This module implements a data type cube
for representing multidimensional cubes.
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
) ]
Values are stored internally as 64bit floating point numbers. This means that numbers with more than about 16 significant digits will be truncated.
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)' 
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)
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. <selkovjr@mcs.anl.gov>
,
Mathematics and Computer Science Division, Argonne National
Laboratory.
My thanks are primarily to Prof. Joe Hellerstein (http://db.cs.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.