postgresql - 旋转多边形使其与 X 轴平行

Question

默认情况下，PostGIS 根据多边形的边界框计算多边形的包络或范围 ((MINX, MINY), (MINX, MAXY), (MAXX, MAXY), (MAXX, MINY) , (MINX, MINY)).

结果如下:

但是，我正在寻找更像这样的结果:

据我所知，我能想到的最佳算法是:

1. 确定角度a 以旋转多边形X 使其与x 轴平行
2. 旋转X a度，计算旋转多边形X的包络Y
3. 旋转 Y -a 度

如何计算 PostGIS 中的第 1 步？

Answer 1

这是一个实现。它不处理退化的情况，你如果区域平局，则可能不喜欢选择的矩形。我正在尝试提交给 postgis，但这应该足以使用直到我得到了 postgis 的补丁。

create or replace function ST_MinimumRectangle(g geometry) returns geometry
language 'plpgsql' as $$
declare
        hull geometry;
begin
        hull = ST_ExteriorRing(ST_ConvexHull(g));
        -- one side must lie along the rectangle.
        -- so, for each side, rotate, bbox, counter-rotate bbox
        with sides as (
                select ST_PointN(hull, n) as a, ST_PointN(hull, n+1) as b,
                        n as side
                        from generate_series(1,ST_NPoints(hull)-1) n
                ),
        angles as (
                select side, a, b, st_azimuth(a, b) as angle from sides
        ),
        boxes as (
                select ST_Rotate(ST_Envelope(ST_Rotate(hull, -angle)),angle) as rect, side, angle from angles
        )
        select rect into hull from boxes order by ST_Area(rect), side limit 1
        ;
        return hull;
end;
$$ immutable strict;