Can I identify if a point is inside a volume in PostGIS?

Question

We are currently investigating PostGIS as an option to look up three-dimensional blocks which contain a point (and later also lines). At this point in time I cannot see any functionality that operates on the volume of a three dimensional shape, all functions PostGIS offers seem to operate on the surface.

Here are a number of functions we tried:

SELECT 
    ST_Contains(p , mpoly),      ST_Contains(p , ph),      ST_Contains(p , box),
    ST_3DIntersects(p , mpoly),  ST_3DIntersects(p , ph),  ST_3DIntersects(p , box),
    ST_3DDWithin(p , mpoly, 0),  ST_3DDWithin(p , ph, 0),  ST_3DDWithin(p , box, 0)
FROM
  (SELECT 
    'POINT Z (0.5 0.5 0.5)'::geometry AS p,
    'MULTIPOLYGON Z (
        ((0 0 0, 0 1 0, 1 1 0, 0 1 0, 0 0 0)),
        ((0 0 1, 0 1 1, 1 1 1, 0 1 1, 0 0 1)),
        ((0 0 0, 0 0 1, 0 1 1, 0 0 1, 0 0 0)),
        ((1 0 0, 1 0 1, 1 1 1, 1 0 1, 1 0 0)),
        ((0 0 0, 0 0 1, 1 0 1, 1 0 0, 0 0 0)),
        ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0))
    )'::geometry AS mpoly,
    'POLYHEDRALSURFACE (
        ((0 0 0, 0 1 0, 1 1 0, 0 1 0, 0 0 0)),
        ((0 0 1, 0 1 1, 1 1 1, 0 1 1, 0 0 1)),
        ((0 0 0, 0 0 1, 0 1 1, 0 0 1, 0 0 0)),
        ((1 0 0, 1 0 1, 1 1 1, 1 0 1, 1 0 0)),
        ((0 0 0, 0 0 1, 1 0 1, 1 0 0, 0 0 0)),
        ((0 1 0, 0 1 1, 1 1 1, 1 1 0, 0 1 0))
    )'::geometry AS ph,
    ST_3DMakeBox('POINT Z (0 0 0)'::geometry, 'POINT Z (1 1 1)'::geometry) AS box
  ) AS foo
;

All of these return false. Given that we are using polygons and polyhedral surfaces this seems correct, but is there a way to have PostGIS apply volumetric calculations?

Answer 1

You could use the &&& operator. It returns true if two n-d bounding boxes intersect:

SELECT 'POINT Z (0.5 0.5 0.5)' &&& 'LINESTRING Z(0 0 0, 1 1 1)' AS intersects;

intersects 
------------
 t
(1 row)

SELECT 'POINT Z (1.5 0.5 0.5)' &&& 'LINESTRING Z(0 0 0, 1 1 1)' AS intersects;
intersects 
------------
 f
(1 row)

For both POINT Z and LINESTRING Z their bounding box is used. So this would only work without further tests for points. For arbitrary lines you could get false positives (the cases were only the bounding box of a line intersects, not the line itself). For this query you should use a n-d index, SFCGAL is not needed.

Alternatively, you could go with ST_3DDWithin and choose a query plane geometry along with a distance that would include your complete query bounding box. This, however, would also mean you would have to throw away the results that are outside of your original bounding box. For this query you should use a 2-d index and also don't need SFCGAL.

Edit: After some more testing and consulting the PostGIS mailing list, it seems best to actually use both methods described above together (using AND). This way &&& reduce the number of distance tests that ST_3DDWithin has to do.