10, 10), (10, 20), (20, 20), (20, 10), (10, 10)])]))
200.0
>>> area(Polygon())
0.0
>>> area(None)
nan
```
bounds(geometry, **kwargs)#

Computes the bounds (extent) of a geometry.

For each geometry these 4 numbers are returned: min x, min y, max x, max y.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString, Point, Polygon
>>> bounds(Point(2, 3)).tolist()
[2.0, 3.0, 2.0, 3.0]
>>> bounds(LineString([(0, 0), (0, 2), (3, 2)])).tolist()
[0.0, 0.0, 3.0, 2.0]
>>> bounds(Polygon()).tolist()
[nan, nan, nan, nan]
>>> bounds(None).tolist()
[nan, nan, nan, nan]
```
distance(a, b, **kwargs)#

Computes the Cartesian distance between two geometries.

Parameters
a, bGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString, Point, Polygon
>>> point = Point(0, 0)
>>> distance(Point(10, 0), point)
10.0
>>> distance(LineString([(1, 1), (1, -1)]), point)
1.0
>>> distance(Polygon([(3, 0), (5, 0), (5, 5), (3, 5), (3, 0)]), point)
3.0
>>> distance(Point(), point)
nan
>>> distance(None, point)
nan
```
frechet_distance(a, b, densify=None, **kwargs)#

Compute the discrete Fréchet distance between two geometries.

The Fréchet distance is a measure of similarity: it is the greatest distance between any point in A and the closest point in B. The discrete distance is an approximation of this metric: only vertices are considered. The parameter ‘densify’ makes this approximation less coarse by splitting the line segments between vertices before computing the distance.

Fréchet distance sweep continuously along their respective curves and the direction of curves is significant. This makes it a better measure of similarity than Hausdorff distance for curve or surface matching.

Parameters
a, bGeometry or array_like
densifyfloat or array_like, optional

The value of densify is required to be between 0 and 1.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString
>>> line1 = LineString([(0, 0), (100, 0)])
>>> line2 = LineString([(0, 0), (50, 50), (100, 0)])
>>> frechet_distance(line1, line2)
70.71...
>>> frechet_distance(line1, line2, densify=0.5)
50.0
>>> frechet_distance(line1, LineString())
nan
>>> frechet_distance(line1, None)
nan
```
hausdorff_distance(a, b, densify=None, **kwargs)#

Compute the discrete Hausdorff distance between two geometries.

The Hausdorff distance is a measure of similarity: it is the greatest distance between any point in A and the closest point in B. The discrete distance is an approximation of this metric: only vertices are considered. The parameter ‘densify’ makes this approximation less coarse by splitting the line segments between vertices before computing the distance.

Parameters
a, bGeometry or array_like
densifyfloat or array_like, optional

The value of densify is required to be between 0 and 1.

**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString
>>> line1 = LineString([(130, 0), (0, 0), (0, 150)])
>>> line2 = LineString([(10, 10), (10, 150), (130, 10)])
>>> hausdorff_distance(line1, line2)
14.14...
>>> hausdorff_distance(line1, line2, densify=0.5)
70.0
>>> hausdorff_distance(line1, LineString())
nan
>>> hausdorff_distance(line1, None)
nan
```
length(geometry, **kwargs)#

Computes the length of a (multi)linestring or polygon perimeter.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import LineString, MultiLineString, Polygon
>>> length(LineString([(0, 0), (0, 2), (3, 2)]))
5.0
>>> length(MultiLineString([
...     LineString([(0, 0), (1, 0)]),
...     LineString([(1, 0), (2, 0)])
... ]))
2.0
>>> length(Polygon([(0, 0), (0, 10), (10, 10), (10, 0), (0, 0)]))
40.0
>>> length(LineString())
0.0
>>> length(None)
nan
```

Computes the radius of the minimum bounding circle that encloses an input geometry.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

`minimum_bounding_circle`

Examples

```>>> from shapely import GeometryCollection, LineString, MultiPoint, Point, Polygon
>>> minimum_bounding_radius(Polygon([(0, 5), (5, 10), (10, 5), (5, 0), (0, 5)]))
5.0
4.5
1.0
0.0
0.0
```
minimum_clearance(geometry, **kwargs)#

Computes the Minimum Clearance distance.

A geometry’s “minimum clearance” is the smallest distance by which a vertex of the geometry could be moved to produce an invalid geometry.

If no minimum clearance exists for a geometry (for example, a single point, or an empty geometry), infinity is returned.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Examples

```>>> from shapely import Polygon
>>> polygon = Polygon([(0, 0), (0, 10), (5, 6), (10, 10), (10, 0), (5, 4), (0, 0)])
>>> minimum_clearance(polygon)
2.0
>>> minimum_clearance(Polygon())
inf
>>> minimum_clearance(None)
nan
```
total_bounds(geometry, **kwargs)#

Computes the total bounds (extent) of the geometry.

Parameters
geometryGeometry or array_like
**kwargs

For other keyword-only arguments, see the NumPy ufunc docs.

Returns
numpy ndarray of [xmin, ymin, xmax, ymax]

Examples

```>>> from shapely import LineString, Point, Polygon
>>> total_bounds(Point(2, 3)).tolist()
[2.0, 3.0, 2.0, 3.0]
>>> total_bounds([Point(2, 3), Point(4, 5)]).tolist()
[2.0, 3.0, 4.0, 5.0]
>>> total_bounds([
...     LineString([(0, 1), (0, 2), (3, 2)]),
...     LineString([(4, 4), (4, 6), (6, 7)])
... ]).tolist()
[0.0, 1.0, 6.0, 7.0]
>>> total_bounds(Polygon()).tolist()
[nan, nan, nan, nan]
>>> total_bounds([Polygon(), Point(2, 3)]).tolist()
[2.0, 3.0, 2.0, 3.0]
>>> total_bounds(None).tolist()
[nan, nan, nan, nan]
```