> ## Documentation Index
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> Use this file to discover all available pages before exploring further.

# ST_HausdorffDistanceVertices

Returns the vertex-only (discrete) [Hausdorff distance](https://en.wikipedia.org/wiki/Hausdorff_distance) between the given 2 geometries. Both geometries are treated purely as sets of vertices: for every vertex of one geometry the distance to the *nearest vertex* of the other geometry is computed, and the function returns the largest such distance found in either direction.

This differs from [ST\_HausdorffDistance](/reference/wherobots-db/geometry-data/measurement/ST_HausdorffDistance), which measures each vertex against the other geometry's *segments* and can optionally densify those segments. Because segment interiors are ignored here, `ST_HausdorffDistanceVertices` is never smaller than `ST_HausdorffDistance(g1, g2)`, the overload without a densityFraction. It takes no densityFraction parameter itself.

If either geometry is empty, `null` is returned.

<Note>
  That bound does not extend to the densified overload. Densification adds sampled points along the segments, and those samples can be farther from the other geometry than any of its vertices are, so `ST_HausdorffDistance(g1, g2, densityFrac)` may return a larger value. For example, `LINESTRING (0 0, 10 0)` and `MULTIPOINT ((0 1), (10 1))` give `1.0` from `ST_HausdorffDistanceVertices` but `sqrt(26)` (`5.0990195135927845`) from `ST_HausdorffDistance(..., 0.5)`, which samples the line's midpoint.
</Note>

<Note>
  Even though the function accepts 3D geometry, the z ordinate is ignored and the computed distance is equivalent to the geometries not having the z ordinate.
</Note>

<img src="https://mintcdn.com/wherobots/4T-20ONOb4_nqKpG/images/sql-functions/ST_HausdorffDistanceVertices/ST_HausdorffDistanceVertices.svg?fit=max&auto=format&n=4T-20ONOb4_nqKpG&q=85&s=064a6b2a7271fb83859474d23bf35293" alt="ST_HausdorffDistanceVertices" width="500" height="300" data-path="images/sql-functions/ST_HausdorffDistanceVertices/ST_HausdorffDistanceVertices.svg" />

## Signatures

```sql theme={"system"}
ST_HausdorffDistanceVertices(g1: Geometry, g2: Geometry)
```

## Parameters

<ParamField body="g1" type="Geometry" required>
  The g1 value.
</ParamField>

<ParamField body="g2" type="Geometry" required>
  The g2 value.
</ParamField>

## Return type

<ResponseField type="Double">
  A numeric value.
</ResponseField>

## Examples

```sql theme={"system"}
SELECT ST_HausdorffDistanceVertices(ST_GeomFromWKT('LINESTRING (0 0, 1 1)'), ST_GeomFromWKT('LINESTRING (0 1, 1 0)'))
```

```
1.0
```

The vertices of the second line sit 1 and 2 units above the first line, but their nearest *vertex* is an endpoint of that line, so the result is `sqrt(29)` rather than the segment-based `sqrt(26)`:

```sql theme={"system"}
SELECT ST_HausdorffDistanceVertices(ST_GeomFromWKT('LINESTRING (0 0, 10 0)'), ST_GeomFromWKT('LINESTRING (5 1, 5 2)'))
```

```
5.385164807134504
```