Index: contrib/earthdistance/README.earthdistance
===================================================================
RCS file: /cvsroot/contrib/earthdistance/README.earthdistance,v
retrieving revision 1.2
diff -c -c -r1.2 README.earthdistance
*** contrib/earthdistance/README.earthdistance	20 Sep 2002 03:47:22 -0000	1.2
--- contrib/earthdistance/README.earthdistance	8 Nov 2002 20:18:25 -0000
***************
*** 1,13 ****
! ---------------------------------------------------------------------
! I corrected a bug in the geo_distance code where two double constants
! were declared as int. I changed the distance function to use the
! haversine formula which is more accurate for small distances.
! I added a regression test to the package. I added a grant statement
! to give execute access for geo_distance to public.
  
  Bruno Wolff III
  September 2002
  ---------------------------------------------------------------------
  Date: Wed, 1 Apr 1998 15:19:32 -0600 (CST)
  From: Hal Snyder <hal@vailsys.com>
  To: vmehr@ctp.com
--- 1,107 ----
! This contrib package contains two different approaches to calculating
! great circle distances on the surface of the Earth. The one described
! first depends on the contrib/cube package (which MUST be installed before
! earthdistance is installed). The second one is based on the point
! datatype using latitude and longitude for the coordinates. The install
! script makes the defined functions executable by anyone.
! 
! Make sure contrib/cube has been installed.
! make
! make install
! make installcheck
! 
! To use these functions in a particular database as a postgres superuser do:
! psql databasename < earthdistance.sql
  
+ -------------------------------------------
+ contrib/cube based Earth distance functions
  Bruno Wolff III
  September 2002
+ 
+ A spherical model of the Earth is used.
+ 
+ Data is stored in cubes that are points (both corners are the same) using 3
+ coordinates representing the distance from the center of the Earth.
+ 
+ The radius of the Earth is obtained from the earth() function. It is
+ given in meters. But by changing this one function you can change it
+ to use some other units or to use a different value of the radius
+ that you feel is more appropiate.
+ 
+ This package also has applications to astronomical databases as well.
+ Astronomers will probably want to change earth() to return a radius of
+ 180/pi() so that distances are in degrees.
+ 
+ Functions are provided to allow for input in latitude and longitude (in
+ degrees), to allow for output of latitude and longitude, to calculate
+ the great circle distance between two points and to easily specify a
+ bounding box usable for index searches.
+ 
+ The functions are all 'sql' functions. If you want to make these functions
+ executable by other people you will also have to make the referenced
+ cube functions executable. cube(text), cube_distance(cube,cube),
+ cube_ll_coord(cube,int) and cube_enlarge(cube,float8,int) are used indirectly
+ by the earth distance functions. is_point(cube) and cube_dim(cube) are used
+ in suggested constraints for data in domain earth. cube_ur_coord(cube,int)
+ is used in the regression tests and might be useful for looking at bounding
+ box coordinates in user applications.
+ 
+ A domain of type cube named earth is defined. Since check constraints
+ are not supported for domains yet, this isn't as useful as it might be.
+ However the checks that should be supplied to all data of type earth are:
+ 
+ constraint not_point check(is_point(earth))
+ constraint not_3d check(cube_dim(earth) <= 3)
+ constraint on_surface check(abs(cube_distance(earth, '(0)'::cube) /
+            earth() - 1) < '10e-12'::float8);
+ 
+ The following functions are provided:
+ 
+ earth() - Returns the radius of the earth in meters.
+ 
+ sec_to_gc(float8) - Converts the normal straight line (secant) distance between
+ between two points on the surface of the Earth to the great circle distance
+ between them.
+ 
+ gc_to_sec(float8) - Converts the great circle distance between two points
+ on the surface of the Earth to the normal straight line (secant) distance
+ between them.
+ 
+ ll_to_cube(float8, float8) - Returns the location of a point on the surface of
+ the Earth given its latitude (argument 1) and longitude (argument 2) in degrees.
+ 
+ latitude(earth) - Returns the latitude in degrees of a point on the surface
+ of the Earth.
+ 
+ longitude(earth) - Returns the longitude in degrees of a point on the surface
+ of the Earth.
+ 
+ earth_distance(earth, earth) - Returns the great circle distance between
+ two points on the surface of the Earth.
+ 
+ earth_box(earth, float8)  - Returns a box suitable for an indexed search using
+ the cube @ operator for points within a given great circle distance of a
+ location. Some points in this box are further than the specified great circle
+ distance from the location so a second check using earth_distance should be
+ made at the same time.
+ 
+ One advantage of using cube representation over a point using latitude and
+ longitude for coordinates, is that you don't have to worry about special
+ conditions at +/- 180 degrees of longitude or near the poles.
+ 
+ Below is the documentation for the Earth distance operator that works
+ with the point data type.
+ 
+ ---------------------------------------------------------------------
+ 
+ I corrected a bug in the geo_distance code where two double constants
+ were declared as int. I also changed the distance function to use
+ the haversine formula which is more accurate for small distances.
+ Bruno Wolff
+ September 2002
+ 
  ---------------------------------------------------------------------
+ 
  Date: Wed, 1 Apr 1998 15:19:32 -0600 (CST)
  From: Hal Snyder <hal@vailsys.com>
  To: vmehr@ctp.com
Index: contrib/earthdistance/earthdistance.c
===================================================================
RCS file: /cvsroot/contrib/earthdistance/earthdistance.c,v
retrieving revision 1.6
diff -c -c -r1.6 earthdistance.c
*** contrib/earthdistance/earthdistance.c	20 Sep 2002 03:47:22 -0000	1.6
--- contrib/earthdistance/earthdistance.c	8 Nov 2002 20:18:25 -0000
***************
*** 50,56 ****
  				long2,
  				lat2;
  	double		longdiff;
!         double		sino;
  	double	   *resultp = palloc(sizeof(double));
  
  	/* convert degrees to radians */
--- 50,56 ----
  				long2,
  				lat2;
  	double		longdiff;
! 	double		sino;
  	double	   *resultp = palloc(sizeof(double));
  
  	/* convert degrees to radians */
Index: contrib/earthdistance/earthdistance.sql.in
===================================================================
RCS file: /cvsroot/contrib/earthdistance/earthdistance.sql.in,v
retrieving revision 1.4
diff -c -c -r1.4 earthdistance.sql.in
*** contrib/earthdistance/earthdistance.sql.in	18 Oct 2002 18:41:20 -0000	1.4
--- contrib/earthdistance/earthdistance.sql.in	8 Nov 2002 20:18:25 -0000
***************
*** 3,8 ****
--- 3,79 ----
  
  SET autocommit TO 'on';
  
+ -- The earth functions rely on contrib/cube having been installed and loaded.
+ 
+ -- earth() returns the radius of the earth in meters. This is the only
+ -- place you need to change things for the cube base distance functions
+ -- in order to use different units (or a better value for the Earth's radius).
+ 
+ CREATE OR REPLACE FUNCTION earth() RETURNS float8
+ LANGUAGE 'sql' IMMUTABLE
+ AS 'SELECT \'6378168\'::float8';
+ 
+ -- Astromers may want to change the earth function so that distances will be
+ -- returned in degrees. To do this comment out the above definition and
+ -- uncomment the one below. Note that doing this will break the regression
+ -- tests.
+ --
+ -- CREATE OR REPLACE FUNCTION earth() RETURNS float8
+ -- LANGUAGE 'sql' IMMUTABLE
+ -- AS 'SELECT 180/pi()';
+ 
+ -- Define domain for locations on the surface of the earth using a cube
+ -- datatype with constraints. cube provides 3D indexing.
+ -- Check constraints aren't currently supported.
+ 
+ CREATE DOMAIN earth AS cube;
+ --  CONSTRAINT not_point check(is_point(earth))
+ --  CONSTRAINT not_3d check(cube_dim(earth) <= 3)
+ --  CONSTRAINT on_surface check(abs(cube_distance(earth, '(0)'::cube) /
+ --  earth() - 1) < '10e-12'::float8);
+ 
+ CREATE OR REPLACE FUNCTION sec_to_gc(float8) 
+ RETURNS float8
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT CASE WHEN $1 < 0 THEN 0::float8 WHEN $1/(2*earth()) > 1 THEN pi()*earth() ELSE 2*earth()*asin($1/(2*earth())) END';
+ 
+ CREATE OR REPLACE FUNCTION gc_to_sec(float8)
+ RETURNS float8
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT CASE WHEN $1 < 0 THEN 0::float8 WHEN $1/earth() > pi() THEN 2*earth() ELSE 2*earth()*sin($1/(2*earth())) END';
+ 
+ CREATE OR REPLACE FUNCTION ll_to_earth(float8, float8)
+ RETURNS earth
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT cube(\'(\'||earth()*cos(radians($1))*cos(radians($2))||\',\'||earth()*cos(radians($1))*sin(radians($2))||\',\'||earth()*sin(radians($1))||\')\')';
+ 
+ CREATE OR REPLACE FUNCTION latitude(earth)
+ RETURNS float8
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT CASE WHEN cube_ll_coord($1, 3)/earth() < -1 THEN -90::float8 WHEN cube_ll_coord($1, 3)/earth() > 1 THEN 90::float8 ELSE degrees(asin(cube_ll_coord($1, 3)/earth())) END';
+ 
+ CREATE OR REPLACE FUNCTION longitude(earth)
+ RETURNS float8
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT degrees(atan2(cube_ll_coord($1, 2), cube_ll_coord($1, 1)))';
+ 
+ CREATE OR REPLACE FUNCTION earth_distance(earth, earth)
+ RETURNS float8
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT sec_to_gc(cube_distance($1, $2))';
+ 
+ CREATE OR REPLACE FUNCTION earth_box(earth, float8)
+ RETURNS cube
+ LANGUAGE 'sql'
+ IMMUTABLE STRICT
+ AS 'SELECT cube_enlarge($1, gc_to_sec($2), 3)';
+   
  --------------- geo_distance
  
  CREATE OR REPLACE FUNCTION geo_distance (point, point)
Index: contrib/earthdistance/expected/earthdistance.out
===================================================================
RCS file: /cvsroot/contrib/earthdistance/expected/earthdistance.out,v
retrieving revision 1.3
diff -c -c -r1.3 earthdistance.out
*** contrib/earthdistance/expected/earthdistance.out	21 Oct 2002 20:33:21 -0000	1.3
--- contrib/earthdistance/expected/earthdistance.out	8 Nov 2002 20:18:26 -0000
***************
*** 3,81 ****
  --
  --
  -- first, define the datatype.  Turn off echoing so that expected file
! -- does not depend on contents of earthdistance.sql.
  --
  \set ECHO none
  --
  -- Test getting the distance between two points using geo_distance.
  --
! SELECT geo_distance('(0,0)'::point,'(0,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
        0.00000
  (1 row)
  
! SELECT geo_distance('(0,0)'::point,'(180,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
    12436.77274
  (1 row)
  
! SELECT geo_distance('(0,0)'::point,'(0,90)'::point)::numeric(20,5);
   geo_distance 
  --------------
     6218.38637
  (1 row)
  
! SELECT geo_distance('(0,0)'::point,'(90,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
     6218.38637
  (1 row)
  
! SELECT geo_distance('(0,0)'::point,'(1,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! SELECT geo_distance('(0,0)'::point,'(0,1)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! SELECT geo_distance('(0,30)'::point,'(1,30)'::point)::numeric(20,5);
   geo_distance 
  --------------
       59.83626
  (1 row)
  
! SELECT geo_distance('(0,30)'::point,'(0,31)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! SELECT geo_distance('(0,60)'::point,'(1,60)'::point)::numeric(20,5);
   geo_distance 
  --------------
       34.54626
  (1 row)
  
! SELECT geo_distance('(0,60)'::point,'(0,61)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! SELECT geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)::numeric(20,5);
   geo_distance 
  --------------
     1129.18983
  (1 row)
  
! SELECT (geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
      numeric    
  ---------------
   1817254.87730
--- 3,628 ----
  --
  --
  -- first, define the datatype.  Turn off echoing so that expected file
! -- does not depend on contents of earthdistance.sql or cube.sql.
  --
  \set ECHO none
+ psql:../cube/cube.sql:12: NOTICE:  ProcedureCreate: type cube is not yet defined
+ psql:../cube/cube.sql:17: NOTICE:  Argument type "cube" is only a shell
+ --
+ -- The radius of the Earth we are using.
+ --
+ select earth()::numeric(20,5);
+      earth     
+ ---------------
+  6378168.00000
+ (1 row)
+ 
+ --
+ -- Convert straight line distances to great circle distances.
+ --
+ select (pi()*earth())::numeric(20,5);
+     numeric     
+ ----------------
+  20037605.73216
+ (1 row)
+ 
+ select sec_to_gc(0)::numeric(20,5);
+  sec_to_gc 
+ -----------
+    0.00000
+ (1 row)
+ 
+ select sec_to_gc(2*earth())::numeric(20,5);
+    sec_to_gc    
+ ----------------
+  20037605.73216
+ (1 row)
+ 
+ select sec_to_gc(10*earth())::numeric(20,5);
+    sec_to_gc    
+ ----------------
+  20037605.73216
+ (1 row)
+ 
+ select sec_to_gc(-earth())::numeric(20,5);
+  sec_to_gc 
+ -----------
+    0.00000
+ (1 row)
+ 
+ select sec_to_gc(1000)::numeric(20,5);
+  sec_to_gc  
+ ------------
+  1000.00000
+ (1 row)
+ 
+ select sec_to_gc(10000)::numeric(20,5);
+   sec_to_gc  
+ -------------
+  10000.00102
+ (1 row)
+ 
+ select sec_to_gc(100000)::numeric(20,5);
+   sec_to_gc   
+ --------------
+  100001.02426
+ (1 row)
+ 
+ select sec_to_gc(1000000)::numeric(20,5);
+    sec_to_gc   
+ ---------------
+  1001027.07131
+ (1 row)
+ 
+ --
+ -- Convert great circle distances to straight line distances.
+ --
+ select gc_to_sec(0)::numeric(20,5);
+  gc_to_sec 
+ -----------
+    0.00000
+ (1 row)
+ 
+ select gc_to_sec(sec_to_gc(2*earth()))::numeric(20,5);
+    gc_to_sec    
+ ----------------
+  12756336.00000
+ (1 row)
+ 
+ select gc_to_sec(10*earth())::numeric(20,5);
+    gc_to_sec    
+ ----------------
+  12756336.00000
+ (1 row)
+ 
+ select gc_to_sec(pi()*earth())::numeric(20,5);
+    gc_to_sec    
+ ----------------
+  12756336.00000
+ (1 row)
+ 
+ select gc_to_sec(-1000)::numeric(20,5);
+  gc_to_sec 
+ -----------
+    0.00000
+ (1 row)
+ 
+ select gc_to_sec(1000)::numeric(20,5);
+  gc_to_sec  
+ ------------
+  1000.00000
+ (1 row)
+ 
+ select gc_to_sec(10000)::numeric(20,5);
+  gc_to_sec  
+ ------------
+  9999.99898
+ (1 row)
+ 
+ select gc_to_sec(100000)::numeric(20,5);
+   gc_to_sec  
+ -------------
+  99998.97577
+ (1 row)
+ 
+ select gc_to_sec(1000000)::numeric(20,5);
+   gc_to_sec   
+ --------------
+  998976.08618
+ (1 row)
+ 
+ --
+ -- Set coordinates using latitude and longitude.
+ -- Extract each coordinate separately so we can round them.
+ --
+ select cube_ll_coord(ll_to_earth(0,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,0),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord 
+ ---------------+---------------+---------------
+  6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(360,360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(360,360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(360,360),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord 
+ ---------------+---------------+---------------
+  6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(180,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,180),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord 
+ ---------------+---------------+---------------
+  6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(180,360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,360),3)::numeric(20,5);
+  cube_ll_coord  | cube_ll_coord | cube_ll_coord 
+ ----------------+---------------+---------------
+  -6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(-180,-360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-180,-360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-180,-360),3)::numeric(20,5);
+  cube_ll_coord  | cube_ll_coord | cube_ll_coord 
+ ----------------+---------------+---------------
+  -6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(0,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,180),3)::numeric(20,5);
+  cube_ll_coord  | cube_ll_coord | cube_ll_coord 
+ ----------------+---------------+---------------
+  -6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(0,-180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,-180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,-180),3)::numeric(20,5);
+  cube_ll_coord  | cube_ll_coord | cube_ll_coord 
+ ----------------+---------------+---------------
+  -6378168.00000 |       0.00000 |       0.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(90,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,0),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord 
+ ---------------+---------------+---------------
+        0.00000 |       0.00000 | 6378168.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(90,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,180),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord 
+ ---------------+---------------+---------------
+        0.00000 |       0.00000 | 6378168.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(-90,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,0),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord  
+ ---------------+---------------+----------------
+        0.00000 |       0.00000 | -6378168.00000
+ (1 row)
+ 
+ select cube_ll_coord(ll_to_earth(-90,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,180),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord  
+ ---------------+---------------+----------------
+        0.00000 |       0.00000 | -6378168.00000
+ (1 row)
+ 
+ --
+ -- Test getting the latitude of a location.
+ --
+ select latitude(ll_to_earth(0,0))::numeric(20,10);
+    latitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(45,0))::numeric(20,10);
+    latitude    
+ ---------------
+  45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(90,0))::numeric(20,10);
+    latitude    
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-45,0))::numeric(20,10);
+     latitude    
+ ----------------
+  -45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-90,0))::numeric(20,10);
+     latitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(0,90))::numeric(20,10);
+    latitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(45,90))::numeric(20,10);
+    latitude    
+ ---------------
+  45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(90,90))::numeric(20,10);
+    latitude    
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-45,90))::numeric(20,10);
+     latitude    
+ ----------------
+  -45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-90,90))::numeric(20,10);
+     latitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(0,180))::numeric(20,10);
+    latitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(45,180))::numeric(20,10);
+    latitude    
+ ---------------
+  45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(90,180))::numeric(20,10);
+    latitude    
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-45,180))::numeric(20,10);
+     latitude    
+ ----------------
+  -45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-90,180))::numeric(20,10);
+     latitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(0,-90))::numeric(20,10);
+    latitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(45,-90))::numeric(20,10);
+    latitude    
+ ---------------
+  45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(90,-90))::numeric(20,10);
+    latitude    
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-45,-90))::numeric(20,10);
+     latitude    
+ ----------------
+  -45.0000000000
+ (1 row)
+ 
+ select latitude(ll_to_earth(-90,-90))::numeric(20,10);
+     latitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ --
+ -- Test getting the longitude of a location.
+ --
+ select longitude(ll_to_earth(0,0))::numeric(20,10);
+   longitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(45,0))::numeric(20,10);
+   longitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(90,0))::numeric(20,10);
+   longitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-45,0))::numeric(20,10);
+   longitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-90,0))::numeric(20,10);
+   longitude   
+ --------------
+  0.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(0,90))::numeric(20,10);
+    longitude   
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(45,90))::numeric(20,10);
+    longitude   
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(90,90))::numeric(20,10);
+    longitude   
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-45,90))::numeric(20,10);
+    longitude   
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-90,90))::numeric(20,10);
+    longitude   
+ ---------------
+  90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(0,180))::numeric(20,10);
+    longitude    
+ ----------------
+  180.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(45,180))::numeric(20,10);
+    longitude    
+ ----------------
+  180.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(90,180))::numeric(20,10);
+    longitude    
+ ----------------
+  180.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-45,180))::numeric(20,10);
+    longitude    
+ ----------------
+  180.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-90,180))::numeric(20,10);
+    longitude    
+ ----------------
+  180.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(0,-90))::numeric(20,10);
+    longitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(45,-90))::numeric(20,10);
+    longitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(90,-90))::numeric(20,10);
+    longitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-45,-90))::numeric(20,10);
+    longitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ select longitude(ll_to_earth(-90,-90))::numeric(20,10);
+    longitude    
+ ----------------
+  -90.0000000000
+ (1 row)
+ 
+ --
+ -- For the distance tests the following is some real life data.
+ --
+ -- Chicago has a latitude of 41.8 and a longitude of 87.6.
+ -- Albuquerque has a latitude of 35.1 and a longitude of 106.7.
+ -- (Note that latitude and longitude are specified differently
+ -- in the cube based functions than for the point based functions.)
+ --
+ --
+ -- Test getting the distance between two points using earth_distance.
+ --
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,0))::numeric(20,5);
+  earth_distance 
+ ----------------
+         0.00000
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,180))::numeric(20,5);
+  earth_distance 
+ ----------------
+  20037605.73216
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(90,0))::numeric(20,5);
+  earth_distance 
+ ----------------
+  10018802.86608
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,90))::numeric(20,5);
+  earth_distance 
+ ----------------
+  10018802.86608
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))::numeric(20,5);
+  earth_distance 
+ ----------------
+    111320.03185
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(1,0))::numeric(20,5);
+  earth_distance 
+ ----------------
+    111320.03185
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(30,0),ll_to_earth(30,1))::numeric(20,5);
+  earth_distance 
+ ----------------
+     96405.66962
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(30,0),ll_to_earth(31,0))::numeric(20,5);
+  earth_distance 
+ ----------------
+    111320.03185
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(60,0),ll_to_earth(60,1))::numeric(20,5);
+  earth_distance 
+ ----------------
+     55659.48608
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(60,0),ll_to_earth(61,0))::numeric(20,5);
+  earth_distance 
+ ----------------
+    111320.03185
+ (1 row)
+ 
+ select earth_distance(ll_to_earth(41.8,87.6),ll_to_earth(35.1,106.7))::numeric(20,5);
+  earth_distance 
+ ----------------
+   1819303.21265
+ (1 row)
+ 
+ select (earth_distance(ll_to_earth(41.8,87.6),ll_to_earth(35.1,106.7))*
+       100./2.54/12./5280.)::numeric(20,5);
+   numeric   
+ ------------
+  1130.46261
+ (1 row)
+ 
  --
  -- Test getting the distance between two points using geo_distance.
  --
! select geo_distance('(0,0)'::point,'(0,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
        0.00000
  (1 row)
  
! select geo_distance('(0,0)'::point,'(180,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
    12436.77274
  (1 row)
  
! select geo_distance('(0,0)'::point,'(0,90)'::point)::numeric(20,5);
   geo_distance 
  --------------
     6218.38637
  (1 row)
  
! select geo_distance('(0,0)'::point,'(90,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
     6218.38637
  (1 row)
  
! select geo_distance('(0,0)'::point,'(1,0)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! select geo_distance('(0,0)'::point,'(0,1)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! select geo_distance('(0,30)'::point,'(1,30)'::point)::numeric(20,5);
   geo_distance 
  --------------
       59.83626
  (1 row)
  
! select geo_distance('(0,30)'::point,'(0,31)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! select geo_distance('(0,60)'::point,'(1,60)'::point)::numeric(20,5);
   geo_distance 
  --------------
       34.54626
  (1 row)
  
! select geo_distance('(0,60)'::point,'(0,61)'::point)::numeric(20,5);
   geo_distance 
  --------------
       69.09318
  (1 row)
  
! select geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)::numeric(20,5);
   geo_distance 
  --------------
     1129.18983
  (1 row)
  
! select (geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
      numeric    
  ---------------
   1817254.87730
***************
*** 84,158 ****
  --
  -- Test getting the distance between two points using the <@> operator.
  --
! SELECT ('(0,0)'::point <@> '(0,0)'::point)::numeric(20,5);
   numeric 
  ---------
   0.00000
  (1 row)
  
! SELECT ('(0,0)'::point <@> '(180,0)'::point)::numeric(20,5);
     numeric   
  -------------
   12436.77274
  (1 row)
  
! SELECT ('(0,0)'::point <@> '(0,90)'::point)::numeric(20,5);
    numeric   
  ------------
   6218.38637
  (1 row)
  
! SELECT ('(0,0)'::point <@> '(90,0)'::point)::numeric(20,5);
    numeric   
  ------------
   6218.38637
  (1 row)
  
! SELECT ('(0,0)'::point <@> '(1,0)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! SELECT ('(0,0)'::point <@> '(0,1)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! SELECT ('(0,30)'::point <@> '(1,30)'::point)::numeric(20,5);
   numeric  
  ----------
   59.83626
  (1 row)
  
! SELECT ('(0,30)'::point <@> '(0,31)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! SELECT ('(0,60)'::point <@> '(1,60)'::point)::numeric(20,5);
   numeric  
  ----------
   34.54626
  (1 row)
  
! SELECT ('(0,60)'::point <@> '(0,61)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! SELECT ('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)::numeric(20,5);
    numeric   
  ------------
   1129.18983
  (1 row)
  
! SELECT (('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
      numeric    
  ---------------
   1817254.87730
  (1 row)
  
--- 631,948 ----
  --
  -- Test getting the distance between two points using the <@> operator.
  --
! select ('(0,0)'::point <@> '(0,0)'::point)::numeric(20,5);
   numeric 
  ---------
   0.00000
  (1 row)
  
! select ('(0,0)'::point <@> '(180,0)'::point)::numeric(20,5);
     numeric   
  -------------
   12436.77274
  (1 row)
  
! select ('(0,0)'::point <@> '(0,90)'::point)::numeric(20,5);
    numeric   
  ------------
   6218.38637
  (1 row)
  
! select ('(0,0)'::point <@> '(90,0)'::point)::numeric(20,5);
    numeric   
  ------------
   6218.38637
  (1 row)
  
! select ('(0,0)'::point <@> '(1,0)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! select ('(0,0)'::point <@> '(0,1)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! select ('(0,30)'::point <@> '(1,30)'::point)::numeric(20,5);
   numeric  
  ----------
   59.83626
  (1 row)
  
! select ('(0,30)'::point <@> '(0,31)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! select ('(0,60)'::point <@> '(1,60)'::point)::numeric(20,5);
   numeric  
  ----------
   34.54626
  (1 row)
  
! select ('(0,60)'::point <@> '(0,61)'::point)::numeric(20,5);
   numeric  
  ----------
   69.09318
  (1 row)
  
! select ('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)::numeric(20,5);
    numeric   
  ------------
   1129.18983
  (1 row)
  
! select (('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
      numeric    
  ---------------
   1817254.87730
+ (1 row)
+ 
+ --
+ -- Test getting a bounding box around points.
+ --
+ select cube_ll_coord(earth_box(ll_to_earth(0,0),112000),1)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),112000),2)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),112000),3)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),1)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),2)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),3)::numeric(20,5);
+  cube_ll_coord | cube_ll_coord | cube_ll_coord | cube_ur_coord | cube_ur_coord | cube_ur_coord 
+ ---------------+---------------+---------------+---------------+---------------+---------------
+  6266169.43896 | -111998.56104 | -111998.56104 | 6490166.56104 |  111998.56104 |  111998.56104
+ (1 row)
+ 
+ select cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),1)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),2)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),3)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),1)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),2)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),3)::numeric(20,5);
+  cube_ll_coord  |  cube_ll_coord  |  cube_ll_coord  | cube_ur_coord  | cube_ur_coord  | cube_ur_coord  
+ ----------------+-----------------+-----------------+----------------+----------------+----------------
+  -6378168.00000 | -12756336.00000 | -12756336.00000 | 19134504.00000 | 12756336.00000 | 12756336.00000
+ (1 row)
+ 
+ select cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),1)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),2)::numeric(20,5),
+        cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),3)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),1)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),2)::numeric(20,5),
+        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),3)::numeric(20,5);
+  cube_ll_coord  |  cube_ll_coord  |  cube_ll_coord  | cube_ur_coord  | cube_ur_coord  | cube_ur_coord  
+ ----------------+-----------------+-----------------+----------------+----------------+----------------
+  -6378168.00000 | -12756336.00000 | -12756336.00000 | 19134504.00000 | 12756336.00000 | 12756336.00000
+ (1 row)
+ 
+ --
+ -- Test for points that should be in bounding boxes.
+ --
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))*1.00001) @
+        ll_to_earth(0,1);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.1))*1.00001) @
+        ll_to_earth(0,0.1);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.01))*1.00001) @
+        ll_to_earth(0,0.01);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.001))*1.00001) @
+        ll_to_earth(0,0.001);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.0001))*1.00001) @
+        ll_to_earth(0,0.0001);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0.0001,0.0001))*1.00001) @
+        ll_to_earth(0.0001,0.0001);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(45,45),
+        earth_distance(ll_to_earth(45,45),ll_to_earth(45.0001,45.0001))*1.00001) @
+        ll_to_earth(45.0001,45.0001);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select earth_box(ll_to_earth(90,180),
+        earth_distance(ll_to_earth(90,180),ll_to_earth(90.0001,180.0001))*1.00001) @
+        ll_to_earth(90.0001,180.0001);
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ --
+ -- Test for points that shouldn't be in bounding boxes. Note that we need
+ -- to make points way outside, since some points close may be in the box
+ -- but further away than the distance we are testing.
+ --
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))*.57735) @
+        ll_to_earth(0,1);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.1))*.57735) @
+        ll_to_earth(0,0.1);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.01))*.57735) @
+        ll_to_earth(0,0.01);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.001))*.57735) @
+        ll_to_earth(0,0.001);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.0001))*.57735) @
+        ll_to_earth(0,0.0001);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(0,0),
+        earth_distance(ll_to_earth(0,0),ll_to_earth(0.0001,0.0001))*.57735) @
+        ll_to_earth(0.0001,0.0001);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(45,45),
+        earth_distance(ll_to_earth(45,45),ll_to_earth(45.0001,45.0001))*.57735) @
+        ll_to_earth(45.0001,45.0001);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ select earth_box(ll_to_earth(90,180),
+        earth_distance(ll_to_earth(90,180),ll_to_earth(90.0001,180.0001))*.57735) @
+        ll_to_earth(90.0001,180.0001);
+  ?column? 
+ ----------
+  f
+ (1 row)
+ 
+ --
+ -- Test the recommended constraints.
+ --
+ select is_point(ll_to_earth(0,0));
+ ERROR:  Function is_point(earth) does not exist
+ 	Unable to identify a function that satisfies the given argument types
+ 	You may need to add explicit typecasts
+ select cube_dim(ll_to_earth(0,0)) <= 3;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select abs(cube_distance(ll_to_earth(0,0), '(0)'::cube) / earth() - 1) <
+        '10e-12'::float8;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select is_point(ll_to_earth(30,60));
+ ERROR:  Function is_point(earth) does not exist
+ 	Unable to identify a function that satisfies the given argument types
+ 	You may need to add explicit typecasts
+ select cube_dim(ll_to_earth(30,60)) <= 3;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select abs(cube_distance(ll_to_earth(30,60), '(0)'::cube) / earth() - 1) <
+        '10e-12'::float8;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select is_point(ll_to_earth(60,90));
+ ERROR:  Function is_point(earth) does not exist
+ 	Unable to identify a function that satisfies the given argument types
+ 	You may need to add explicit typecasts
+ select cube_dim(ll_to_earth(60,90)) <= 3;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select abs(cube_distance(ll_to_earth(60,90), '(0)'::cube) / earth() - 1) <
+        '10e-12'::float8;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select is_point(ll_to_earth(-30,-90));
+ ERROR:  Function is_point(earth) does not exist
+ 	Unable to identify a function that satisfies the given argument types
+ 	You may need to add explicit typecasts
+ select cube_dim(ll_to_earth(-30,-90)) <= 3;
+  ?column? 
+ ----------
+  t
+ (1 row)
+ 
+ select abs(cube_distance(ll_to_earth(-30,-90), '(0)'::cube) / earth() - 1) <
+        '10e-12'::float8;
+  ?column? 
+ ----------
+  t
  (1 row)
  
Index: contrib/earthdistance/sql/earthdistance.sql
===================================================================
RCS file: /cvsroot/contrib/earthdistance/sql/earthdistance.sql,v
retrieving revision 1.5
diff -c -c -r1.5 earthdistance.sql
*** contrib/earthdistance/sql/earthdistance.sql	21 Oct 2002 20:33:21 -0000	1.5
--- contrib/earthdistance/sql/earthdistance.sql	8 Nov 2002 20:18:27 -0000
***************
*** 4,45 ****
  
  --
  -- first, define the datatype.  Turn off echoing so that expected file
! -- does not depend on contents of earthdistance.sql.
  --
  \set ECHO none
  \i earthdistance.sql
  \set ECHO all
  
  --
  -- Test getting the distance between two points using geo_distance.
  --
  
! SELECT geo_distance('(0,0)'::point,'(0,0)'::point)::numeric(20,5);
! SELECT geo_distance('(0,0)'::point,'(180,0)'::point)::numeric(20,5);
! SELECT geo_distance('(0,0)'::point,'(0,90)'::point)::numeric(20,5);
! SELECT geo_distance('(0,0)'::point,'(90,0)'::point)::numeric(20,5);
! SELECT geo_distance('(0,0)'::point,'(1,0)'::point)::numeric(20,5);
! SELECT geo_distance('(0,0)'::point,'(0,1)'::point)::numeric(20,5);
! SELECT geo_distance('(0,30)'::point,'(1,30)'::point)::numeric(20,5);
! SELECT geo_distance('(0,30)'::point,'(0,31)'::point)::numeric(20,5);
! SELECT geo_distance('(0,60)'::point,'(1,60)'::point)::numeric(20,5);
! SELECT geo_distance('(0,60)'::point,'(0,61)'::point)::numeric(20,5);
! SELECT geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)::numeric(20,5);
! SELECT (geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
  
  --
  -- Test getting the distance between two points using the <@> operator.
  --
  
! SELECT ('(0,0)'::point <@> '(0,0)'::point)::numeric(20,5);
! SELECT ('(0,0)'::point <@> '(180,0)'::point)::numeric(20,5);
! SELECT ('(0,0)'::point <@> '(0,90)'::point)::numeric(20,5);
! SELECT ('(0,0)'::point <@> '(90,0)'::point)::numeric(20,5);
! SELECT ('(0,0)'::point <@> '(1,0)'::point)::numeric(20,5);
! SELECT ('(0,0)'::point <@> '(0,1)'::point)::numeric(20,5);
! SELECT ('(0,30)'::point <@> '(1,30)'::point)::numeric(20,5);
! SELECT ('(0,30)'::point <@> '(0,31)'::point)::numeric(20,5);
! SELECT ('(0,60)'::point <@> '(1,60)'::point)::numeric(20,5);
! SELECT ('(0,60)'::point <@> '(0,61)'::point)::numeric(20,5);
! SELECT ('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)::numeric(20,5);
! SELECT (('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
--- 4,299 ----
  
  --
  -- first, define the datatype.  Turn off echoing so that expected file
! -- does not depend on contents of earthdistance.sql or cube.sql.
  --
  \set ECHO none
+ \i ../cube/cube.sql
  \i earthdistance.sql
  \set ECHO all
  
  --
+ -- The radius of the Earth we are using.
+ --
+ 
+ select earth()::numeric(20,5);
+ 
+ --
+ -- Convert straight line distances to great circle distances.
+ --
+ select (pi()*earth())::numeric(20,5);
+ select sec_to_gc(0)::numeric(20,5);
+ select sec_to_gc(2*earth())::numeric(20,5);
+ select sec_to_gc(10*earth())::numeric(20,5);
+ select sec_to_gc(-earth())::numeric(20,5);
+ select sec_to_gc(1000)::numeric(20,5);
+ select sec_to_gc(10000)::numeric(20,5);
+ select sec_to_gc(100000)::numeric(20,5);
+ select sec_to_gc(1000000)::numeric(20,5);
+ 
+ --
+ -- Convert great circle distances to straight line distances.
+ --
+ 
+ select gc_to_sec(0)::numeric(20,5);
+ select gc_to_sec(sec_to_gc(2*earth()))::numeric(20,5);
+ select gc_to_sec(10*earth())::numeric(20,5);
+ select gc_to_sec(pi()*earth())::numeric(20,5);
+ select gc_to_sec(-1000)::numeric(20,5);
+ select gc_to_sec(1000)::numeric(20,5);
+ select gc_to_sec(10000)::numeric(20,5);
+ select gc_to_sec(100000)::numeric(20,5);
+ select gc_to_sec(1000000)::numeric(20,5);
+ 
+ --
+ -- Set coordinates using latitude and longitude.
+ -- Extract each coordinate separately so we can round them.
+ --
+ 
+ select cube_ll_coord(ll_to_earth(0,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,0),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(360,360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(360,360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(360,360),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(180,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,180),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(180,360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(180,360),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(-180,-360),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-180,-360),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-180,-360),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(0,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,180),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(0,-180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,-180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(0,-180),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(90,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,0),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(90,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(90,180),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(-90,0),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,0),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,0),3)::numeric(20,5);
+ select cube_ll_coord(ll_to_earth(-90,180),1)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,180),2)::numeric(20,5),
+  cube_ll_coord(ll_to_earth(-90,180),3)::numeric(20,5);
+ 
+ --
+ -- Test getting the latitude of a location.
+ --
+ 
+ select latitude(ll_to_earth(0,0))::numeric(20,10);
+ select latitude(ll_to_earth(45,0))::numeric(20,10);
+ select latitude(ll_to_earth(90,0))::numeric(20,10);
+ select latitude(ll_to_earth(-45,0))::numeric(20,10);
+ select latitude(ll_to_earth(-90,0))::numeric(20,10);
+ select latitude(ll_to_earth(0,90))::numeric(20,10);
+ select latitude(ll_to_earth(45,90))::numeric(20,10);
+ select latitude(ll_to_earth(90,90))::numeric(20,10);
+ select latitude(ll_to_earth(-45,90))::numeric(20,10);
+ select latitude(ll_to_earth(-90,90))::numeric(20,10);
+ select latitude(ll_to_earth(0,180))::numeric(20,10);
+ select latitude(ll_to_earth(45,180))::numeric(20,10);
+ select latitude(ll_to_earth(90,180))::numeric(20,10);
+ select latitude(ll_to_earth(-45,180))::numeric(20,10);
+ select latitude(ll_to_earth(-90,180))::numeric(20,10);
+ select latitude(ll_to_earth(0,-90))::numeric(20,10);
+ select latitude(ll_to_earth(45,-90))::numeric(20,10);
+ select latitude(ll_to_earth(90,-90))::numeric(20,10);
+ select latitude(ll_to_earth(-45,-90))::numeric(20,10);
+ select latitude(ll_to_earth(-90,-90))::numeric(20,10);
+ 
+ --
+ -- Test getting the longitude of a location.
+ --
+ 
+ select longitude(ll_to_earth(0,0))::numeric(20,10);
+ select longitude(ll_to_earth(45,0))::numeric(20,10);
+ select longitude(ll_to_earth(90,0))::numeric(20,10);
+ select longitude(ll_to_earth(-45,0))::numeric(20,10);
+ select longitude(ll_to_earth(-90,0))::numeric(20,10);
+ select longitude(ll_to_earth(0,90))::numeric(20,10);
+ select longitude(ll_to_earth(45,90))::numeric(20,10);
+ select longitude(ll_to_earth(90,90))::numeric(20,10);
+ select longitude(ll_to_earth(-45,90))::numeric(20,10);
+ select longitude(ll_to_earth(-90,90))::numeric(20,10);
+ select longitude(ll_to_earth(0,180))::numeric(20,10);
+ select longitude(ll_to_earth(45,180))::numeric(20,10);
+ select longitude(ll_to_earth(90,180))::numeric(20,10);
+ select longitude(ll_to_earth(-45,180))::numeric(20,10);
+ select longitude(ll_to_earth(-90,180))::numeric(20,10);
+ select longitude(ll_to_earth(0,-90))::numeric(20,10);
+ select longitude(ll_to_earth(45,-90))::numeric(20,10);
+ select longitude(ll_to_earth(90,-90))::numeric(20,10);
+ select longitude(ll_to_earth(-45,-90))::numeric(20,10);
+ select longitude(ll_to_earth(-90,-90))::numeric(20,10);
+ 
+ --
+ -- For the distance tests the following is some real life data.
+ --
+ -- Chicago has a latitude of 41.8 and a longitude of 87.6.
+ -- Albuquerque has a latitude of 35.1 and a longitude of 106.7.
+ -- (Note that latitude and longitude are specified differently
+ -- in the cube based functions than for the point based functions.)
+ --
+ 
+ --
+ -- Test getting the distance between two points using earth_distance.
+ --
+ 
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,0))::numeric(20,5);
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,180))::numeric(20,5);
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(90,0))::numeric(20,5);
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,90))::numeric(20,5);
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))::numeric(20,5);
+ select earth_distance(ll_to_earth(0,0),ll_to_earth(1,0))::numeric(20,5);
+ select earth_distance(ll_to_earth(30,0),ll_to_earth(30,1))::numeric(20,5);
+ select earth_distance(ll_to_earth(30,0),ll_to_earth(31,0))::numeric(20,5);
+ select earth_distance(ll_to_earth(60,0),ll_to_earth(60,1))::numeric(20,5);
+ select earth_distance(ll_to_earth(60,0),ll_to_earth(61,0))::numeric(20,5);
+ select earth_distance(ll_to_earth(41.8,87.6),ll_to_earth(35.1,106.7))::numeric(20,5);
+ select (earth_distance(ll_to_earth(41.8,87.6),ll_to_earth(35.1,106.7))*
+       100./2.54/12./5280.)::numeric(20,5);
+ 
+ --
  -- Test getting the distance between two points using geo_distance.
  --
  
! select geo_distance('(0,0)'::point,'(0,0)'::point)::numeric(20,5);
! select geo_distance('(0,0)'::point,'(180,0)'::point)::numeric(20,5);
! select geo_distance('(0,0)'::point,'(0,90)'::point)::numeric(20,5);
! select geo_distance('(0,0)'::point,'(90,0)'::point)::numeric(20,5);
! select geo_distance('(0,0)'::point,'(1,0)'::point)::numeric(20,5);
! select geo_distance('(0,0)'::point,'(0,1)'::point)::numeric(20,5);
! select geo_distance('(0,30)'::point,'(1,30)'::point)::numeric(20,5);
! select geo_distance('(0,30)'::point,'(0,31)'::point)::numeric(20,5);
! select geo_distance('(0,60)'::point,'(1,60)'::point)::numeric(20,5);
! select geo_distance('(0,60)'::point,'(0,61)'::point)::numeric(20,5);
! select geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)::numeric(20,5);
! select (geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
  
  --
  -- Test getting the distance between two points using the <@> operator.
  --
  
! select ('(0,0)'::point <@> '(0,0)'::point)::numeric(20,5);
! select ('(0,0)'::point <@> '(180,0)'::point)::numeric(20,5);
! select ('(0,0)'::point <@> '(0,90)'::point)::numeric(20,5);
! select ('(0,0)'::point <@> '(90,0)'::point)::numeric(20,5);
! select ('(0,0)'::point <@> '(1,0)'::point)::numeric(20,5);
! select ('(0,0)'::point <@> '(0,1)'::point)::numeric(20,5);
! select ('(0,30)'::point <@> '(1,30)'::point)::numeric(20,5);
! select ('(0,30)'::point <@> '(0,31)'::point)::numeric(20,5);
! select ('(0,60)'::point <@> '(1,60)'::point)::numeric(20,5);
! select ('(0,60)'::point <@> '(0,61)'::point)::numeric(20,5);
! select ('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)::numeric(20,5);
! select (('(87.6,41.8)'::point <@> '(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
! 
! --
! -- Test getting a bounding box around points.
! --
! 
! select cube_ll_coord(earth_box(ll_to_earth(0,0),112000),1)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),112000),2)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),112000),3)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),1)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),2)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),112000),3)::numeric(20,5);
! select cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),1)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),2)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),pi()*earth()),3)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),1)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),2)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),pi()*earth()),3)::numeric(20,5);
! select cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),1)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),2)::numeric(20,5),
!        cube_ll_coord(earth_box(ll_to_earth(0,0),10*earth()),3)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),1)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),2)::numeric(20,5),
!        cube_ur_coord(earth_box(ll_to_earth(0,0),10*earth()),3)::numeric(20,5);
! 
! --
! -- Test for points that should be in bounding boxes.
! --
! 
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))*1.00001) @
!        ll_to_earth(0,1);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.1))*1.00001) @
!        ll_to_earth(0,0.1);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.01))*1.00001) @
!        ll_to_earth(0,0.01);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.001))*1.00001) @
!        ll_to_earth(0,0.001);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.0001))*1.00001) @
!        ll_to_earth(0,0.0001);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0.0001,0.0001))*1.00001) @
!        ll_to_earth(0.0001,0.0001);
! select earth_box(ll_to_earth(45,45),
!        earth_distance(ll_to_earth(45,45),ll_to_earth(45.0001,45.0001))*1.00001) @
!        ll_to_earth(45.0001,45.0001);
! select earth_box(ll_to_earth(90,180),
!        earth_distance(ll_to_earth(90,180),ll_to_earth(90.0001,180.0001))*1.00001) @
!        ll_to_earth(90.0001,180.0001);
! 
! --
! -- Test for points that shouldn't be in bounding boxes. Note that we need
! -- to make points way outside, since some points close may be in the box
! -- but further away than the distance we are testing.
! --
! 
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,1))*.57735) @
!        ll_to_earth(0,1);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.1))*.57735) @
!        ll_to_earth(0,0.1);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.01))*.57735) @
!        ll_to_earth(0,0.01);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.001))*.57735) @
!        ll_to_earth(0,0.001);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0,0.0001))*.57735) @
!        ll_to_earth(0,0.0001);
! select earth_box(ll_to_earth(0,0),
!        earth_distance(ll_to_earth(0,0),ll_to_earth(0.0001,0.0001))*.57735) @
!        ll_to_earth(0.0001,0.0001);
! select earth_box(ll_to_earth(45,45),
!        earth_distance(ll_to_earth(45,45),ll_to_earth(45.0001,45.0001))*.57735) @
!        ll_to_earth(45.0001,45.0001);
! select earth_box(ll_to_earth(90,180),
!        earth_distance(ll_to_earth(90,180),ll_to_earth(90.0001,180.0001))*.57735) @
!        ll_to_earth(90.0001,180.0001);
! 
! --
! -- Test the recommended constraints.
! --
! 
! select is_point(ll_to_earth(0,0));
! select cube_dim(ll_to_earth(0,0)) <= 3;
! select abs(cube_distance(ll_to_earth(0,0), '(0)'::cube) / earth() - 1) <
!        '10e-12'::float8;
! select is_point(ll_to_earth(30,60));
! select cube_dim(ll_to_earth(30,60)) <= 3;
! select abs(cube_distance(ll_to_earth(30,60), '(0)'::cube) / earth() - 1) <
!        '10e-12'::float8;
! select is_point(ll_to_earth(60,90));
! select cube_dim(ll_to_earth(60,90)) <= 3;
! select abs(cube_distance(ll_to_earth(60,90), '(0)'::cube) / earth() - 1) <
!        '10e-12'::float8;
! select is_point(ll_to_earth(-30,-90));
! select cube_dim(ll_to_earth(-30,-90)) <= 3;
! select abs(cube_distance(ll_to_earth(-30,-90), '(0)'::cube) / earth() - 1) <
!        '10e-12'::float8;