Categories:

Geospatial Functions

# ST_HAUSDORFFDISTANCE¶

Returns the discrete Hausdorff distance between two GEOGRAPHY objects.

The Hausdorff distance indicates how similar the two objects are. Two objects are considered to be similar if each point in one object is close to a point in the other object. The Hausdorff distance is the greatest distance between a point in one object and a point in the other object.

ST_HAUSDORFFDISTANCE returns the discrete Hausdorff distance, which is calculated by comparing only the vertices (discrete points) and not arbitrary points along the edge.

## Syntax¶

```ST_HAUSDORFFDISTANCE( <geography_expression_1> , <geography_expression_2> )
```

## Arguments¶

`geography_expression_1`

The argument must be an expression of type GEOGRAPHY.

`geography_expression_2`

The argument must be an expression of type GEOGRAPHY.

## Returns¶

Returns a value of type REAL that represents the discrete Hausdorff distance in degrees.

## Usage Notes¶

• Returns NULL if one or more input points are NULL.

## Examples¶

This example returns the Hausdorff distance between two points (point `0 0` and point `0 1`):

```SELECT ST_HAUSDORFFDISTANCE(ST_POINT(0, 0), ST_POINT(0, 1));
+------------------------------------------------------+
| ST_HAUSDORFFDISTANCE(ST_POINT(0, 0), ST_POINT(0, 1)) |
|------------------------------------------------------|
|                                                    1 |
+------------------------------------------------------+
```

The next example compares three Polygons (`a`, `b`, and `c`).

The distance between the farthest points in `a` and `c` (point `0 1` and point `0 3`) is greater than the distance between the farthest points in `a` and `b` (point `1 0` and point `2 0`).

As a result, the value returned by ST_HAUSDORFFDISTANCE is smaller for `a` and `c`. This indicates that `a` and `c` are more similar than `a` and `b`.

```WITH
a AS (TO_GEOGRAPHY('POLYGON((-1 0, 0 1, 1 0, 0 -1, -1 0))')),
b AS (TO_GEOGRAPHY('POLYGON((-1 0, 0 1, 2 0, 0 -1, -1 0))')),
c AS (TO_GEOGRAPHY('POLYGON((-1 0, 0 3, 1 0, 0 -1, -1 0))'))
SELECT
ST_HAUSDORFFDISTANCE(a, b) as distance_between_a_and_b,
ST_HAUSDORFFDISTANCE(a, c) as distance_between_a_and_c;
+--------------------------+--------------------------+
| DISTANCE_BETWEEN_A_AND_B | DISTANCE_BETWEEN_A_AND_C |
|--------------------------+--------------------------|
|                        1 |                        2 |
+--------------------------+--------------------------+
``` 