F.9. cube
This module implements a data type
cube
for
representing multidimensional cubes.
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 operators provided for
type
cube
.
Table F.3. Cube Operators
Operator  Result  Description 

a = b

boolean

The cubes a and b are identical. 
a && b

boolean

The cubes a and b overlap. 
a @> b

boolean

The cube a contains the cube b. 
a <@ b

boolean

The cube a is contained in the cube b. 
a < b

boolean

The cube a is less than the cube b. 
a <= b

boolean

The cube a is less than or equal to the cube b. 
a > b

boolean

The cube a is greater than the cube b. 
a >= b

boolean

The cube a is greater than or equal to the cube b. 
a <> b

boolean

The cube a is not equal to the cube b. 
a > n

float8

Get
n
th coordinate of cube (counting from 1).

a ~> n

float8

Get
n
th coordinate of cube in following way:
n = 2 * k  1 means lower bound of
k
th
dimension, n = 2 * k means upper bound of
k
th dimension. Negative
n
denotes the inverse value of the corresponding
positive coordinate. This operator is designed for KNNGiST support.

a <> b

float8

Euclidean distance between a and b. 
a <#> b

float8

Taxicab (L1 metric) distance between a and b. 
a <=> b

float8

Chebyshev (Linf metric) distance between a and b. 
(Before PostgreSQL 8.2, the containment operators
@>
and
<@
were
respectively called
@
and
~
. These names are still available, but are
deprecated and will eventually be retired. Notice that the old names
are reversed from the convention formerly followed by the core geometric
data types!)
The scalar ordering operators (
<
,
>=
, etc)
do not make a lot of sense for any practical purpose but sorting. 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.
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  Result  Description  Example 

cube(float8)

cube

Makes a one dimensional cube with both coordinates the same. 
cube(1) == '(1)'

cube(float8, float8)

cube

Makes a one dimensional cube. 
cube(1,2) == '(1),(2)'

cube(float8[])

cube

Makes a zerovolume cube using the coordinates defined by the array. 
cube(ARRAY[1,2]) == '(1,2)'

cube(float8[], float8[])

cube

Makes a cube with upper right and lower left coordinates as defined by the two arrays, which must be of the same length. 
cube(ARRAY[1,2], ARRAY[3,4]) == '(1,2),(3,4)'

cube(cube, float8)

cube

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. 
cube('(1,2),(3,4)'::cube, 5) == '(1,2,5),(3,4,5)'

cube(cube, float8, float8)

cube

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. 
cube('(1,2),(3,4)'::cube, 5, 6) == '(1,2,5),(3,4,6)'

cube_dim(cube)

integer

Returns the number of dimensions of the cube. 
cube_dim('(1,2),(3,4)') == '2'

cube_ll_coord(cube, integer)

float8

Returns the
n
th coordinate value for the lower
left corner of the cube.

cube_ll_coord('(1,2),(3,4)', 2) == '2'

cube_ur_coord(cube, integer)

float8

Returns the
n
th coordinate value for the
upper right corner of the cube.

cube_ur_coord('(1,2),(3,4)', 2) == '4'

cube_is_point(cube)

boolean

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

float8

Returns the distance between two cubes. If both cubes are points, this is the normal distance function.  
cube_subset(cube, integer[])

cube

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. 
cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) == '(3),(7)'
cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) ==
'(5,3,1,1),(8,7,6,6)'

cube_union(cube, cube)

cube

Produces the union of two cubes.  
cube_inter(cube, cube)

cube

Produces the intersection of two cubes.  
cube_enlarge(c cube, r double, n integer)

cube

Increases the size of the cube by the specified
radius
r
in at least
n
dimensions.
If the radius is negative the cube is shrunk instead.
All defined dimensions are changed by the radius
r
.
Lowerleft coordinates are decreased by
r
and
upperright coordinates are increased by
r
. If a
lowerleft coordinate is increased to more than the corresponding
upperright coordinate (this can only happen when
r
< 0) than both coordinates are set to their average.
If
n
is greater than the number of defined dimensions
and the cube is being enlarged (
r
> 0), then extra
dimensions are added to make
n
altogether;
0 is used as the initial value for the extra coordinates.
This function is useful for creating bounding boxes around a point for
searching for nearby points.

cube_enlarge('(1,2),(3,4)', 0.5, 3) ==
'(0.5,1.5,0.5),(3.5,4.5,0.5)'

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.