--
-- GEOMETRY
--
-- Back off displayed precision a little bit to reduce platform-to-platform
-- variation in results.
SET extra_float_digits TO -3;
--
-- Points
--
SELECT '' AS four, center(f1) AS center
   FROM BOX_TBL;
 four | center  
------+---------
      | (1,1)
      | (2,2)
      | (2.5,3)
      | (3,3)
(4 rows)

SELECT '' AS four, (@@ f1) AS center
   FROM BOX_TBL;
 four | center  
------+---------
      | (1,1)
      | (2,2)
      | (2.5,3)
      | (3,3)
(4 rows)

SELECT '' AS six, point(f1) AS center
   FROM CIRCLE_TBL;
 six |  center   
-----+-----------
     | (5,1)
     | (1,2)
     | (1,3)
     | (1,2)
     | (100,200)
     | (100,1)
(6 rows)

SELECT '' AS six, (@@ f1) AS center
   FROM CIRCLE_TBL;
 six |  center   
-----+-----------
     | (5,1)
     | (1,2)
     | (1,3)
     | (1,2)
     | (100,200)
     | (100,1)
(6 rows)

SELECT '' AS two, (@@ f1) AS center
   FROM POLYGON_TBL
   WHERE (# f1) > 2;
 two |            center             
-----+-------------------------------
     | (1.33333333333,1.33333333333)
     | (2.33333333333,1.33333333333)
(2 rows)

-- "is horizontal" function
SELECT '' AS two, p1.f1
   FROM POINT_TBL p1
   WHERE ishorizontal(p1.f1, point '(0,0)');
 two |   f1    
-----+---------
     | (0,0)
     | (-10,0)
(2 rows)

-- "is horizontal" operator
SELECT '' AS two, p1.f1
   FROM POINT_TBL p1
   WHERE p1.f1 ?- point '(0,0)';
 two |   f1    
-----+---------
     | (0,0)
     | (-10,0)
(2 rows)

-- "is vertical" function
SELECT '' AS one, p1.f1
   FROM POINT_TBL p1
   WHERE isvertical(p1.f1, point '(5.1,34.5)');
 one |     f1     
-----+------------
     | (5.1,34.5)
(1 row)

-- "is vertical" operator
SELECT '' AS one, p1.f1
   FROM POINT_TBL p1
   WHERE p1.f1 ?| point '(5.1,34.5)';
 one |     f1     
-----+------------
     | (5.1,34.5)
(1 row)

--
-- Line segments
--
-- intersection
SELECT '' AS count, p.f1, l.s, l.s # p.f1 AS intersection
   FROM LSEG_TBL l, POINT_TBL p;
ERROR:  operator does not exist: lseg # point
LINE 1: SELECT '' AS count, p.f1, l.s, l.s # p.f1 AS intersection
                                           ^
HINT:  No operator matches the given name and argument type(s). You might need to add explicit type casts.
-- closest point
SELECT '' AS thirty, p.f1, l.s, p.f1 ## l.s AS closest
   FROM LSEG_TBL l, POINT_TBL p;
 thirty |     f1     |               s               |             closest              
--------+------------+-------------------------------+----------------------------------
        | (0,0)      | [(1,2),(3,4)]                 | (1,2)
        | (0,0)      | [(0,0),(6,6)]                 | (0,0)
        | (0,0)      | [(10,-10),(-3,-4)]            | (-2.0487804878,-4.43902439024)
        | (0,0)      | [(-1000000,200),(300000,-40)] | (0.00284023658959,15.3846148603)
        | (0,0)      | [(11,22),(33,44)]             | (11,22)
        | (-10,0)    | [(1,2),(3,4)]                 | (1,2)
        | (-10,0)    | [(0,0),(6,6)]                 | (0,0)
        | (-10,0)    | [(10,-10),(-3,-4)]            | (-3,-4)
        | (-10,0)    | [(-1000000,200),(300000,-40)] | (-9.99715942258,15.386461014)
        | (-10,0)    | [(11,22),(33,44)]             | (11,22)
        | (-3,4)     | [(1,2),(3,4)]                 | (1,2)
        | (-3,4)     | [(0,0),(6,6)]                 | (0.5,0.5)
        | (-3,4)     | [(10,-10),(-3,-4)]            | (-3,-4)
        | (-3,4)     | [(-1000000,200),(300000,-40)] | (-2.99789812268,15.3851688427)
        | (-3,4)     | [(11,22),(33,44)]             | (11,22)
        | (5.1,34.5) | [(1,2),(3,4)]                 | (3,4)
        | (5.1,34.5) | [(0,0),(6,6)]                 | (6,6)
        | (5.1,34.5) | [(10,-10),(-3,-4)]            | (-3,-4)
        | (5.1,34.5) | [(-1000000,200),(300000,-40)] | (5.09647083221,15.3836744977)
        | (5.1,34.5) | [(11,22),(33,44)]             | (14.3,25.3)
        | (-5,-12)   | [(1,2),(3,4)]                 | (1,2)
        | (-5,-12)   | [(0,0),(6,6)]                 | (0,0)
        | (-5,-12)   | [(10,-10),(-3,-4)]            | (-1.60487804878,-4.64390243902)
        | (-5,-12)   | [(-1000000,200),(300000,-40)] | (-4.99494420846,15.3855375282)
        | (-5,-12)   | [(11,22),(33,44)]             | (11,22)
        | (10,10)    | [(1,2),(3,4)]                 | (3,4)
        | (10,10)    | [(0,0),(6,6)]                 | (6,6)
        | (10,10)    | [(10,-10),(-3,-4)]            | (2.39024390244,-6.48780487805)
        | (10,10)    | [(-1000000,200),(300000,-40)] | (10.000993742,15.3827690473)
        | (10,10)    | [(11,22),(33,44)]             | (11,22)
(30 rows)

--
-- Boxes
--
SELECT '' as six, box(f1) AS box FROM CIRCLE_TBL;
 six |                              box                               
-----+----------------------------------------------------------------
     | (7.12132034356,3.12132034356),(2.87867965644,-1.12132034356)
     | (71.7106781187,72.7106781187),(-69.7106781187,-68.7106781187)
     | (4.53553390593,6.53553390593),(-2.53553390593,-0.535533905933)
     | (3.12132034356,4.12132034356),(-1.12132034356,-0.12132034356)
     | (107.071067812,207.071067812),(92.9289321881,192.928932188)
     | (181.317279836,82.3172798365),(18.6827201635,-80.3172798365)
(6 rows)

-- translation
SELECT '' AS twentyfour, b.f1 + p.f1 AS translation
   FROM BOX_TBL b, POINT_TBL p;
 twentyfour |       translation       
------------+-------------------------
            | (2,2),(0,0)
            | (3,3),(1,1)
            | (2.5,3.5),(2.5,2.5)
            | (3,3),(3,3)
            | (-8,2),(-10,0)
            | (-7,3),(-9,1)
            | (-7.5,3.5),(-7.5,2.5)
            | (-7,3),(-7,3)
            | (-1,6),(-3,4)
            | (0,7),(-2,5)
            | (-0.5,7.5),(-0.5,6.5)
            | (0,7),(0,7)
            | (7.1,36.5),(5.1,34.5)
            | (8.1,37.5),(6.1,35.5)
            | (7.6,38),(7.6,37)
            | (8.1,37.5),(8.1,37.5)
            | (-3,-10),(-5,-12)
            | (-2,-9),(-4,-11)
            | (-2.5,-8.5),(-2.5,-9.5)
            | (-2,-9),(-2,-9)
            | (12,12),(10,10)
            | (13,13),(11,11)
            | (12.5,13.5),(12.5,12.5)
            | (13,13),(13,13)
(24 rows)

SELECT '' AS twentyfour, b.f1 - p.f1 AS translation
   FROM BOX_TBL b, POINT_TBL p;
 twentyfour |        translation        
------------+---------------------------
            | (2,2),(0,0)
            | (3,3),(1,1)
            | (2.5,3.5),(2.5,2.5)
            | (3,3),(3,3)
            | (12,2),(10,0)
            | (13,3),(11,1)
            | (12.5,3.5),(12.5,2.5)
            | (13,3),(13,3)
            | (5,-2),(3,-4)
            | (6,-1),(4,-3)
            | (5.5,-0.5),(5.5,-1.5)
            | (6,-1),(6,-1)
            | (-3.1,-32.5),(-5.1,-34.5)
            | (-2.1,-31.5),(-4.1,-33.5)
            | (-2.6,-31),(-2.6,-32)
            | (-2.1,-31.5),(-2.1,-31.5)
            | (7,14),(5,12)
            | (8,15),(6,13)
            | (7.5,15.5),(7.5,14.5)
            | (8,15),(8,15)
            | (-8,-8),(-10,-10)
            | (-7,-7),(-9,-9)
            | (-7.5,-6.5),(-7.5,-7.5)
            | (-7,-7),(-7,-7)
(24 rows)

-- scaling and rotation
SELECT '' AS twentyfour, b.f1 * p.f1 AS rotation
   FROM BOX_TBL b, POINT_TBL p;
 twentyfour |          rotation           
------------+-----------------------------
            | (0,0),(0,0)
            | (0,0),(0,0)
            | (0,0),(0,0)
            | (0,0),(0,0)
            | (0,0),(-20,-20)
            | (-10,-10),(-30,-30)
            | (-25,-25),(-25,-35)
            | (-30,-30),(-30,-30)
            | (0,2),(-14,0)
            | (-7,3),(-21,1)
            | (-17.5,2.5),(-21.5,-0.5)
            | (-21,3),(-21,3)
            | (0,79.2),(-58.8,0)
            | (-29.4,118.8),(-88.2,39.6)
            | (-73.5,104.1),(-108,99)
            | (-88.2,118.8),(-88.2,118.8)
            | (14,0),(0,-34)
            | (21,-17),(7,-51)
            | (29.5,-42.5),(17.5,-47.5)
            | (21,-51),(21,-51)
            | (0,40),(0,0)
            | (0,60),(0,20)
            | (0,60),(-10,50)
            | (0,60),(0,60)
(24 rows)

SELECT '' AS twenty, b.f1 / p.f1 AS rotation
   FROM BOX_TBL b, POINT_TBL p
   WHERE (p.f1 <-> point '(0,0)') >= 1;
 twenty |                               rotation                               
--------+----------------------------------------------------------------------
        | (0,0),(-0.2,-0.2)
        | (0.08,0),(0,-0.56)
        | (0.0651176557644,0),(0,-0.0483449262493)
        | (0,0.0828402366864),(-0.201183431953,0)
        | (0.2,0),(0,0)
        | (-0.1,-0.1),(-0.3,-0.3)
        | (0.12,-0.28),(0.04,-0.84)
        | (0.0976764836466,-0.0241724631247),(0.0325588278822,-0.072517389374)
        | (-0.100591715976,0.12426035503),(-0.301775147929,0.0414201183432)
        | (0.3,0),(0.1,0)
        | (-0.25,-0.25),(-0.25,-0.35)
        | (0.26,-0.7),(0.1,-0.82)
        | (0.109762715209,-0.0562379754329),(0.0813970697055,-0.0604311578117)
        | (-0.251479289941,0.103550295858),(-0.322485207101,0.0739644970414)
        | (0.3,0.05),(0.25,0)
        | (-0.3,-0.3),(-0.3,-0.3)
        | (0.12,-0.84),(0.12,-0.84)
        | (0.0976764836466,-0.072517389374),(0.0976764836466,-0.072517389374)
        | (-0.301775147929,0.12426035503),(-0.301775147929,0.12426035503)
        | (0.3,0),(0.3,0)
(20 rows)

SELECT f1::box
	FROM POINT_TBL;
          f1           
-----------------------
 (0,0),(0,0)
 (-10,0),(-10,0)
 (-3,4),(-3,4)
 (5.1,34.5),(5.1,34.5)
 (-5,-12),(-5,-12)
 (10,10),(10,10)
(6 rows)

SELECT bound_box(a.f1, b.f1)
	FROM BOX_TBL a, BOX_TBL b;
      bound_box      
---------------------
 (2,2),(0,0)
 (3,3),(0,0)
 (2.5,3.5),(0,0)
 (3,3),(0,0)
 (3,3),(0,0)
 (3,3),(1,1)
 (3,3.5),(1,1)
 (3,3),(1,1)
 (2.5,3.5),(0,0)
 (3,3.5),(1,1)
 (2.5,3.5),(2.5,2.5)
 (3,3.5),(2.5,2.5)
 (3,3),(0,0)
 (3,3),(1,1)
 (3,3.5),(2.5,2.5)
 (3,3),(3,3)
(16 rows)

--
-- Paths
--
SELECT '' AS eight, npoints(f1) AS npoints, f1 AS path FROM PATH_TBL;
 eight | npoints |           path            
-------+---------+---------------------------
       |       2 | [(1,2),(3,4)]
       |       2 | ((1,2),(3,4))
       |       4 | [(0,0),(3,0),(4,5),(1,6)]
       |       2 | ((1,2),(3,4))
       |       2 | ((1,2),(3,4))
       |       2 | [(1,2),(3,4)]
       |       2 | [(11,12),(13,14)]
       |       2 | ((11,12),(13,14))
(8 rows)

SELECT '' AS four, path(f1) FROM POLYGON_TBL;
 four |        path         
------+---------------------
      | ((2,0),(2,4),(0,0))
      | ((3,1),(3,3),(1,0))
      | ((0,0))
      | ((0,1),(0,1))
(4 rows)

-- translation
SELECT '' AS eight, p1.f1 + point '(10,10)' AS dist_add
   FROM PATH_TBL p1;
 eight |             dist_add              
-------+-----------------------------------
       | [(11,12),(13,14)]
       | ((11,12),(13,14))
       | [(10,10),(13,10),(14,15),(11,16)]
       | ((11,12),(13,14))
       | ((11,12),(13,14))
       | [(11,12),(13,14)]
       | [(21,22),(23,24)]
       | ((21,22),(23,24))
(8 rows)

-- scaling and rotation
SELECT '' AS eight, p1.f1 * point '(2,-1)' AS dist_mul
   FROM PATH_TBL p1;
 eight |           dist_mul           
-------+------------------------------
       | [(4,3),(10,5)]
       | ((4,3),(10,5))
       | [(0,0),(6,-3),(13,6),(8,11)]
       | ((4,3),(10,5))
       | ((4,3),(10,5))
       | [(4,3),(10,5)]
       | [(34,13),(40,15)]
       | ((34,13),(40,15))
(8 rows)

--
-- Polygons
--
-- containment
SELECT '' AS twentyfour, p.f1, poly.f1, poly.f1 @> p.f1 AS contains
   FROM POLYGON_TBL poly, POINT_TBL p;
 twentyfour |     f1     |         f1          | contains 
------------+------------+---------------------+----------
            | (0,0)      | ((2,0),(2,4),(0,0)) | t
            | (0,0)      | ((3,1),(3,3),(1,0)) | f
            | (0,0)      | ((0,0))             | t
            | (0,0)      | ((0,1),(0,1))       | f
            | (-10,0)    | ((2,0),(2,4),(0,0)) | f
            | (-10,0)    | ((3,1),(3,3),(1,0)) | f
            | (-10,0)    | ((0,0))             | f
            | (-10,0)    | ((0,1),(0,1))       | f
            | (-3,4)     | ((2,0),(2,4),(0,0)) | f
            | (-3,4)     | ((3,1),(3,3),(1,0)) | f
            | (-3,4)     | ((0,0))             | f
            | (-3,4)     | ((0,1),(0,1))       | f
            | (5.1,34.5) | ((2,0),(2,4),(0,0)) | f
            | (5.1,34.5) | ((3,1),(3,3),(1,0)) | f
            | (5.1,34.5) | ((0,0))             | f
            | (5.1,34.5) | ((0,1),(0,1))       | f
            | (-5,-12)   | ((2,0),(2,4),(0,0)) | f
            | (-5,-12)   | ((3,1),(3,3),(1,0)) | f
            | (-5,-12)   | ((0,0))             | f
            | (-5,-12)   | ((0,1),(0,1))       | f
            | (10,10)    | ((2,0),(2,4),(0,0)) | f
            | (10,10)    | ((3,1),(3,3),(1,0)) | f
            | (10,10)    | ((0,0))             | f
            | (10,10)    | ((0,1),(0,1))       | f
(24 rows)

SELECT '' AS twentyfour, p.f1, poly.f1, p.f1 <@ poly.f1 AS contained
   FROM POLYGON_TBL poly, POINT_TBL p;
 twentyfour |     f1     |         f1          | contained 
------------+------------+---------------------+-----------
            | (0,0)      | ((2,0),(2,4),(0,0)) | t
            | (0,0)      | ((3,1),(3,3),(1,0)) | f
            | (0,0)      | ((0,0))             | t
            | (0,0)      | ((0,1),(0,1))       | f
            | (-10,0)    | ((2,0),(2,4),(0,0)) | f
            | (-10,0)    | ((3,1),(3,3),(1,0)) | f
            | (-10,0)    | ((0,0))             | f
            | (-10,0)    | ((0,1),(0,1))       | f
            | (-3,4)     | ((2,0),(2,4),(0,0)) | f
            | (-3,4)     | ((3,1),(3,3),(1,0)) | f
            | (-3,4)     | ((0,0))             | f
            | (-3,4)     | ((0,1),(0,1))       | f
            | (5.1,34.5) | ((2,0),(2,4),(0,0)) | f
            | (5.1,34.5) | ((3,1),(3,3),(1,0)) | f
            | (5.1,34.5) | ((0,0))             | f
            | (5.1,34.5) | ((0,1),(0,1))       | f
            | (-5,-12)   | ((2,0),(2,4),(0,0)) | f
            | (-5,-12)   | ((3,1),(3,3),(1,0)) | f
            | (-5,-12)   | ((0,0))             | f
            | (-5,-12)   | ((0,1),(0,1))       | f
            | (10,10)    | ((2,0),(2,4),(0,0)) | f
            | (10,10)    | ((3,1),(3,3),(1,0)) | f
            | (10,10)    | ((0,0))             | f
            | (10,10)    | ((0,1),(0,1))       | f
(24 rows)

SELECT '' AS four, npoints(f1) AS npoints, f1 AS polygon
   FROM POLYGON_TBL;
 four | npoints |       polygon       
------+---------+---------------------
      |       3 | ((2,0),(2,4),(0,0))
      |       3 | ((3,1),(3,3),(1,0))
      |       1 | ((0,0))
      |       2 | ((0,1),(0,1))
(4 rows)

SELECT '' AS four, polygon(f1)
   FROM BOX_TBL;
 four |                  polygon                  
------+-------------------------------------------
      | ((0,0),(0,2),(2,2),(2,0))
      | ((1,1),(1,3),(3,3),(3,1))
      | ((2.5,2.5),(2.5,3.5),(2.5,3.5),(2.5,2.5))
      | ((3,3),(3,3),(3,3),(3,3))
(4 rows)

SELECT '' AS four, polygon(f1)
   FROM PATH_TBL WHERE isclosed(f1);
 four |      polygon      
------+-------------------
      | ((1,2),(3,4))
      | ((1,2),(3,4))
      | ((1,2),(3,4))
      | ((11,12),(13,14))
(4 rows)

SELECT '' AS four, f1 AS open_path, polygon( pclose(f1)) AS polygon
   FROM PATH_TBL
   WHERE isopen(f1);
 four |         open_path         |          polygon          
------+---------------------------+---------------------------
      | [(1,2),(3,4)]             | ((1,2),(3,4))
      | [(0,0),(3,0),(4,5),(1,6)] | ((0,0),(3,0),(4,5),(1,6))
      | [(1,2),(3,4)]             | ((1,2),(3,4))
      | [(11,12),(13,14)]         | ((11,12),(13,14))
(4 rows)

-- convert circles to polygons using the default number of points
SELECT '' AS six, polygon(f1)
   FROM CIRCLE_TBL;
 six |                                                                                                       polygon                                                                                                        
-----+----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
     | ((2,1),(2.40192378865,2.5),(3.5,3.59807621135),(5,4),(6.5,3.59807621135),(7.59807621135,2.5),(8,1),(7.59807621135,-0.5),(6.5,-1.59807621135),(5,-2),(3.5,-1.59807621135),(2.40192378865,-0.5))
     | ((-99,2),(-85.6025403784,52),(-49,88.6025403784),(1,102),(51,88.6025403784),(87.6025403784,52),(101,2),(87.6025403784,-48),(51,-84.6025403784),(1,-98),(-49,-84.6025403784),(-85.6025403784,-48))
     | ((-4,3),(-3.33012701892,5.5),(-1.5,7.33012701892),(1,8),(3.5,7.33012701892),(5.33012701892,5.5),(6,3),(5.33012701892,0.5),(3.5,-1.33012701892),(1,-2),(-1.5,-1.33012701892),(-3.33012701892,0.5))
     | ((-2,2),(-1.59807621135,3.5),(-0.5,4.59807621135),(1,5),(2.5,4.59807621135),(3.59807621135,3.5),(4,2),(3.59807621135,0.5),(2.5,-0.598076211353),(1,-1),(-0.5,-0.598076211353),(-1.59807621135,0.5))
     | ((90,200),(91.3397459622,205),(95,208.660254038),(100,210),(105,208.660254038),(108.660254038,205),(110,200),(108.660254038,195),(105,191.339745962),(100,190),(95,191.339745962),(91.3397459622,195))
     | ((-15,1),(0.40707856479,58.5),(42.5,100.592921435),(100,116),(157.5,100.592921435),(199.592921435,58.5),(215,1),(199.592921435,-56.5),(157.5,-98.5929214352),(100,-114),(42.5,-98.5929214352),(0.40707856479,-56.5))
(6 rows)

-- convert the circle to an 8-point polygon
SELECT '' AS six, polygon(8, f1)
   FROM CIRCLE_TBL;
 six |                                                                             polygon                                                                              
-----+------------------------------------------------------------------------------------------------------------------------------------------------------------------
     | ((2,1),(2.87867965644,3.12132034356),(5,4),(7.12132034356,3.12132034356),(8,1),(7.12132034356,-1.12132034356),(5,-2),(2.87867965644,-1.12132034356))
     | ((-99,2),(-69.7106781187,72.7106781187),(1,102),(71.7106781187,72.7106781187),(101,2),(71.7106781187,-68.7106781187),(1,-98),(-69.7106781187,-68.7106781187))
     | ((-4,3),(-2.53553390593,6.53553390593),(1,8),(4.53553390593,6.53553390593),(6,3),(4.53553390593,-0.535533905933),(1,-2),(-2.53553390593,-0.535533905933))
     | ((-2,2),(-1.12132034356,4.12132034356),(1,5),(3.12132034356,4.12132034356),(4,2),(3.12132034356,-0.12132034356),(1,-1),(-1.12132034356,-0.12132034356))
     | ((90,200),(92.9289321881,207.071067812),(100,210),(107.071067812,207.071067812),(110,200),(107.071067812,192.928932188),(100,190),(92.9289321881,192.928932188))
     | ((-15,1),(18.6827201635,82.3172798365),(100,116),(181.317279836,82.3172798365),(215,1),(181.317279836,-80.3172798365),(100,-114),(18.6827201635,-80.3172798365))
(6 rows)

--
-- Circles
--
SELECT '' AS six, circle(f1, 50.0)
   FROM POINT_TBL;
 six |     circle      
-----+-----------------
     | <(0,0),50>
     | <(-10,0),50>
     | <(-3,4),50>
     | <(5.1,34.5),50>
     | <(-5,-12),50>
     | <(10,10),50>
(6 rows)

SELECT '' AS four, circle(f1)
   FROM BOX_TBL;
 four |        circle         
------+-----------------------
      | <(1,1),1.41421356237>
      | <(2,2),1.41421356237>
      | <(2.5,3),0.5>
      | <(3,3),0>
(4 rows)

SELECT '' AS two, circle(f1)
   FROM POLYGON_TBL
   WHERE (# f1) >= 3;
 two |                    circle                     
-----+-----------------------------------------------
     | <(1.33333333333,1.33333333333),2.04168905064>
     | <(2.33333333333,1.33333333333),1.47534300379>
(2 rows)

SELECT '' AS twentyfour, c1.f1 AS circle, p1.f1 AS point, (p1.f1 <-> c1.f1) AS distance
   FROM CIRCLE_TBL c1, POINT_TBL p1
   WHERE (p1.f1 <-> c1.f1) > 0
   ORDER BY distance, area(c1.f1), p1.f1[0];
 twentyfour |     circle     |   point    |   distance    
------------+----------------+------------+---------------
            | <(1,2),3>      | (-3,4)     |   1.472135955
            | <(5,1),3>      | (0,0)      | 2.09901951359
            | <(5,1),3>      | (-3,4)     | 5.54400374532
            | <(1,3),5>      | (-10,0)    | 6.40175425099
            | <(1,3),5>      | (10,10)    | 6.40175425099
            | <(5,1),3>      | (10,10)    | 7.29563014099
            | <(1,2),3>      | (-10,0)    |  8.1803398875
            | <(1,2),3>      | (10,10)    | 9.04159457879
            | <(1,3),5>      | (-5,-12)   | 11.1554944214
            | <(5,1),3>      | (-10,0)    | 12.0332963784
            | <(1,2),3>      | (-5,-12)   | 12.2315462117
            | <(5,1),3>      | (-5,-12)   | 13.4012194669
            | <(1,3),5>      | (5.1,34.5) | 26.7657047773
            | <(1,2),3>      | (5.1,34.5) | 29.7575945393
            | <(5,1),3>      | (5.1,34.5) | 30.5001492534
            | <(100,200),10> | (5.1,34.5) | 180.778038568
            | <(100,200),10> | (10,10)    | 200.237960416
            | <(100,200),10> | (-3,4)     | 211.415898255
            | <(100,200),10> | (0,0)      |  213.60679775
            | <(100,200),10> | (-10,0)    |  218.25424421
            | <(100,200),10> | (-5,-12)   | 226.577682802
(21 rows)

