--EDIT--

The PostGIS info from SELECT postgis_full_version();' is as below (Ubuntu 16.04).

POSTGIS="2.3.3 r15473" GEOS="3.5.1-CAPI-1.9.1 r4246" SFCGAL="1.2.2" PROJ="Rel. 4.9.2, 08 September 2015" GDAL="GDAL 1.11.3, released 2015/09/16" LIBXML="2.9.3" LIBJSON="0.11.99" (core procs from "2.3.2 r15302" need upgrade) TOPOLOGY (topology procs from "2.3.2 r15302" need upgrade) RASTER (raster procs from "2.3.2 r15302" need upgrade) (sfcgal procs from "2.3.2 r15302" need upgrade)

I was wondering how to implement a directed (or one-sided) Hausdorff distance function in PostGIS?

I looked into the PostGIS 2.3.3 source code, and it seems that ST_HausdorffDistance is implemented as a simple C wrapper function that calls the corresponding GEOS function as follows:

PG_FUNCTION_INFO_V1(hausdorffdistance);
Datum hausdorffdistance(PG_FUNCTION_ARGS)
{
    GSERIALIZED *geom1;
    GSERIALIZED *geom2;
    GEOSGeometry *g1;
    GEOSGeometry *g2;
    double result;
    int retcode;

    POSTGIS_DEBUG(2, "hausdorff_distance called");

    geom1 = PG_GETARG_GSERIALIZED_P(0);
    geom2 = PG_GETARG_GSERIALIZED_P(1);

    if ( gserialized_is_empty(geom1) || gserialized_is_empty(geom2) )
        PG_RETURN_NULL();

    initGEOS(lwpgnotice, lwgeom_geos_error);

    g1 = (GEOSGeometry *)POSTGIS2GEOS(geom1);
    if ( 0 == g1 )   /* exception thrown at construction */
    {
        HANDLE_GEOS_ERROR("First argument geometry could not be converted to GEOS");
        PG_RETURN_NULL();
    }

    g2 = (GEOSGeometry *)POSTGIS2GEOS(geom2);
    if ( 0 == g2 )   /* exception thrown */
    {
        HANDLE_GEOS_ERROR("Second argument geometry could not be converted to GEOS");
        GEOSGeom_destroy(g1);
        PG_RETURN_NULL();
    }

    retcode = GEOSHausdorffDistance(g1, g2, &result);
    GEOSGeom_destroy(g1);
    GEOSGeom_destroy(g2);

    if (retcode == 0)
    {
        HANDLE_GEOS_ERROR("GEOSHausdorffDistance");
        PG_RETURN_NULL(); /*never get here */
    }

    PG_FREE_IF_COPY(geom1, 0);
    PG_FREE_IF_COPY(geom2, 1);

    PG_RETURN_FLOAT8(result);
}

I don't have much experience with GEOS or interfacing it with PostGIS. The only thing I found in GEOS is that in that in geos::algorithm::distance::DiscreteHausdorffDistance, it is said that there is an double orientedDistance () member function. I am not sure if the documentation is even current.

Can some with the knowledge suggest how to adapt the above code to obtain the directed (or one-sided) Hausdorff distance from GEOS?

I was wondering how to implement a directed (or one-sided) Hausdorff distance function in PostGIS?

I looked into the PostGIS 2.3.3 source code, and it seems that ST_HausdorffDistance is implemented as a simple C wrapper function that calls the corresponding GEOS function as follows:

PG_FUNCTION_INFO_V1(hausdorffdistance);
Datum hausdorffdistance(PG_FUNCTION_ARGS)
{
    GSERIALIZED *geom1;
    GSERIALIZED *geom2;
    GEOSGeometry *g1;
    GEOSGeometry *g2;
    double result;
    int retcode;

    POSTGIS_DEBUG(2, "hausdorff_distance called");

    geom1 = PG_GETARG_GSERIALIZED_P(0);
    geom2 = PG_GETARG_GSERIALIZED_P(1);

    if ( gserialized_is_empty(geom1) || gserialized_is_empty(geom2) )
        PG_RETURN_NULL();

    initGEOS(lwpgnotice, lwgeom_geos_error);

    g1 = (GEOSGeometry *)POSTGIS2GEOS(geom1);
    if ( 0 == g1 )   /* exception thrown at construction */
    {
        HANDLE_GEOS_ERROR("First argument geometry could not be converted to GEOS");
        PG_RETURN_NULL();
    }

    g2 = (GEOSGeometry *)POSTGIS2GEOS(geom2);
    if ( 0 == g2 )   /* exception thrown */
    {
        HANDLE_GEOS_ERROR("Second argument geometry could not be converted to GEOS");
        GEOSGeom_destroy(g1);
        PG_RETURN_NULL();
    }

    retcode = GEOSHausdorffDistance(g1, g2, &result);
    GEOSGeom_destroy(g1);
    GEOSGeom_destroy(g2);

    if (retcode == 0)
    {
        HANDLE_GEOS_ERROR("GEOSHausdorffDistance");
        PG_RETURN_NULL(); /*never get here */
    }

    PG_FREE_IF_COPY(geom1, 0);
    PG_FREE_IF_COPY(geom2, 1);

    PG_RETURN_FLOAT8(result);
}

I don't have much experience with GEOS or interfacing it with PostGIS. The only thing I found in GEOS is that in that in geos::algorithm::distance::DiscreteHausdorffDistance, it is said that there is an double orientedDistance () member function. I am not sure if the documentation is even current.

Can some with the knowledge suggest how to adapt the above code to obtain the directed (or one-sided) Hausdorff distance from GEOS?