This directory contains the code for the user-defined type,
CUBE, representing multidimensional cubes.


FILES
-----

Makefile		building instructions for the shared library

README.cube		the file you are now reading

cube.c			the implementation of this data type in c

cube.sql.in		SQL code needed to register this type with postgres
                        (transformed to cube.sql by make)
               
cubedata.h		the data structure used to store the cubes

cubeparse.y		the grammar file for the parser (used by cube_in() in cube.c)
 
cubescan.l		scanner rules (used by cube_yyparse() in cubeparse.y)


INSTALLATION
============

To install the type, run

	make
	make install

For this to work, make sure that:

. the cube source directory is in the postgres contrib directory
. the user running "make install" has postgres administrative authority
. this user's environment defines the PGLIB and PGDATA variables and has
  postgres binaries in the PATH.

This only installs the type implementation and documentation.  To make the
type available in any particular database, as a postgres superuser do:

	psql -d databasename < cube.sql

If you install the type in the template1 database, all subsequently created
databases will inherit it.

To test the new type, after "make install" do

	make installcheck

If it fails, examine the file regression.diffs to find out the reason (the
test code is a direct adaptation of the regression tests from the main
source tree).

By default the external functions are made executable by anyone.

SYNTAX
======

The following are valid external representations for the CUBE type:

'x'			A floating point value representing
			a one-dimensional point or one-dimensional
			zero length cubement

'(x)'			Same as above

'x1,x2,x3,...,xn'	A point in n-dimensional space,
			represented internally as a zero volume box

'(x1,x2,x3,...,xn)'	Same as above

'(x),(y)'		1-D cubement starting at x and ending at y
			or vice versa; the order does not matter

'(x1,...,xn),(y1,...,yn)'	n-dimensional box represented by 
			a pair of its opposite corners, no matter which.
			Functions take care of swapping to achieve
			"lower left -- upper right" representation
			before computing any values

Grammar
-------

rule 1    box -> O_BRACKET paren_list COMMA paren_list C_BRACKET
rule 2    box -> paren_list COMMA paren_list
rule 3    box -> paren_list
rule 4    box -> list
rule 5    paren_list -> O_PAREN list C_PAREN
rule 6    list -> FLOAT
rule 7    list -> list COMMA FLOAT

Tokens
------

n		[0-9]+
integer		[+-]?{n}
real		[+-]?({n}\.{n}?|\.{n})
FLOAT		({integer}|{real})([eE]{integer})?
O_BRACKET	\[
C_BRACKET	\]
O_PAREN		\(
C_PAREN		\)
COMMA		\,


Examples of valid CUBE representations:
--------------------------------------

'x'				A floating point value representing
				a one-dimensional point (or, zero-length
				one-dimensional interval)

'(x)'				Same as above

'x1,x2,x3,...,xn'		A point in n-dimensional space,
				represented internally as a zero volume cube

'(x1,x2,x3,...,xn)'		Same as above

'(x),(y)'			A 1-D interval starting at x and ending at y
				or vice versa; the order does not matter

'[(x),(y)]'			Same as above

'(x1,...,xn),(y1,...,yn)'	An n-dimensional box represented by 
				a pair of its diagonally opposite corners, 
				regardless of order. Swapping is provided
				by all comarison routines to ensure the 
				"lower left -- upper right" representation
				before actaul comparison takes place.

'[(x1,...,xn),(y1,...,yn)]'	Same as above


White space is ignored, so '[(x),(y)]' can be: '[ ( x ), ( y ) ]'


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 to the 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 sized boxes, I assume the smaller
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 the special Point type
and functions for (box,point) predicates.

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


PRECISION
=========

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


USAGE
=====

The access method for CUBE is a GiST (gist_cube_ops), which is a
generalization of R-tree. GiSTs allow the postgres implementation of
R-tree, originally encoded to support 2-D geometric types such as
boxes and polygons, to be used with any data type whose data domain
can be partitioned using the concepts of containment, intersection and
equality. In other words, everything that can intersect or contain
its own kind can be indexed with a GiST. That includes, among other
things, all geometric data types, regardless of their dimensionality
(see also contrib/seg).

The operators supported by the GiST access method include:


[a, b] << [c, d]	Is left of

	The left operand, [a, b], occurs entirely to the left of the
	right operand, [c, d], on the axis (-inf, inf). It means,
	[a, b] << [c, d] is true if b < c and false otherwise

[a, b] >> [c, d]	Is right of

	[a, b] is occurs entirely to the right of [c, d]. 
	[a, b] >> [c, d] is true if b > c and false otherwise

[a, b] &< [c, d]	Over left

	The cubement [a, b] overlaps the cubement [c, d] in such a way
	that a <= c <= b and b <= d

[a, b] &> [c, d]	Over right

	The cubement [a, b] overlaps the cubement [c, d] in such a way
	that a > c and b <= c <= d

[a, b] = [c, d]		Same as

	The cubements [a, b] and [c, d] are identical, that is, a == b
	and c == d

[a, b] @ [c, d]		Contains

	The cubement [a, b] contains the cubement [c, d], that is, 
	a <= c and b >= d

[a, b] @ [c, d]		Contained in

	The cubement [a, b] is contained in [c, d], that is, 
	a >= c and b <= d

Although the mnemonics of the following operators is questionable, I
preserved them to maintain visual consistency with other geometric
data types defined in Postgres.

Other operators:

[a, b] < [c, d]		Less than
[a, b] > [c, d]		Greater than

	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 accounts for
	reasonably good sorting in most cases, which is useful if
	you want to use ORDER BY with this type

The following functions are available:

cube_distance(cube, cube) returns double
  cube_distance returns the distance between two cubes. If both cubes are
  points, this is the normal distance function.

cube(text) returns cube
  cube takes text input and returns a cube. This is useful for making cubes
  from computed strings.

cube(float8) returns cube
  This makes a one dimensional cube with both coordinates the same.
  If the type of the argument is a numeric type other than float8 an
  explicit cast to float8 may be needed.
  cube(1) == '(1)'

cube(float8, float8) returns cube
  This makes a one dimensional cube.
  cube(1,2) == '(1),(2)'

cube(cube, float8) returns cube
  This builds 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.
  cube('(1)',2) == '(1,2),(1,2)'

cube(cube, float8, float8) returns cube
  This builds 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) == '(1,3),(2,4)'

cube_dim(cube) returns int
  cube_dim returns the number of dimensions stored in the the data structure
  for a cube. This is useful for constraints on the dimensions of a cube.

cube_ll_coord(cube, int) returns double
  cube_ll_coord returns the nth coordinate value for the lower left corner
  of a cube. This is useful for doing coordinate transformations.

cube_ur_coord(cube, int) returns double
  cube_ur_coord returns the nth coordinate value for the upper right corner
  of a cube. This is useful for doing coordinate transformations.

cube_is_point(cube) returns bool
  cube_is_point returns true if a cube is also a point. This is true when the
  two defining corners are the same.

cube_enlarge(cube, double, int) returns cube
  cube_enlarge increases the size of a cube by a specified radius in at least
  n dimensions. If the radius is negative the box 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. 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.
  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. To make it harder for people to break things there is an effective
  maximum on the dimension of cubes of 100. This is set in cubedata.h if
  you need something bigger.

There are a few other potentially useful functions defined in cube.c 
that vanished from the schema because I stopped using them. Some of 
these were meant to support type casting. Let me know if I was wrong: 
I will then add them back to the schema. I would also appreciate 
other ideas that would enhance the type and make it more useful.

For examples of usage, see sql/cube.sql


CREDITS
=======

This code is essentially based on the example written for
Illustra, http://garcia.me.berkeley.edu/~adong/rtree

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
(http://best.me.berkeley.edu/~adong/), for his exemplar.
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.

------------------------------------------------------------------------
Gene Selkov, Jr.
Computational Scientist
Mathematics and Computer Science Division
Argonne National Laboratory
9700 S Cass Ave.
Building 221
Argonne, IL 60439-4844

selkovjr@mcs.anl.gov

------------------------------------------------------------------------

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.
