boolean ST_3DIntersects(geometry
            geomA, geometry
            geomB)

SELECT ST_3DIntersects(pt, line), ST_Intersects(pt, line)
  FROM (SELECT 'POINT(0 0 2)'::geometry As pt, 'LINESTRING (0 0 1, 0 2 3)'::geometry As line) As foo;
 st_3dintersects | st_intersects
-----------------+---------------
 f               | t
(1 row)

SELECT ST_3DIntersects('TIN(((0 0 0,1 0 0,0 1 0,0 0 0)))'::geometry, 'POINT(.1 .1 0)'::geometry);
 st_3dintersects
-----------------
 t

boolean ST_Contains(geometry
      geomA, geometry
      geomB)

-- A circle within a circle
SELECT ST_Contains(smallc, bigc) As smallcontainsbig,
     ST_Contains(bigc,smallc) As bigcontainssmall,
     ST_Contains(bigc, ST_Union(smallc, bigc)) as bigcontainsunion,
     ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion,
     ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
     ST_Contains(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
       ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;

-- Result
  smallcontainsbig | bigcontainssmall | bigcontainsunion | bigisunion | bigcoversexterior | bigcontainsexterior
------------------+------------------+------------------+------------+-------------------+---------------------
 f                | t                | t                | t          | t        | f

-- Example demonstrating difference between contains and contains properly
SELECT ST_GeometryType(geomA) As geomtype, ST_Contains(geomA,geomA) AS acontainsa, ST_ContainsProperly(geomA, geomA) AS acontainspropa,
   ST_Contains(geomA, ST_Boundary(geomA)) As acontainsba, ST_ContainsProperly(geomA, ST_Boundary(geomA)) As acontainspropba
FROM (VALUES ( ST_Buffer(ST_Point(1,1), 5,1) ),
       ( ST_MakeLine(ST_Point(1,1), ST_Point(-1,-1) ) ),
       ( ST_Point(1,1) )
    ) As foo(geomA);

  geomtype    | acontainsa | acontainspropa | acontainsba | acontainspropba
--------------+------------+----------------+-------------+-----------------
ST_Polygon    | t          | f              | f           | f
ST_LineString | t          | f              | f           | f
ST_Point      | t          | t              | f           | f

boolean ST_ContainsProperly(geometry
      geomA, geometry
      geomB)

  --a circle within a circle
  SELECT ST_ContainsProperly(smallc, bigc) As smallcontainspropbig,
  ST_ContainsProperly(bigc,smallc) As bigcontainspropsmall,
  ST_ContainsProperly(bigc, ST_Union(smallc, bigc)) as bigcontainspropunion,
  ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion,
  ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
  ST_ContainsProperly(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
  FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
  --Result
  smallcontainspropbig | bigcontainspropsmall | bigcontainspropunion | bigisunion | bigcoversexterior | bigcontainsexterior
------------------+------------------+------------------+------------+-------------------+---------------------
 f                     | t                    | f                    | t          | t                 | f

 --example demonstrating difference between contains and contains properly
 SELECT ST_GeometryType(geomA) As geomtype, ST_Contains(geomA,geomA) AS acontainsa, ST_ContainsProperly(geomA, geomA) AS acontainspropa,
 ST_Contains(geomA, ST_Boundary(geomA)) As acontainsba, ST_ContainsProperly(geomA, ST_Boundary(geomA)) As acontainspropba
 FROM (VALUES ( ST_Buffer(ST_Point(1,1), 5,1) ),
      ( ST_MakeLine(ST_Point(1,1), ST_Point(-1,-1) ) ),
      ( ST_Point(1,1) )
  ) As foo(geomA);

  geomtype    | acontainsa | acontainspropa | acontainsba | acontainspropba
--------------+------------+----------------+-------------+-----------------
ST_Polygon    | t          | f              | f           | f
ST_LineString | t          | f              | f           | f
ST_Point      | t          | t              | f           | f

boolean ST_CoveredBy(geometry
      geomA, geometry
      geomB)
boolean ST_CoveredBy(geography
      geogA, geography
      geogB)

  --a circle coveredby a circle
SELECT ST_CoveredBy(smallc,smallc) As smallinsmall,
  ST_CoveredBy(smallc, bigc) As smallcoveredbybig,
  ST_CoveredBy(ST_ExteriorRing(bigc), bigc) As exteriorcoveredbybig,
  ST_Within(ST_ExteriorRing(bigc),bigc) As exeriorwithinbig
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
  --Result
 smallinsmall | smallcoveredbybig | exteriorcoveredbybig | exeriorwithinbig
--------------+-------------------+----------------------+------------------
 t            | t                 | t                    | f
(1 row)

boolean ST_Covers(geometry
      geomA, geometry
      geomB)
boolean ST_Covers(geography
      geogpolyA, geography
      geogpointB)

  --a circle covering a circle
SELECT ST_Covers(smallc,smallc) As smallinsmall,
  ST_Covers(smallc, bigc) As smallcoversbig,
  ST_Covers(bigc, ST_ExteriorRing(bigc)) As bigcoversexterior,
  ST_Contains(bigc, ST_ExteriorRing(bigc)) As bigcontainsexterior
FROM (SELECT ST_Buffer(ST_GeomFromText('POINT(1 2)'), 10) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(1 2)'), 20) As bigc) As foo;
  --Result
 smallinsmall | smallcoversbig | bigcoversexterior | bigcontainsexterior
--------------+----------------+-------------------+---------------------
 t            | f              | t                 | f
(1 row)

-- a point with a 300 meter buffer compared to a point, a point and its 10 meter buffer
SELECT ST_Covers(geog_poly, geog_pt) As poly_covers_pt,
  ST_Covers(ST_Buffer(geog_pt,10), geog_pt) As buff_10m_covers_cent
  FROM (SELECT ST_Buffer(ST_GeogFromText('SRID=4326;POINT(-99.327 31.4821)'), 300) As geog_poly,
        ST_GeogFromText('SRID=4326;POINT(-99.33 31.483)') As geog_pt ) As foo;

 poly_covers_pt | buff_10m_covers_cent
----------------+------------------
 f              | t

boolean ST_Crosses(geometry g1, geometry g2)

SELECT roads.id
FROM roads, highways
WHERE ST_Crosses(roads.geom, highways.geom);

boolean ST_Disjoint(geometry
            A, geometry
            B)

SELECT ST_Disjoint('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
 st_disjoint
---------------
 t
(1 row)
SELECT ST_Disjoint('POINT(0 0)'::geometry, 'LINESTRING ( 0 0, 0 2 )'::geometry);
 st_disjoint
---------------
 f
(1 row)

boolean ST_Equals(geometry  A, geometry  B)

SELECT ST_Equals(ST_GeomFromText('LINESTRING(0 0, 10 10)'),
    ST_GeomFromText('LINESTRING(0 0, 5 5, 10 10)'));
 st_equals
-----------
 t
(1 row)

SELECT ST_Equals(ST_Reverse(ST_GeomFromText('LINESTRING(0 0, 10 10)')),
    ST_GeomFromText('LINESTRING(0 0, 5 5, 10 10)'));
 st_equals
-----------
 t
(1 row)

boolean ST_Intersects(geometry
            geomA, geometry
            geomB)
boolean ST_Intersects(geography
            geogA, geography
            geogB)

SELECT ST_Intersects('POINT(0 0)'::geometry, 'LINESTRING ( 2 0, 0 2 )'::geometry);
 st_intersects
---------------
 f
(1 row)
SELECT ST_Intersects('POINT(0 0)'::geometry, 'LINESTRING ( 0 0, 0 2 )'::geometry);
 st_intersects
---------------
 t
(1 row)

-- Look up in table. Make sure table has a GiST index on geometry column for faster lookup.
SELECT id, name FROM cities WHERE ST_Intersects(geom, 'SRID=4326;POLYGON((28 53,27.707 52.293,27 52,26.293 52.293,26 53,26.293 53.707,27 54,27.707 53.707,28 53))');
 id | name
----+-------
  2 | Minsk
(1 row)

SELECT ST_Intersects(
    'SRID=4326;LINESTRING(-43.23456 72.4567,-43.23456 72.4568)'::geography,
    'SRID=4326;POINT(-43.23456 72.4567772)'::geography
    );

 st_intersects
---------------
t

integer ST_LineCrossingDirection(geometry  linestringA, geometry  linestringB)

SELECT ST_LineCrossingDirection(lineA, lineB) As A_cross_B,
       ST_LineCrossingDirection(lineB, lineA) As B_cross_A
FROM (SELECT
  ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As lineA,
  ST_GeomFromText('LINESTRING (20 140, 71 74, 161 53)') As lineB
  ) As foo;

 A_cross_B | B_cross_A
-----------+-----------
        -1 |         1

SELECT ST_LineCrossingDirection(lineA, lineB) As A_cross_B,
       ST_LineCrossingDirection(lineB, lineA) As B_cross_A
FROM (SELECT
 ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As lineA,
 ST_GeomFromText('LINESTRING(171 154,20 140,71 74,161 53)') As lineB
  ) As foo;

 A_cross_B | B_cross_A
-----------+-----------
         3 |        -3

SELECT ST_LineCrossingDirection(lineA, lineB) As A_cross_B,
       ST_LineCrossingDirection(lineB, lineA) As B_cross_A
FROM (SELECT
  ST_GeomFromText('LINESTRING(25 169,89 114,40 70,86 43)') As lineA,
  ST_GeomFromText('LINESTRING(5 90, 71 74, 20 140, 171 154)') As lineB
  ) As foo;

 A_cross_B | B_cross_A
-----------+-----------
        -2 |         2

SELECT s1.gid, s2.gid, ST_LineCrossingDirection(s1.geom, s2.geom)
  FROM streets s1 CROSS JOIN streets s2
         ON (s1.gid != s2.gid AND s1.geom && s2.geom )
WHERE ST_LineCrossingDirection(s1.geom, s2.geom) > 0;

boolean ST_OrderingEquals(geometry  A, geometry  B)

SELECT ST_OrderingEquals(
  'LINESTRING(0 0, 10 10)',
  'LINESTRING(0 0, 5 5, 10 10)');

 st_orderingequals
-----------
 f


SELECT ST_OrderingEquals(
  'LINESTRING(0 0, 10 10)',
  'LINESTRING(0 0, 10 10)');

 st_orderingequals
-----------
 t


SELECT ST_OrderingEquals(
  'POLYGON((0 0, 0 1, 1 1, 1 0, 0 0))',
  'POLYGON((0 0, 1 0, 1 1, 0 1, 0 0))');

 st_orderingequals
-----------
 f

boolean ST_Overlaps(geometry  A, geometry  B)

SELECT ST_Overlaps(a,b) AS overlaps,       ST_Crosses(a,b) AS crosses,
       ST_Intersects(a, b) AS intersects,  ST_Contains(b,a) AS b_contains_a
FROM (SELECT ST_GeomFromText('POINT (100 100)') As a,
             ST_GeomFromText('LINESTRING (30 50, 40 160, 160 40, 180 160)')  AS b) AS t

overlaps | crosses | intersects | b_contains_a
---------+----------------------+--------------
f        | f       | t          | t

SELECT ST_Overlaps(a,b) AS overlaps,        ST_Crosses(a,b) AS crosses,
       ST_Intersects(a, b) AS intersects,   ST_Contains(a,b) AS contains
FROM (SELECT ST_GeomFromText('POLYGON ((40 170, 90 30, 180 100, 40 170))') AS a,
             ST_GeomFromText('LINESTRING(10 10, 190 190)') AS b) AS t;

 overlap | crosses | intersects | contains
---------+---------+------------+--------------
 f       | t       | t          | f

SELECT ST_Overlaps(a,b) AS overlaps,       ST_Crosses(a,b) AS crosses,
       ST_Intersects(a, b) AS intersects,  ST_Contains(b, a) AS b_contains_a,
       ST_Dimension(a) AS dim_a, ST_Dimension(b) AS dim_b,
       ST_Dimension(ST_Intersection(a,b)) AS dim_int
FROM (SELECT ST_GeomFromText('POLYGON ((40 170, 90 30, 180 100, 40 170))') AS a,
             ST_GeomFromText('POLYGON ((110 180, 20 60, 130 90, 110 180))') AS b) As t;

 overlaps | crosses | intersects | b_contains_a | dim_a | dim_b | dim_int
----------+---------+------------+--------------+-------+-------+-----------
 t        | f       | t          | f            |     2 |     2 |       2

boolean ST_Relate(geometry  geomA, geometry  geomB, text  intersectionMatrixPattern)
text ST_Relate(geometry  geomA, geometry  geomB)
text ST_Relate(geometry  geomA, geometry  geomB, integer  boundaryNodeRule)

SELECT ST_Relate('POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '0FFFFF212');
st_relate
-----------
t

SELECT ST_Relate(POINT(1 2)', ST_Buffer( 'POINT(1 2)', 2), '*FF*FF212');
st_relate
-----------
t

-- Find compounds that properly intersect (not just touch) a poly (Interior Intersects)

SELECT c.* , p.name As poly_name
    FROM polys AS p
    INNER JOIN compounds As c
          ON c.geom && p.geom
             AND ST_Relate(p.geom, c.geom,'T********');

SELECT ST_Relate( 'POINT(1 2)',
                  ST_Buffer( 'POINT(1 2)', 2));
-----------
0FFFFF212

SELECT ST_Relate( 'LINESTRING(1 2, 3 4)',
                  'LINESTRING(5 6, 7 8)' );
-----------
FF1FF0102

WITH data AS (SELECT
  'LINESTRING(1 1, 3 3)'::geometry AS a_line,
  'MULTILINESTRING((3 3, 3 5), (3 3, 5 3))':: geometry AS b_multiline
)
SELECT ST_Relate( a_line, b_multiline, 1) AS bnr_mod2,
       ST_Relate( a_line, b_multiline, 2) AS bnr_endpoint
    FROM data;

 bnr_mod2  | bnr_endpoint
-----------+--------------
 FF10F0102 | FF1F00102

boolean ST_RelateMatch(text  intersectionMatrix, text  intersectionMatrixPattern)

SELECT ST_RelateMatch('101202FFF', 'TTTTTTFFF') ;
-- result --
t

SELECT pat.name AS relationship, pat.val AS pattern,
       mat.name AS position, mat.val AS matrix,
       ST_RelateMatch(mat.val, pat.val) AS match
    FROM (VALUES ( 'Equality', 'T1FF1FFF1' ),
                 ( 'Overlaps', 'T*T***T**' ),
                 ( 'Within',   'T*F**F***' ),
                 ( 'Disjoint', 'FF*FF****' )) AS pat(name,val)
    CROSS JOIN
        (VALUES  ('non-intersecting', 'FF1FF0212'),
                 ('overlapping',      '1010F0212'),
                 ('inside',           '1FF0FF212')) AS mat(name,val);

 relationship |  pattern  |     position     |  matrix   | match
--------------+-----------+------------------+-----------+-------
 Equality     | T1FF1FFF1 | non-intersecting | FF1FF0212 | f
 Equality     | T1FF1FFF1 | overlapping      | 1010F0212 | f
 Equality     | T1FF1FFF1 | inside           | 1FF0FF212 | f
 Overlaps     | T*T***T** | non-intersecting | FF1FF0212 | f
 Overlaps     | T*T***T** | overlapping      | 1010F0212 | t
 Overlaps     | T*T***T** | inside           | 1FF0FF212 | f
 Within       | T*F**F*** | non-intersecting | FF1FF0212 | f
 Within       | T*F**F*** | overlapping      | 1010F0212 | f
 Within       | T*F**F*** | inside           | 1FF0FF212 | t
 Disjoint     | FF*FF**** | non-intersecting | FF1FF0212 | t
 Disjoint     | FF*FF**** | overlapping      | 1010F0212 | f
 Disjoint     | FF*FF**** | inside           | 1FF0FF212 | f

boolean ST_Touches(geometry
      A, geometry
      B)

SELECT ST_Touches('LINESTRING(0 0, 1 1, 0 2)'::geometry, 'POINT(1 1)'::geometry);
 st_touches
------------
 f
(1 row)

SELECT ST_Touches('LINESTRING(0 0, 1 1, 0 2)'::geometry, 'POINT(0 2)'::geometry);
 st_touches
------------
 t
(1 row)

boolean ST_Within(geometry
      A, geometry
      B)

--a circle within a circle
SELECT ST_Within(smallc,smallc) As smallinsmall,
  ST_Within(smallc, bigc) As smallinbig,
  ST_Within(bigc,smallc) As biginsmall,
  ST_Within(ST_Union(smallc, bigc), bigc) as unioninbig,
  ST_Within(bigc, ST_Union(smallc, bigc)) as biginunion,
  ST_Equals(bigc, ST_Union(smallc, bigc)) as bigisunion
FROM
(
SELECT ST_Buffer(ST_GeomFromText('POINT(50 50)'), 20) As smallc,
  ST_Buffer(ST_GeomFromText('POINT(50 50)'), 40) As bigc) As foo;
--Result
 smallinsmall | smallinbig | biginsmall | unioninbig | biginunion | bigisunion
--------------+------------+------------+------------+------------+------------
 t            | t          | f          | t          | t          | t
(1 row)

boolean ST_3DDWithin(geometry
      g1, geometry
      g2, double precision
      distance_of_srid)

-- Geometry example - units in meters (SRID: 2163 US National Atlas Equal area) (3D point and line compared 2D point and line)
-- Note: currently no vertical datum support so Z is not transformed and assumed to be same units as final.
SELECT ST_3DDWithin(
      ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 4)'),2163),
      ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163),
      126.8
    ) As within_dist_3d,
ST_DWithin(
      ST_Transform(ST_GeomFromEWKT('SRID=4326;POINT(-72.1235 42.3521 4)'),2163),
      ST_Transform(ST_GeomFromEWKT('SRID=4326;LINESTRING(-72.1260 42.45 15, -72.123 42.1546 20)'),2163),
      126.8
    ) As within_dist_2d;

 within_dist_3d | within_dist_2d
----------------+----------------
 f              | t

boolean ST_3DDFullyWithin(geometry
      g1, geometry
      g2, double precision
      distance)

    -- This compares the difference between fully within and distance within as well
    -- as the distance fully within for the 2D footprint of the line/point vs. the 3d fully within
    SELECT ST_3DDFullyWithin(geom_a, geom_b, 10) as D3DFullyWithin10, ST_3DDWithin(geom_a, geom_b, 10) as D3DWithin10,
  ST_DFullyWithin(geom_a, geom_b, 20) as D2DFullyWithin20,
  ST_3DDFullyWithin(geom_a, geom_b, 20) as D3DFullyWithin20 from
    (select ST_GeomFromEWKT('POINT(1 1 2)') as geom_a,
    ST_GeomFromEWKT('LINESTRING(1 5 2, 2 7 20, 1 9 100, 14 12 3)') as geom_b) t1;
 d3dfullywithin10 | d3dwithin10 | d2dfullywithin20 | d3dfullywithin20
------------------+-------------+------------------+------------------
 f                | t           | t                | f

boolean ST_DFullyWithin(geometry
      g1, geometry
      g2, double precision
      distance)

SELECT
    ST_DFullyWithin(geom_a, geom_b, 10) AS DFullyWithin10,
    ST_DWithin(geom_a, geom_b, 10) AS DWithin10,
    ST_DFullyWithin(geom_a, geom_b, 20) AS DFullyWithin20
FROM (VALUES
    ('POINT(1 1)', 'LINESTRING(1 5, 2 7, 1 9, 14 12)')
    ) AS v(geom_a, geom_b)

 dfullywithin10 | dwithin10 | dfullywithin20
----------------+-----------+----------------
 f              | t         | t

boolean ST_DWithin(geometry
        g1, geometry
        g2, double precision
        distance_of_srid)
boolean ST_DWithin(geography
        gg1, geography
        gg2, double precision
        distance_meters, boolean
        use_spheroid = true)

-- Find the nearest hospital to each school
-- that is within 3000 units of the school.
--  We do an ST_DWithin search to utilize indexes to limit our search list
--  that the non-indexable ST_Distance needs to process
-- If the units of the spatial reference is meters then units would be meters
SELECT DISTINCT ON (s.gid) s.gid, s.school_name, s.geom, h.hospital_name
  FROM schools s
    LEFT JOIN hospitals h ON ST_DWithin(s.geom, h.geom, 3000)
  ORDER BY s.gid, ST_Distance(s.geom, h.geom);

-- The schools with no close hospitals
-- Find all schools with no hospital within 3000 units
-- away from the school.  Units is in units of spatial ref (e.g. meters, feet, degrees)
SELECT s.gid, s.school_name
  FROM schools s
    LEFT JOIN hospitals h ON ST_DWithin(s.geom, h.geom, 3000)
  WHERE h.gid IS NULL;

-- Find broadcasting towers that receiver with limited range can receive.
-- Data is geometry in Spherical Mercator (SRID=3857), ranges are approximate.

-- Create geometry index that will check proximity limit of user to tower
CREATE INDEX ON broadcasting_towers using gist (geom);

-- Create geometry index that will check proximity limit of tower to user
CREATE INDEX ON broadcasting_towers using gist (ST_Expand(geom, sending_range));

-- Query towers that 4-kilometer receiver in Minsk Hackerspace can get
-- Note: two conditions, because shorter LEAST(b.sending_range, 4000) will not use index.
SELECT b.tower_id, b.geom
  FROM broadcasting_towers b
  WHERE ST_DWithin(b.geom, 'SRID=3857;POINT(3072163.4 7159374.1)', 4000)
    AND ST_DWithin(b.geom, 'SRID=3857;POINT(3072163.4 7159374.1)', b.sending_range);

boolean ST_PointInsideCircle(geometry  a_point, float  center_x, float  center_y, float  radius)

SELECT ST_PointInsideCircle(ST_Point(1,2), 0.5, 2, 3);
 st_pointinsidecircle
------------------------
 t