ST_MinimumBoundingCircle
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Name

ST_MinimumBoundingCircle — Returns the smallest circle polygon that contains a geometry.

Synopsis

geometry ST_MinimumBoundingCircle(geometry geomA, integer num_segs_per_qt_circ=48);

Description

Returns the smallest circle polygon that contains a geometry.

[Note]

The bounding circle is approximated by a polygon with a default of 48 segments per quarter circle. Because the polygon is an approximation of the minimum bounding circle, some points in the input geometry may not be contained within the polygon. The approximation can be improved by increasing the number of segments. For applications where an approximation is not suitable ST_MinimumBoundingRadius may be used.

Use with ST_Collect to get the minimum bounding circle of a set of geometries.

To compute two points lying on the minimum circle (the "maximum diameter") use ST_LongestLine.

The ratio of the area of a polygon divided by the area of its Minimum Bounding Circle is referred to as the Reock compactness score.

Performed by the GEOS module.

Availability: 1.4.0

Examples

SELECT d.disease_type,
    ST_MinimumBoundingCircle(ST_Collect(d.geom)) As geom
    FROM disease_obs As d
    GROUP BY d.disease_type;

Minimum bounding circle of a point and linestring. Using 8 segs to approximate a quarter circle

SELECT ST_AsText(ST_MinimumBoundingCircle(ST_Collect(ST_GeomFromText('LINESTRING(55 75,125 150)'),
                ST_Point(20, 80)), 8
                )) As wktmbc;
POLYGON((72.5 178.4024474346694,84.86920388664029 177.18418718546332,96.76306620464646 173.57622349601382,107.72451249529237 167.71720838753708,117.33230052487836 159.83230052487838,125.21720838753708 150.22451249529237,131.07622349601382 139.26306620464646,134.68418718546332 127.3692038866403,135.9024474346694 115,134.68418718546332 102.63079611335971,131.07622349601382 90.73693379535354,125.21720838753708 79.77548750470766,117.33230052487838 70.16769947512164,107.72451249529237 62.282791612462916,96.76306620464648 56.42377650398619,84.86920388664032 52.815812814536685,72.50000000000001 51.59755256533059,60.13079611335969 52.815812814536685,48.236933795353536 56.42377650398618,37.27548750470765 62.28279161246291,27.667699475121637 70.16769947512162,19.782791612462923 79.77548750470763,13.923776503986204 90.7369337953535,10.315812814536692 102.63079611335968,9.097552565330588 114.99999999999999,10.315812814536685 127.3692038866403,13.923776503986197 139.2630662046465,19.78279161246291 150.22451249529234,27.667699475121623 159.83230052487835,37.275487504707634 167.71720838753708,48.236933795353494 173.5762234960138,60.13079611335967 177.18418718546332,72.49999999999999 178.4024474346694))