F.9. cube
This module implements a data type
cube
for
representing multidimensional cubes.
This module is considered
"
trusted
"
, that is, it can be
installed by nonsuperusers who have
CREATE
privilege
on the current database.
F.9.1. Syntax
Table F.2
shows the valid external
representations for the
cube
type.
x
,
y
, etc. denote
floatingpoint numbers.
Table F.2. Cube External Representations
External Syntax  Meaning 


A onedimensional point (or, zerolength onedimensional interval) 
(

Same as above 

A point in ndimensional space, represented internally as a zerovolume cube 
(

Same as above 
(

A onedimensional interval starting at
x
and ending at
y
or vice versa; the
order does not matter

[(

Same as above 
(

An ndimensional cube represented by a pair of its diagonally opposite corners 
[(

Same as above 
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
[(
is the same as
x
),(
y
)]
[ (
.
x
), (
y
) ]
F.9.2. Precision
Values are stored internally as 64bit floating point numbers. This means that numbers with more than about 16 significant digits will be truncated.
F.9.3. Usage
Table F.3
shows the specialized operators
provided for type
cube
.
Table F.3. Cube Operators
Operator Description 

Do the cubes overlap? 
Does the first cube contain the second? 
Is the first cube contained in the second? 
Extracts the

Extracts the

Computes the Euclidean distance between the two cubes. 
Computes the taxicab (L1 metric) distance between the two cubes. 
Computes the Chebyshev (Linf metric) distance between the two cubes. 
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
btree 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 3D 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 2D 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.
Table F.4. Cube Functions
Function Description Example(s) 

Makes a one dimensional cube with both coordinates the same.

Makes a one dimensional cube.

Makes a zerovolume cube using the coordinates defined by the array.

Makes a cube with upper right and lower left coordinates as defined by the two arrays, which must be of the same length.

Makes a new cube by adding a dimension on to an existing cube, with the same values for both endpoints of the new coordinate. This is useful for building cubes piece by piece from calculated values.

Makes a new cube by adding a dimension on to an existing cube. This is useful for building cubes piece by piece from calculated values.

Returns the number of dimensions of the cube.

Returns the

Returns the

Returns true if the cube is a point, that is, the two defining corners are the same.

Returns the distance between two cubes. If both cubes are points, this is the normal distance function.

Makes a new cube from an existing cube, using a list of dimension indexes from an array. Can be used to extract the endpoints of a single dimension, or to drop dimensions, or to reorder them as desired.

Produces the union of two cubes.

Produces the intersection of two cubes.

Increases the size of the cube by the specified
radius

F.9.4. Defaults
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 differentlydimensioned cubes, I assume the lowerdimensional 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)
F.9.5. Notes
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.
F.9.6. Credits
Original author: Gene Selkov, Jr.
<
selkovjr@mcs.anl.gov
>
,
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
<
bruno@wolff.to
>
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
<
josh@root.net
>
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.