<!-- doc/src/sgml/cube.sgml -->
<sect1 id="cube" xreflabel="cube">
<title>cube</title>
<indexterm zone="cube">
<primary>cube</primary>
</indexterm>
&common;
<para>
This module implements a data type <type>cube</> for
representing multidimensional cubes.
</para>
<sect2>
<title>Syntax</title>
&common;
<para>
<xref linkend="cube-repr-table"> shows the valid external
representations for the <type>cube</>
type. <replaceable>x</>, <replaceable>y</>, etc. denote
floating-point numbers.
</para>
<table id="cube-repr-table">
<title>Cube External Representations</title>
<tgroup cols="2">
<tbody>
<row>
<entry><literal><replaceable>x</></literal></entry>
<entry>A one-dimensional point
(or, zero-length one-dimensional interval)
</entry>
</row>
<row>
<entry><literal>(<replaceable>x</>)</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry><literal><replaceable>x1</>,<replaceable>x2</>,...,<replaceable>xn</></literal></entry>
<entry>A point in n-dimensional space, represented internally as a
zero-volume cube
</entry>
</row>
<row>
<entry><literal>(<replaceable>x1</>,<replaceable>x2</>,...,<replaceable>xn</>)</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry><literal>(<replaceable>x</>),(<replaceable>y</>)</literal></entry>
<entry>A one-dimensional interval starting at <replaceable>x</> and ending at <replaceable>y</> or vice versa; the
order does not matter
</entry>
</row>
<row>
<entry><literal>[(<replaceable>x</>),(<replaceable>y</>)]</literal></entry>
<entry>Same as above</entry>
</row>
<row>
<entry><literal>(<replaceable>x1</>,...,<replaceable>xn</>),(<replaceable>y1</>,...,<replaceable>yn</>)</literal></entry>
<entry>An n-dimensional cube represented by a pair of its diagonally
opposite corners
</entry>
</row>
<row>
<entry><literal>[(<replaceable>x1</>,...,<replaceable>xn</>),(<replaceable>y1</>,...,<replaceable>yn</>)]</literal></entry>
<entry>Same as above</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
It does not matter which order the opposite corners of a cube are
entered in. The <type>cube</> functions
automatically swap values if needed to create a uniform
<quote>lower left — upper right</> internal representation.
</para>
<para>
White space is ignored, so <literal>[(<replaceable>x</>),(<replaceable>y</>)]</literal> is the same as
<literal>[ ( <replaceable>x</> ), ( <replaceable>y</> ) ]</literal>.
</para>
</sect2>
<sect2>
<title>Precision</title>
&common;
<para>
Values are stored internally as 64-bit floating point numbers. This means
that numbers with more than about 16 significant digits will be truncated.
</para>
</sect2>
<sect2>
<title>Usage</title>
&common;
<para>
The <filename>cube</> module includes a GiST index operator class for
<type>cube</> values.
The operators supported by the GiST operator class are shown in <xref linkend="cube-gist-operators">.
</para>
<table id="cube-gist-operators">
<title>Cube GiST Operators</title>
<tgroup cols="2">
<thead>
<row>
<entry>Operator</entry>
<entry>Description</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal>a = b</></entry>
<entry>The cubes a and b are identical.</entry>
</row>
<row>
<entry><literal>a && b</></entry>
<entry>The cubes a and b overlap.</entry>
</row>
<row>
<entry><literal>a @> b</></entry>
<entry>The cube a contains the cube b.</entry>
</row>
<row>
<entry><literal>a <@ b</></entry>
<entry>The cube a is contained in the cube b.</entry>
</row>
</tbody>
</tgroup>
</table>
<para>
(Before PostgreSQL 8.2, the containment operators <literal>@></> and <literal><@</> were
respectively called <literal>@</> and <literal>~</>. 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!)
</para>
<para>
The standard B-tree operators are also provided, for example
<informaltable>
<tgroup cols="2">
<thead>
<row>
<entry>Operator</entry>
<entry>Description</entry>
</row>
</thead>
<tbody>
<row>
<entry><literal>[a, b] < [c, d]</literal></entry>
<entry>Less than</entry>
</row>
<row>
<entry><literal>[a, b] > [c, d]</literal></entry>
<entry>Greater than</entry>
</row>
</tbody>
</tgroup>
</informaltable>
These operators do not make a lot of sense for any practical
purpose but sorting. These operators first compare (a) to (c),
and if these are equal, compare (b) to (d). That results in
reasonably good sorting in most cases, which is useful if
you want to use ORDER BY with this type.
</para>
<para>
<xref linkend="cube-functions-table"> shows the available functions.
</para>
<table id="cube-functions-table">
<title>Cube Functions</title>
<tgroup cols="2">
<tbody>
<row>
<entry><literal>cube(float8) returns cube</literal></entry>
<entry>Makes a one dimensional cube with both coordinates the same.
<literal>cube(1) == '(1)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8, float8) returns cube</literal></entry>
<entry>Makes a one dimensional cube.
<literal>cube(1,2) == '(1),(2)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8[]) returns cube</literal></entry>
<entry>Makes a zero-volume cube using the coordinates
defined by the array.
<literal>cube(ARRAY[1,2]) == '(1,2)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(float8[], float8[]) returns cube</literal></entry>
<entry>Makes a cube with upper right and lower left
coordinates as defined by the two arrays, which must be of the
same length.
<literal>cube('{1,2}'::float[], '{3,4}'::float[]) == '(1,2),(3,4)'
</literal>
</entry>
</row>
<row>
<entry><literal>cube(cube, float8) returns cube</literal></entry>
<entry>Makes a new cube by adding a dimension on to an
existing cube with the same values for both parts of the new coordinate.
This is useful for building cubes piece by piece from calculated values.
<literal>cube('(1)',2) == '(1,2),(1,2)'</literal>
</entry>
</row>
<row>
<entry><literal>cube(cube, float8, float8) returns cube</literal></entry>
<entry>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. <literal>cube('(1,2)',3,4) == '(1,3),(2,4)'</literal>
</entry>
</row>
<row>
<entry><literal>cube_dim(cube) returns int</literal></entry>
<entry>Returns the number of dimensions of the cube
</entry>
</row>
<row>
<entry><literal>cube_ll_coord(cube, int) returns double </literal></entry>
<entry>Returns the n'th coordinate value for the lower left
corner of a cube
</entry>
</row>
<row>
<entry><literal>cube_ur_coord(cube, int) returns double
</literal></entry>
<entry>Returns the n'th coordinate value for the
upper right corner of a cube
</entry>
</row>
<row>
<entry><literal>cube_is_point(cube) returns bool</literal></entry>
<entry>Returns true if a cube is a point, that is,
the two defining corners are the same.</entry>
</row>
<row>
<entry><literal>cube_distance(cube, cube) returns double</literal></entry>
<entry>Returns the distance between two cubes. If both
cubes are points, this is the normal distance function.
</entry>
</row>
<row>
<entry><literal>cube_subset(cube, int[]) returns cube
</literal></entry>
<entry>Makes a new cube from an existing cube, using a list of
dimension indexes from an array. Can be used to find both the LL and UR
coordinates of a single dimension, e.g.
<literal>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[2]) = '(3),(7)'</>.
Or can be used to drop dimensions, or reorder them as desired, e.g.
<literal>cube_subset(cube('(1,3,5),(6,7,8)'), ARRAY[3,2,1,1]) = '(5, 3,
1, 1),(8, 7, 6, 6)'</>.
</entry>
</row>
<row>
<entry><literal>cube_union(cube, cube) returns cube</literal></entry>
<entry>Produces the union of two cubes
</entry>
</row>
<row>
<entry><literal>cube_inter(cube, cube) returns cube</literal></entry>
<entry>Produces the intersection of two cubes
</entry>
</row>
<row>
<entry><literal>cube_enlarge(cube c, double r, int n) returns cube</literal></entry>
<entry>Increases the size of a cube by a specified radius in at least
n dimensions. If the radius is negative the cube is shrunk instead. This
is useful for creating bounding boxes around a point for searching for
nearby points. All defined dimensions are changed by the radius r.
LL coordinates are decreased by r and UR coordinates are increased by r.
If a LL coordinate is increased to larger than the corresponding UR
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 increased (r >= 0) then 0 is used
as the base for the extra coordinates.
</entry>
</row>
</tbody>
</tgroup>
</table>
</sect2>
<sect2>
<title>Defaults</title>
&common;
<para>
I believe this union:
</para>
<programlisting>
select cube_union('(0,5,2),(2,3,1)', '0');
cube_union
-------------------
(0, 0, 0),(2, 5, 2)
(1 row)
</programlisting>
<para>
does not contradict common sense, neither does the intersection
</para>
<programlisting>
select cube_inter('(0,-1),(1,1)', '(-2),(2)');
cube_inter
-------------
(0, 0),(1, 0)
(1 row)
</programlisting>
<para>
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:
</para>
<programlisting>
cube_union('(0,5,2),(2,3,1)','(0,0,0),(0,0,0)');
cube_inter('(0,-1),(1,1)','(-2,0),(2,0)');
</programlisting>
<para>
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.
</para>
<programlisting>
select cube_contains('(0,0),(1,1)', '0.5,0.5');
cube_contains
--------------
t
(1 row)
</programlisting>
</sect2>
<sect2>
<title>Notes</title>
&common;
<para>
For examples of usage, see the regression test <filename>sql/cube.sql</>.
</para>
<para>
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 <filename>cubedata.h</> if you need something bigger.
</para>
</sect2>
<sect2>
<title>Credits</title>
<para>
Original author: Gene Selkov, Jr. <email>selkovjr@mcs.anl.gov</email>,
Mathematics and Computer Science Division, Argonne National Laboratory.
</para>
<para>
My thanks are primarily to Prof. Joe Hellerstein
(<ulink url="http://db.cs.berkeley.edu/jmh/"></ulink>) for elucidating the
gist of the GiST (<ulink url="http://gist.cs.berkeley.edu/"></ulink>), and
to his former student, Andy Dong (<ulink
url="http://best.me.berkeley.edu/~adong/"></ulink>), for his example
written for Illustra,
<ulink url="http://best.berkeley.edu/~adong/rtree/index.html"></ulink>.
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.
</para>
<para>
Minor updates to this package were made by Bruno Wolff III
<email>bruno@wolff.to</email> in August/September of 2002. These include
changing the precision from single precision to double precision and adding
some new functions.
</para>
<para>
Additional updates were made by Joshua Reich <email>josh@root.net</email> in
July 2006. These include <literal>cube(float8[], float8[])</literal> and
cleaning up the code to use the V1 call protocol instead of the deprecated
V0 protocol.
</para>
</sect2>
</sect1>