----------------------------------------------------------------------
-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.
+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
long2,
lat2;
double longdiff;
- double sino;
+ double sino;
double *resultp = palloc(sizeof(double));
/* convert degrees to radians */
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)
--
--
-- first, define the datatype. Turn off echoing so that expected file
--- does not depend on contents of earthdistance.sql.
+-- 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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+select (geo_distance('(87.6,41.8)'::point,'(106.7,35.1)'::point)*5280.*12.*2.54/100.)::numeric(20,5);
numeric
---------------
1817254.87730
--
-- Test getting the distance between two points using the <@> operator.
--
-SELECT ('(0,0)'::point <@> '(0,0)'::point)::numeric(20,5);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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);
+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)
+
--
-- first, define the datatype. Turn off echoing so that expected file
--- does not depend on contents of earthdistance.sql.
+-- 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);
+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);
+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;
projects / postgresql / commitdiff