Table F.2 shows the valid external representations for the cube type. x, y, etc. denote floating-point numbers.

It does not matter which order the opposite corners of a cube are entered in. The cube functions automatically swap values if needed to create a uniform “lower left — upper right” internal representation. When the corners coincide, cube stores only one corner along with an “is point” flag to avoid wasting space.

White space is ignored on input, so [(x),(y)] is the same as [ ( x ), ( y ) ].

Values are stored internally as 64-bit floating point numbers. This means that numbers with more than about 16 significant digits will be truncated.

Table F.3 shows the specialized operators provided for type cube.

In addition to the above operators, the usual comparison operators shown in Table 9.1 are available for type cube. These operators first compare the first coordinates, and if those are equal, compare the second coordinates, etc. They exist mainly to support the b-tree index operator class for cube, which can be useful for example if you would like a UNIQUE constraint on a cube column. Otherwise, this ordering is not of much practical use.

The cube module also provides a GiST index operator class for cube values. A cube GiST index can be used to search for values using the =, &&, @>, and <@ operators in WHERE clauses.

In addition, a cube GiST index can be used to find nearest neighbors using the metric operators <->, <#>, and <=> in ORDER BY clauses. For example, the nearest neighbor of the 3-D point (0.5, 0.5, 0.5) could be found efficiently with:

SELECT c FROM test ORDER BY c <-> cube(array[0.5,0.5,0.5]) LIMIT 1;

The ~> operator can also be used in this way to efficiently retrieve the first few values sorted by a selected coordinate. For example, to get the first few cubes ordered by the first coordinate (lower left corner) ascending one could use the following query:

SELECT c FROM test ORDER BY c ~> 1 LIMIT 5;

And to get 2-D cubes ordered by the first coordinate of the upper right corner descending:

SELECT c FROM test ORDER BY c ~> 3 DESC LIMIT 5;

Table F.4 shows the available functions.

I believe this union:

select cube_union('(0,5,2),(2,3,1)', '0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)

does not contradict common sense, neither does the intersection

select cube_inter('(0,-1),(1,1)', '(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)

In all binary operations on differently-dimensioned cubes, I assume the lower-dimensional one to be a Cartesian projection, i. e., having zeroes in place of coordinates omitted in the string representation. The above examples are equivalent to:

cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');

The following containment predicate uses the point syntax, while in fact the second argument is internally represented by a box. This syntax makes it unnecessary to define a separate point type and functions for (box,point) predicates.

select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)

For examples of usage, see the regression test sql/cube.sql.

To make it harder for people to break things, there is a limit of 100 on the number of dimensions of cubes. This is set in cubedata.h if you need something bigger.

Original author: Gene Selkov, Jr. <[email protected]>, Mathematics and Computer Science Division, Argonne National Laboratory.

My thanks are primarily to Prof. Joe Hellerstein (https://dsf.berkeley.edu/jmh/) for elucidating the gist of the GiST (http://gist.cs.berkeley.edu/), and to his former student Andy Dong for his example written for Illustra. I am also grateful to all Postgres developers, present and past, for enabling myself to create my own world and live undisturbed in it. And I would like to acknowledge my gratitude to Argonne Lab and to the U.S. Department of Energy for the years of faithful support of my database research.

Minor updates to this package were made by Bruno Wolff III <[email protected]> in August/September of 2002. These include changing the precision from single precision to double precision and adding some new functions.

Additional updates were made by Joshua Reich <[email protected]> in July 2006. These include cube(float8[], float8[]) and cleaning up the code to use the V1 call protocol instead of the deprecated V0 protocol.