ST_HausdorffDistance

ST_HausdorffDistance takes two geometry columns and returns a double column. The output column represents the Hausdorff distance between the two input geometries.

Hausdorff distance is defined as the greatest distance among all vertices of a given geometry to the closest vertex in the reference geometry. Below is an example that calculates the Hausdorff distance between two lines.

The result will be in the same units as the input geometry data. For example, if your input geometries are in a spatial reference that uses meters, the result values will be in meters.

If the two geometry columns are in different spatial references, the function will automatically transform the second geometry into the spatial reference of the first.

If one of the input geometries has an unknown spatial reference the function will use planar distance calculations.

This function can be used to measure the similarity between two geometries. For more details, go to the core topic for similarity measures.

For more details, go to the GeoAnalytics for Microsoft Fabric API reference for hausdorff_distance.

Examples

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from geoanalytics_fabric.sql import functions as ST, Linestring

data = [
    ("LINESTRING (10 10, 20 20)", "LINESTRING (10 30, 20 40)"),
    ("LINESTRING (0 20, 10 20)", "LINESTRING (0 80, -10 20)")
]

df = spark.createDataFrame(data, ["line1_wkt", "line2_wkt"]) \
          .withColumn("line1", ST.line_from_text("line1_wkt", 4326)) \
          .withColumn("line2", ST.line_from_text("line2_wkt", 4326))

df.select(ST.hausdorff_distance("line1", "line2").alias("hausdorff_distance")).show()

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+------------------+
|hausdorff_distance|
+------------------+
|              20.0|
|              60.0|
+------------------+

Version table

Related topics

• SQL functions
• ST_Distance
• ST_GeodesicDistance
• ST_EuclideanDistance
• ST_FrechetDistance
• Data sources
• Coordinate systems and transformations