PostGIS多边形之间的递归交集

我正在尝试在空间表中的所有多边形之间执行递归交集，并获取生成的（多）多边形以及有关每个多边形的每个交集的信息。

An image (not really in scale) to explain it:

假设有A, B, C表格中的正方形。我想要A, B, C, A+B, A+C, B+C, A+B+C输出中的多边形，我需要知道A+B是 的交集A and B等等。

到目前为止，我有一个执行相交的查询，但它不会“切断”原始多边形的相交部分。例如：

Polygon A should be      A - (A+B) - (A+C) - (A+B+C)
Polygon A+C should be    A+C - (A+B+C)

我现在得到的结果的图像A and A+C多边形：

这是一个测试脚本，使用图像中的方块作为数据。看着area列，很明显缺少一些递归 ST_Difference，我只是不知道如何。任何想法都受到欢迎。

-- Create a test table
CREATE TABLE test (
    name text PRIMARY KEY,
    geom geometry(POLYGON)
);

-- Insert test data
INSERT INTO test (name, geom) VALUES 
    ('A', ST_GeomFromText('POLYGON((1 2, 1 6, 5 6, 5 2, 1 2))')),
    ('B', ST_GeomFromText('POLYGON((0 0, 0 4, 4 4, 4 0, 0 0))')),
    ('C', ST_GeomFromText('POLYGON((2 0, 2 4, 6 4, 6 0, 2 0))'));


-- Query    
WITH RECURSIVE 
source (rownum, geom, ret) AS (
    SELECT row_number() OVER (ORDER BY name ASC), ST_Multi(geom), ARRAY[name] FROM test 
),
r (rownum, geom, ret, incroci) AS (
    SELECT rownum, geom, ret, 0 FROM source 
    UNION ALL
    SELECT s.rownum, ST_CollectionExtract(ST_Intersection(s.geom, r.geom), 3), (r.ret || s.ret), (r.incroci + 1) 
        FROM source AS s INNER JOIN r ON s.rownum > r.rownum AND ST_Intersects(s.geom, r.geom) AND ST_Area(ST_Intersection(s.geom, r.geom)) > 0.5
),
result (geom, ret) AS (
    SELECT ST_Union(geom) AS geom, ret FROM r GROUP BY ret
)
SELECT geom, ST_Area(geom) AS area, ret FROM result ORDER BY ret

当然，在这个特定的示例中，窗口函数并不是绝对必要的，但这段代码是我的真实案例的简化版本，它还做了一些额外的事情。

我正在使用 PostgreSQL 9.2 和 PostGIS 2.0

ST_DIFFRENCE 不必是递归的，您已经拥有所有多边形，因此您必须从每个几何图形中减去包含该 ret 但不等于它的其他几何图形的并集。这是可行的，所以你应该这样做：

    WITH RECURSIVE 
source (rownum, geom, ret) AS (
    SELECT row_number() OVER (ORDER BY name ASC), ST_Multi(geom), ARRAY[name] FROM test 
),
r (rownum, geom, ret, incroci) AS (
    SELECT rownum, geom, ret, 0 FROM source 
    UNION ALL
    SELECT s.rownum, ST_CollectionExtract(ST_Intersection(s.geom, r.geom), 3), (r.ret || s.ret), (r.incroci + 1) 
        FROM source AS s INNER JOIN r ON s.rownum > r.rownum AND ST_Intersects(s.geom, r.geom) AND ST_Area(ST_Intersection(s.geom, r.geom)) > 0.5
),
result (geom, ret) AS (
    SELECT ST_Difference(ST_Union(r.geom),q.geom) AS geom, r.ret FROM r JOIN (SELECT r.ret,ST_UNION(COALESCE(r2.geom,ST_GeomFromText('POLYGON EMPTY'))) as geom FROM r LEFT JOIN r AS r2 ON r.ret<@r2.ret AND r.ret!=r2.ret GROUP BY r.ret) AS q on r.ret=q.ret GROUP BY r.ret,q.geom
)
SELECT geom, ST_Area(geom) AS area, ret FROM result ORDER BY ret