geometry modification by iterative ST_MinimumBoundingCircle use

Question

ST_MinimumBoundingCircle returns the smallest circle polygon that can fully contain a geometry, but if you execute this function iteratively on a geometry, it increases more and more, whereas the same geometry should be maintained. Here is an example where a circle is created using ST_buffer with quad_segs by default. Then apply ST_MinimumBoundingCircle on it and then reapply on the same geometry.

As you can see, the area of the geometry starts to increase every time ST_MinimumBoundingCircle is applied.

with gen_circle as(
SELECT ST_Buffer(
ST_GeomFromText('POINT(100 90)'),50) as circle)
select postgis_liblwgeom_version(), 
st_area(ST_MinimumBoundingCircle(circle)),
st_area(ST_MinimumBoundingCircle(ST_MinimumBoundingCircle(circle))),
st_area(ST_MinimumBoundingCircle(ST_MinimumBoundingCircle(ST_MinimumBoundingCircle(circle)))) from gen_circle

I'm using the last postgis version

Answer 1

As ThingamuBob said, this is due to the parameter for number of segments per quarter circle in the ST_MinimumBoundingCircle function. As an illustration, you can see the same behaviour with ST_Buffer and how close the area of a circle with radius 1 approaches PI, as you increase the segments.

WITH segs(x) AS (VALUES(1), (10), (100), (1000), (10000))                                          
SELECT 
    x, 
    ST_Area(ST_Buffer(ST_MakePoint(0,0), 1, x))/PI() 
 FROM segs;

which returns:

    1 | 0.636619772367581
   10 | 0.995892735243561
  100 | 0.999958877155665
 1000 | 0.999999588766537
10000 | 0.999999995887669

Returning to your example:

WTIH gen_circle as(
  SELECT ST_Buffer(
           ST_GeomFromText('POINT(100 90)'),50) as circle)
SELECT        
    ST_Area(ST_MinimumBoundingCircle(circle, 1000)),
    ST_Area(ST_MinimumBoundingCircle(ST_MinimumBoundingCircle(circle, 1000), 1000)),
    ST_Area(ST_MinimumBoundingCircle(ST_MinimumBoundingCircle(
           ST_MinimumBoundingCircle(circle, 1000), 1000), 1000)) 
FROM gen_circle;

now returns:

7853.98324888513 | 7853.98809361888 | 7853.99293835557

which is a lot closer to the same answer -- of course, 4000 segments is still only an approximation of a circle, albeit a very close one.