# shapely.frechet_distance#

frechet_distance(a, b, densify=None, **kwargs)#

Compute the discrete Fréchet distance between two geometries.

Note

‘frechet_distance’ requires at least GEOS 3.7.0.

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
```