Restrictions

Restrictions
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There are two complementary sets of restriction functions. The first set functions restricts the temporal value with respect to a value or a time extent. Examples are atValues or atTime. The second set functions restricts the temporal value with respect to the complement of a value or a time extent. Examples are minusValues or minusTime

Restrict to (the complement of) a set of values

atValues(ttype,values) → ttype

minusValues(ttype,values) → ttype

SELECT atValues(tint '[1@2001-01-01, 1@2001-01-15)', 1);
-- [1@2001-01-01, 1@2001-01-15)
SELECT asText(atValues(tgeompoint '[Point(0 0 0)@2001-01-01, Point(2 2 2)@2001-01-03)',
  geometry 'Point(1 1 1)'));
-- {[POINT Z (1 1 1)@2001-01-02]}
SELECT atValues(tfloat '[1@2001-01-01, 4@2001-01-4)', floatset '{1, 3, 5}');
-- {[1@2001-01-01], [3@2001-01-03]}
SELECT asText(atValues(tgeompoint '[Point(0 0)@2001-01-01, Point(2 2)@2001-01-03)',
  geomset '{"Point(0 0)", "Point(1 1)"}'));
-- {[POINT(0 0)@2001-01-01], [POINT(1 1)@2001-01-02]}
SELECT atValues(tfloat '[1@2001-01-01, 4@2001-01-4)', floatspan '[1,3]');
-- [1@2001-01-01, 3@2001-01-03]
SELECT atValues(tfloat '[1@2001-01-01, 5@2001-01-05)',
  floatspanset '{[1,2], [3,4]}');
-- {[1@2001-01-01, 2@2001-01-02],[3@2001-01-03, 4@2001-01-04]}

SELECT minusValues(tint '[1@2001-01-01, 2@2001-01-02, 2@2001-01-03)', 1);
-- {[2@2001-01-02, 2@2001-01-03)}
SELECT asText(minusValues(tgeompoint '[Point(0 0 0)@2001-01-01, Point(2 2 2)@2001-01-03)',
  geometry 'Point(1 1 1)'));
/* {[POINT Z (0 0 0)@2001-01-01, POINT Z (1 1 1)@2001-01-02),
   (POINT Z (1 1 1)@2001-01-02, POINT Z (2 2 2)@2001-01-03)} */
SELECT minusValues(tfloat '[1@2001-01-01, 4@2001-01-4)', floatset '{2, 3}');
/* {[1@2001-01-01, 2@2001-01-02), (2@2001-01-02, 3@2001-01-03),
   (3@2001-01-03, 4@2001-01-04)} */
SELECT asText(minusValues(tgeompoint '[Point(0 0 0)@2001-01-01, Point(3 3 3)@2001-01-04)',
  geomset '{"Point(1 1 1)', 'Point(2 2 2)"}'));
/* {[POINT Z (0 0 0)@2001-01-01, POINT Z (1 1 1)@2001-01-02),
   (POINT Z (1 1 1)@2001-01-02, POINT Z (2 2 2)@2001-01-03),
  (POINT Z (2 2 2)@2001-01-03, POINT Z (3 3 3)@2001-01-04)} */
SELECT minusValues(tfloat '[1@2001-01-01, 4@2001-01-4)', floatspan '[2,3]');
-- {[1@2001-01-01, 2@2001-01-02), (3@2001-01-03, 4@2001-01-04)}
SELECT minusValues(tfloat '[1@2001-01-01, 5@2001-01-05)',
  floatspanset '{[1,2], [3,4]}');
-- {(2@2001-01-02, 3@2001-01-03), (4@2001-01-04, 5@2001-01-05)}

Restrict to (the complement of) the minimum value

atMin(torder) → torder

minusMin(torder) → torder

The function returns null if the minimum value only happens at exclusive bounds.

SELECT atMin(tint '{1@2001-01-01, 2@2001-01-03, 1@2001-01-05}');
-- {1@2001-01-01, 1@2001-01-05}
SELECT atMin(tint '(1@2001-01-01, 3@2001-01-03]');
-- {(1@2001-01-01, 1@2001-01-03)}
SELECT atMin(tfloat '(1@2001-01-01, 3@2001-01-03]');
-- NULL
SELECT atMin(ttext '{(AA@2001-01-01, AA@2001-01-03), (BB@2001-01-03, AA@2001-01-05]}');
-- {(AA@2001-01-01, AA@2001-01-03), [AA@2001-01-05]}

SELECT minusMin(tint '{1@2001-01-01, 2@2001-01-03, 1@2001-01-05}');
-- {2@2001-01-03}
SELECT minusMin(tfloat '[1@2001-01-01, 3@2001-01-03]');
-- {(1@2001-01-01, 3@2001-01-03]}
SELECT minusMin(tfloat '(1@2001-01-01, 3@2001-01-03)');
-- {(1@2001-01-01, 3@2001-01-03)}
SELECT minusMin(tint '{[1@2001-01-01, 1@2001-01-03), (1@2001-01-03, 1@2001-01-05)}');
-- NULL

Restrict to (the complement of) the maximum value

atMax(torder) → torder

minusMax(torder) → torder

The function returns null if the maximum value only happens at exclusive bounds.

SELECT atMax(tint '{1@2001-01-01, 2@2001-01-03, 3@2001-01-05}');
-- {3@2001-01-05}
SELECT atMax(tfloat '(1@2001-01-01, 3@2001-01-03)');
-- NULL
SELECT atMax(tfloat '{(2@2001-01-01, 1@2001-01-03), [2@2001-01-03, 2@2001-01-05)}');
-- {[2@2001-01-03, 2@2001-01-05]}
SELECT atMax(ttext '{(AA@2001-01-01, AA@2001-01-03), (BB@2001-01-03, AA@2001-01-05]}');
-- {("BB"@2001-01-03, "BB"@2001-01-05)}

SELECT minusMax(tint '{1@2001-01-01, 2@2001-01-03, 3@2001-01-05}');
-- {1@2001-01-01, 2@2001-01-03}
SELECT minusMax(tfloat '[1@2001-01-01, 3@2001-01-03]');
-- {[1@2001-01-01, 3@2001-01-03)}
SELECT minusMax(tfloat '(1@2001-01-01, 3@2001-01-03)');
-- {(1@2001-01-01, 3@2001-01-03)}
SELECT minusMax(tfloat '{[2@2001-01-01, 1@2001-01-03), [2@2001-01-03, 2@2001-01-05)}');
-- {(2@2001-01-01, 1@2001-01-03)}
SELECT minusMax(tfloat '{[1@2001-01-01, 3@2001-01-03), (3@2001-01-03, 1@2001-01-05)}');
-- {[1@2001-01-01, 3@2001-01-03), (3@2001-01-03, 1@2001-01-05)}

Restrict to (the complement of) a geometry, a Z span, and/or a period

atGeometry(tgeompoint,geometry[,zspan]) → tgeompoint

minusGeometry(tgeompoint,geometry[,zspan]) → tgeompoint

atGeometryTime(tgeompoint,geometry[,zspan],period) → tgeompoint

minusGeometryTime(tgeompoint,geometry[,zspan],period) → tgeompoint

The geometry must be in 2D and the computation with respect to it is done in 2D. The result preserves the Z dimension of the temporal point, if it exists.

SELECT asText(atGeometry(tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-04)',
  geometry 'Polygon((1 1,1 2,2 2,2 1,1 1))'));
-- {"[POINT(1 1)@2001-01-02, POINT(2 2)@2001-01-03]"}
SELECT astext(atGeometry(tgeompoint '[Point(0 0 0)@2001-01-01, Point(4 4 4)@2001-01-05]',
  geometry 'Polygon((1 1,1 2,2 2,2 1,1 1))'));
-- {[POINT Z (1 1 1)@2001-01-02, POINT Z (2 2 2)@2001-01-03]}
SELECT asText(atGeometry(tgeompoint '[Point(1 1 1)@2001-01-01, Point(3 1 1)@2001-01-03,
  Point(3 1 3)@2001-01-05]', 'Polygon((2 0,2 2,2 4,4 0,2 0))', '[0,2]'));
-- {[POINT Z (2 1 1)@2001-01-02, POINT Z (3 1 1)@2001-01-03, POINT Z (3 1 2)@2001-01-04]}

SELECT asText(atGeometryTime(tgeompoint '[Point(1 1)@2001-01-01,
  Point(5 1)@2001-01-05, Point(1 1)@2001-01-09]',
  geometry 'Polygon((2 0,2 2,4 2,4 0,2 0))',
  tstzspan '[2001-01-03, 2001-01-05]'));
-- {[POINT(3 1)@2001-01-03, POINT(4 1)@2001-01-04]}
SELECT asText(atGeometryTime(tgeompoint '[Point(1 1 1)@2001-01-01,
  Point(5 1 5)@2001-01-05, Point(1 1 9)@2001-01-09]',
  geometry 'Polygon((2 0,2 2,4 2,4 0,2 0))', floatspan '[0,5]',
  tstzspan '[2001-01-03, 2001-01-06]'));
-- {[POINT Z (3 1 3)@2001-01-03, POINT Z (4 1 4)@2001-01-04]}

SELECT asText(minusGeometry(tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-04)',
  geometry 'Polygon((1 1,1 2,2 2,2 1,1 1))'));
/* {[POINT(0 0)@2001-01-01, POINT(1 1)@2001-01-02), (POINT(2 2)@2001-01-03,
   POINT(3 3)@2001-01-04)} */
SELECT astext(minusGeometry(tgeompoint '[Point(0 0 0)@2001-01-01,
  Point(4 4 4)@2001-01-05]', geometry 'Polygon((1 1,1 2,2 2,2 1,1 1))'));
/* {[POINT Z (0 0 0)@2001-01-01, POINT Z (1 1 1)@2001-01-02),
   (POINT Z (2 2 2)@2001-01-03, POINT Z (4 4 4)@2001-01-05]} */
SELECT asText(minusGeometry(tgeompoint '[Point(1 1 1)@2001-01-01, Point(3 1 1)@2001-01-03,
  Point(3 1 3)@2001-01-05]', 'Polygon((2 0,2 2,2 4,4 0,2 0))', '[0,2]'));
/* {[POINT Z (1 1 1)@2001-01-01, POINT Z (2 1 1)@2001-01-02),
    (POINT Z (3 1 2)@2001-01-04, POINT Z (3 1 3)@2001-01-05]} */

SELECT asText(minusGeometryTime(tgeompoint '[Point(1 1)@2001-01-01,
  Point(5 1)@2001-01-05, Point(1 1)@2001-01-09]',
  geometry 'Polygon((2 0,2 2,4 2,4 0,2 0))',
  tstzspan '[2001-01-03, 2001-01-05]'));
/* {[POINT(1 1)@2001-01-01, POINT(3 1)@2001-01-03), (POINT(4 1)@2001-01-04,
     POINT(5 1)@2001-01-05, POINT(1 1)@2001-01-09]} */
SELECT asText(minusGeometryTime(tgeompoint '[Point(1 1 1)@2001-01-01,
  Point(5 1 5)@2001-01-05, Point(1 1 9)@2001-01-09]',
  geometry 'Polygon((2 0,2 2,4 2,4 0,2 0))', floatspan '[0,5]',
  tstzspan '[2001-01-03, 2001-01-06]'));
/* {[POINT Z (1 1 1)@2001-01-01, POINT Z (3 1 3)@2001-01-03),
    (POINT Z (4 1 4)@2001-01-04, POINT Z (5 1 5)@2001-01-05,
     POINT Z (1 1 9)@2001-01-09]} */

Restrict to (the complement of) a time value

atTime(ttype,times) → ttype

minusTime(ttype,times) → ttype

SELECT atTime(tfloat '[1@2001-01-01, 5@2001-01-05)', timestamptz '2001-01-02');
-- 2@2001-01-02
SELECT atTime(tint '[1@2001-01-01, 1@2001-01-15)',
  tstzset '{2001-01-01, 2001-01-03}');
-- {1@2001-01-01, 1@2001-01-03}
SELECT atTime(tfloat '{[1@2001-01-01, 3@2001-01-03), [3@2001-01-04, 1@2001-01-06)}',
  tstzspan '[2001-01-02,2001-01-05)');
-- {[2@2001-01-02, 3@2001-01-03), [3@2001-01-04, 2@2001-01-05)}
SELECT atTime(tint '[1@2001-01-01, 1@2001-01-15)',
  tstzspanset '{[2001-01-01, 2001-01-03), [2001-01-04, 2001-01-05)}');
-- {[1@2001-01-01, 1@2001-01-03),[1@2001-01-04, 1@2001-01-05)}

SELECT minusTime(tfloat '[1@2001-01-01, 5@2001-01-05)', timestamptz '2001-01-02');
-- {[1@2001-01-01, 2@2001-01-02), (2@2001-01-02, 5@2001-01-05)}
SELECT minusTime(tint '[1@2001-01-01, 1@2001-01-15)',
  tstzset '{2001-01-02, 2001-01-03}');
/* {[1@2001-01-01, 1@2001-01-02), (1@2001-01-02, 1@2001-01-03),
   (1@2001-01-03, 1@2001-01-15)} */
SELECT minusTime(tfloat '{[1@2001-01-01, 3@2001-01-03), [3@2001-01-04, 1@2001-01-06)}',
  tstzspan '[2001-01-02,2001-01-05)');
-- {[1@2001-01-01, 2@2001-01-02), [2@2001-01-05, 1@2001-01-06)}
SELECT minusTime(tint '[1@2001-01-01, 1@2001-01-15)',
  tstzspanset '{[2001-01-02, 2001-01-03), [2001-01-04, 2001-01-05)}');
/* {[1@2001-01-01, 1@2001-01-02), [1@2001-01-03, 1@2001-01-04),
   [1@2001-01-05, 1@2001-01-15)} */

Restrict to (the complement of) a tbox
atTbox(tnumber,tbox) → tnumber
minusTbox(tnumber,tbox) → tnumber
```
SELECT atTbox(tfloat '[0@2001-01-01, 3@2001-01-04)',
  tbox 'TBOXFLOAT XT((0,2),[2001-01-02, 2001-01-04])');
-- {[1@2001-01-02, 2@2001-01-03]}
```
```
SELECT minusTbox(tfloat '[1@2001-01-01, 4@2001-01-04)',
  'TBOXFLOAT XT((1,4),[2001-01-03, 2001-01-04])');
-- {[1@2001-01-01, 3@2001-01-03)}
WITH temp(temp, box) AS (
  SELECT tfloat '[1@2001-01-01, 4@2001-01-04)',
    tbox 'TBOXFLOAT XT((1,2),[2001-01-03, 2001-01-04])' )
SELECT minusValues(minusTime(temp, box::tstzspan), box::floatspan) FROM temp;
-- {[1@2001-01-01], [2@2001-01-02, 3@2001-01-03)}
```
Notice that when the bounding box has both value and time dimensions, the difference is computed by restricting the temporal number to the box using the function atTbox, computing the time extent of this restriction, and restricting the temporal number to the difference of the time extent. This is required to ensure that tnumber = merge(atTbox(tnumber,tbox), minusTbox(tnumber,tbox)) (see the function merge). In other words, while the function atTbox restricts the temporal number with respect to the span and the period defining the bounding box, the function minusTbox restricts the temporal number with respect to the span or the period. To obtain the restriction using an and semantics, both the minusValues and minusTime functions must be applied.

Restrict to (the complement of) an stbox

atStbox(tgeompoint,stbox) → tgeompoint

minusStbox(tgeompoint,stbox) → tgeompoint

SELECT asText(atStbox(tgeompoint '[Point(0 0)@2001-01-01, Point(3 3)@2001-01-04)',
  stbox 'STBOX XT(((0,0),(2,2)),[2001-01-02, 2001-01-04])'));
-- {[POINT(1 1)@2001-01-02, POINT(2 2)@2001-01-03]}
SELECT asText(atStbox(tgeompoint '[Point(1 1 1)@2001-01-01, Point(3 3 3)@2001-01-03,
  Point(3 3 2)@2001-01-04, Point(3 3 7)@2001-01-09]', stbox 'STBOX Z((2,2,2),(3,3,3))'));
/* {[POINT Z (2 2 2)@2001-01-02, POINT Z (3 3 3)@2001-01-03, POINT Z (3 3 2)@2001-01-04,
  POINT Z (3 3 3)@2001-01-05]} */

SELECT asText(minusStbox(tgeompoint '[Point(1 1)@2001-01-01, Point(4 4)@2001-01-04)',
  stbox 'STBOX XT(((1,1),(4,4)),[2001-01-03,2001-01-04])'));
-- {[POINT(1 1)@2001-01-01), POINT(3 3)@2001-01-03)}
SELECT asText(minusStbox(tgeompoint '[Point(1 1 1)@2001-01-01, Point(3 3 3)@2001-01-03,
  Point(3 3 2)@2001-01-04, Point(3 3 7)@2001-01-09]', stbox 'STBOX Z((2,2,2),(3,3,3))'));
/* {[POINT Z (1 1 1)@2001-01-01, POINT Z (2 2 2)@2001-01-02), (POINT Z (3 3 3)@2001-01-05,
  POINT Z (3 3 7)@2001-01-09]} */
WITH temp(temp, box) AS (
  SELECT tgeompoint '[Point(1 1)@2001-01-01, Point(4 4)@2001-01-04)',
    stbox 'STBOX XT(((1,1),(2,2)),[2001-01-03,2001-01-04])')
SELECT asText(minusGeometry(minusTime(temp, box::tstzspan), box::geometry)) FROM temp;
-- {(POINT(2 2)@2001-01-02, POINT(3 3)@2001-01-03)}

Similarly to function minusTbox, when the bounding box has both space and time dimensions, the function minusStbox restricts the temporal point with respect to the space or the time extents of the box. To obtain the restriction using an and semantics, both the minusGeometry and minusTime functions must be applied.