postgresql - Rotate Polygon to be Parallel with the X Axis -

by default, postgis calculates envelope or extent of polygon based on bounding box of polygon ((minx, miny), (minx, maxy), (maxx, maxy), (maxx, miny), (minx, miny)).

this gives result so:

however, i'm looking result more this:

as far know, best algorithm can come is:

1. determine angle a rotate polygon x parallel x-axis
2. rotate x a degrees, calculate envelope y of rotated polygon x
3. rotate y -a degrees

how calculate step #1 in postgis?

here's implementation. doesn't handle degenerate cases , may not rectangle chose if areas tie. i'm working on submission postgis, should enough work until patch postgis.

create or replace function st_minimumrectangle(g geometry) returns geometry language 'plpgsql' $$ declare         hull geometry; begin         hull = st_exteriorring(st_convexhull(g));         -- 1 side must lie along rectangle.         -- so, each side, rotate, bbox, counter-rotate bbox         sides (                 select st_pointn(hull, n) a, st_pointn(hull, n+1) b,                         n side                         generate_series(1,st_npoints(hull)-1) n                 ),         angles (                 select side, a, b, st_azimuth(a, b) angle sides         ),         boxes (                 select st_rotate(st_envelope(st_rotate(hull, -angle)),angle) rect, side, angle angles         )         select rect hull boxes order st_area(rect), side limit 1         ;         return hull; end; $$ immutable strict;