## Name

ST_HausdorffDistance — Returns the Hausdorff distance between two geometries. Basically a measure of how similar or dissimilar 2 geometries are. Units are in the units of the spatial reference system of the geometries.

## Synopsis

`float ST_HausdorffDistance(`geometry g1, geometry g2`)`;

`float ST_HausdorffDistance(`geometry g1, geometry g2, float densifyFrac`)`;

## Description

Implements algorithm for computing a distance metric which can be thought of as the "Discrete Hausdorff Distance". This is the Hausdorff distance restricted to discrete points for one of the geometries. Wikipedia article on Hausdorff distance Martin Davis note on how Hausdorff Distance calculation was used to prove correctness of the CascadePolygonUnion approach.

When densifyFrac is specified, this function performs a segment densification before computing the discrete hausdorff distance. The densifyFrac parameter sets the fraction by which to densify each segment. Each segment will be split into a number of equal-length subsegments, whose fraction of the total length is closest to the given fraction.

 The current implementation supports only vertices as the discrete locations. This could be extended to allow an arbitrary density of points to be used.
 This algorithm is NOT equivalent to the standard Hausdorff distance. However, it computes an approximation that is correct for a large subset of useful cases. One important part of this subset is Linestrings that are roughly parallel to each other, and roughly equal in length. This is a useful metric for line matching.

Availability: 1.5.0 - requires GEOS >= 3.2.0

## Examples

For each building, find the parcel that best represents it. First we require the parcel intersect with the geometry. DISTINCT ON guarantees we get each building listed only once, the ORDER BY .. ST_HausdorffDistance gives us a preference of parcel that is most similar to the building.

```SELECT DISTINCT ON(buildings.gid) buildings.gid, parcels.parcel_id
FROM buildings INNER JOIN parcels ON ST_Intersects(buildings.geom,parcels.geom)
ORDER BY buildings.gid, ST_HausdorffDistance(buildings.geom, parcels.geom);```
```postgis=# SELECT ST_HausdorffDistance(
'LINESTRING (0 0, 2 0)'::geometry,
'MULTIPOINT (0 1, 1 0, 2 1)'::geometry);
st_hausdorffdistance
----------------------
1
(1 row)
```
```postgis=# SELECT st_hausdorffdistance('LINESTRING (130 0, 0 0, 0 150)'::geometry, 'LINESTRING (10 10, 10 150, 130 10)'::geometry, 0.5);
st_hausdorffdistance
----------------------
70
(1 row)
```