-- -- GEOMETRY -- -- -- 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 -----+----------- | (0,0) | (1,2) | (1,3) | (1,2) | (100,200) | (100,0) (6 rows) SELECT '' AS six, (@@ f1) AS center FROM CIRCLE_TBL; six | center -----+----------- | (0,0) | (1,2) | (1,3) | (1,2) | (100,200) | (100,0) (6 rows) SELECT '' AS two, (@@ f1) AS center FROM POLYGON_TBL WHERE (# f1) > 2; two | center -----+------------------------------------- | (1.33333333333333,1.33333333333333) | (2.33333333333333,1.33333333333333) (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: Unable to identify an operator '#' for types 'lseg' and 'point' You will have to retype this query using an explicit cast -- 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) | (-10,0) | [(1,2),(3,4)] | (1,2) | (-3,4) | [(1,2),(3,4)] | (1,2) | (5.1,34.5) | [(1,2),(3,4)] | (3,4) | (-5,-12) | [(1,2),(3,4)] | (1,2) | (10,10) | [(1,2),(3,4)] | (3,4) | (0,0) | [(0,0),(6,6)] | (0,0) | (-10,0) | [(0,0),(6,6)] | (0,0) | (-3,4) | [(0,0),(6,6)] | (0.5,0.5) | (5.1,34.5) | [(0,0),(6,6)] | (6,6) | (-5,-12) | [(0,0),(6,6)] | (0,0) | (10,10) | [(0,0),(6,6)] | (6,6) | (0,0) | [(10,-10),(-3,-4)] | (-2.04878048780488,-4.4390243902439) | (-10,0) | [(10,-10),(-3,-4)] | (-3,-4) | (-3,4) | [(10,-10),(-3,-4)] | (-3,-4) | (5.1,34.5) | [(10,-10),(-3,-4)] | (-3,-4) | (-5,-12) | [(10,-10),(-3,-4)] | (-1.60487804878049,-4.64390243902439) | (10,10) | [(10,-10),(-3,-4)] | (2.39024390243902,-6.48780487804878) | (0,0) | [(-1000000,200),(300000,-40)] | (0.0028402365895872,15.384614860264) | (-10,0) | [(-1000000,200),(300000,-40)] | (-9.99715942258202,15.3864610140473) | (-3,4) | [(-1000000,200),(300000,-40)] | (-2.99789812267519,15.3851688427303) | (5.1,34.5) | [(-1000000,200),(300000,-40)] | (5.09647083221496,15.3836744976925) | (-5,-12) | [(-1000000,200),(300000,-40)] | (-4.99494420845634,15.3855375281616) | (10,10) | [(-1000000,200),(300000,-40)] | (10.000993741978,15.3827690473092) | (0,0) | [(11,22),(33,44)] | (11,22) | (-10,0) | [(11,22),(33,44)] | (11,22) | (-3,4) | [(11,22),(33,44)] | (11,22) | (5.1,34.5) | [(11,22),(33,44)] | (14.3,25.3) | (-5,-12) | [(11,22),(33,44)] | (11,22) | (10,10) | [(11,22),(33,44)] | (11,22) (30 rows) -- -- Lines -- -- -- Boxes -- SELECT '' as six, box(f1) AS box FROM CIRCLE_TBL; six | box -----+---------------------------------------------------------------------------- | (2.12132034355964,2.12132034355964),(-2.12132034355964,-2.12132034355964) | (71.7106781186547,72.7106781186547),(-69.7106781186547,-68.7106781186547) | (4.53553390593274,6.53553390593274),(-2.53553390593274,-0.535533905932737) | (3.12132034355964,4.12132034355964),(-1.12132034355964,-0.121320343559642) | (107.071067811865,207.071067811865),(92.9289321881345,192.928932188135) | (170.710678118655,70.7106781186547),(29.2893218813453,-70.7106781186547) (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) | (-8,2),(-10,0) | (-1,6),(-3,4) | (7.1,36.5),(5.1,34.5) | (-3,-10),(-5,-12) | (12,12),(10,10) | (3,3),(1,1) | (-7,3),(-9,1) | (0,7),(-2,5) | (8.1,37.5),(6.1,35.5) | (-2,-9),(-4,-11) | (13,13),(11,11) | (2.5,3.5),(2.5,2.5) | (-7.5,3.5),(-7.5,2.5) | (-0.5,7.5),(-0.5,6.5) | (7.6,38),(7.6,37) | (-2.5,-8.5),(-2.5,-9.5) | (12.5,13.5),(12.5,12.5) | (3,3),(3,3) | (-7,3),(-7,3) | (0,7),(0,7) | (8.1,37.5),(8.1,37.5) | (-2,-9),(-2,-9) | (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) | (12,2),(10,0) | (5,-2),(3,-4) | (-3.1,-32.5),(-5.1,-34.5) | (7,14),(5,12) | (-8,-8),(-10,-10) | (3,3),(1,1) | (13,3),(11,1) | (6,-1),(4,-3) | (-2.1,-31.5),(-4.1,-33.5) | (8,15),(6,13) | (-7,-7),(-9,-9) | (2.5,3.5),(2.5,2.5) | (12.5,3.5),(12.5,2.5) | (5.5,-0.5),(5.5,-1.5) | (-2.6,-31),(-2.6,-32) | (7.5,15.5),(7.5,14.5) | (-7.5,-6.5),(-7.5,-7.5) | (3,3),(3,3) | (13,3),(13,3) | (6,-1),(6,-1) | (-2.1,-31.5),(-2.1,-31.5) | (8,15),(8,15) | (-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),(-20,-20) | (0,2),(-14,0) | (0,79.2),(-58.8,0) | (14,0),(0,-34) | (0,40),(0,0) | (0,0),(0,0) | (-10,-10),(-30,-30) | (-7,3),(-21,1) | (-29.4,118.8),(-88.2,39.6) | (21,-17),(7,-51) | (0,60),(0,20) | (0,0),(0,0) | (-25,-25),(-25,-35) | (-17.5,2.5),(-21.5,-0.5) | (-73.5,104.1),(-108,99) | (29.5,-42.5),(17.5,-47.5) | (0,60),(-10,50) | (0,0),(0,0) | (-30,-30),(-30,-30) | (-21,3),(-21,3) | (-88.2,118.8),(-88.2,118.8) | (21,-51),(21,-51) | (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) | (-0.1,-0.1),(-0.3,-0.3) | (-0.25,-0.25),(-0.25,-0.35) | (-0.3,-0.3),(-0.3,-0.3) | (0.08,0),(0,-0.56) | (0.12,-0.28),(0.04,-0.84) | (0.26,-0.7),(0.1,-0.82) | (0.12,-0.84),(0.12,-0.84) | (0.0651176557643925,0),(0,-0.0483449262493217) | (0.0976764836465887,-0.0241724631246608),(0.0325588278821962,-0.0725173893739825) | (0.109762715208919,-0.0562379754328844),(0.0813970697054906,-0.0604311578116521) | (0.0976764836465887,-0.0725173893739825),(0.0976764836465887,-0.0725173893739825) | (0,0.0828402366863905),(-0.201183431952663,0) | (-0.100591715976331,0.124260355029586),(-0.301775147928994,0.0414201183431953) | (-0.251479289940828,0.103550295857988),(-0.322485207100592,0.0739644970414201) | (-0.301775147928994,0.124260355029586),(-0.301775147928994,0.124260355029586) | (0.2,0),(0,0) | (0.3,0),(0.1,0) | (0.3,0.05),(0.25,0) | (0.3,0),(0.3,0) (20 rows) -- -- Paths -- SET geqo TO 'off'; 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) RESET geqo; -- -- 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 | (-10,0) | ((2,0),(2,4),(0,0)) | f | (-3,4) | ((2,0),(2,4),(0,0)) | f | (5.1,34.5) | ((2,0),(2,4),(0,0)) | f | (-5,-12) | ((2,0),(2,4),(0,0)) | f | (10,10) | ((2,0),(2,4),(0,0)) | f | (0,0) | ((3,1),(3,3),(1,0)) | f | (-10,0) | ((3,1),(3,3),(1,0)) | f | (-3,4) | ((3,1),(3,3),(1,0)) | f | (5.1,34.5) | ((3,1),(3,3),(1,0)) | f | (-5,-12) | ((3,1),(3,3),(1,0)) | f | (10,10) | ((3,1),(3,3),(1,0)) | f | (0,0) | ((0,0)) | t | (-10,0) | ((0,0)) | f | (-3,4) | ((0,0)) | f | (5.1,34.5) | ((0,0)) | f | (-5,-12) | ((0,0)) | f | (10,10) | ((0,0)) | f | (0,0) | ((0,1),(0,1)) | f | (-10,0) | ((0,1),(0,1)) | f | (-3,4) | ((0,1),(0,1)) | f | (5.1,34.5) | ((0,1),(0,1)) | f | (-5,-12) | ((0,1),(0,1)) | 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 | (-10,0) | ((2,0),(2,4),(0,0)) | f | (-3,4) | ((2,0),(2,4),(0,0)) | f | (5.1,34.5) | ((2,0),(2,4),(0,0)) | f | (-5,-12) | ((2,0),(2,4),(0,0)) | f | (10,10) | ((2,0),(2,4),(0,0)) | f | (0,0) | ((3,1),(3,3),(1,0)) | f | (-10,0) | ((3,1),(3,3),(1,0)) | f | (-3,4) | ((3,1),(3,3),(1,0)) | f | (5.1,34.5) | ((3,1),(3,3),(1,0)) | f | (-5,-12) | ((3,1),(3,3),(1,0)) | f | (10,10) | ((3,1),(3,3),(1,0)) | f | (0,0) | ((0,0)) | t | (-10,0) | ((0,0)) | f | (-3,4) | ((0,0)) | f | (5.1,34.5) | ((0,0)) | f | (-5,-12) | ((0,0)) | f | (10,10) | ((0,0)) | f | (0,0) | ((0,1),(0,1)) | f | (-10,0) | ((0,1),(0,1)) | f | (-3,4) | ((0,1),(0,1)) | f | (5.1,34.5) | ((0,1),(0,1)) | f | (-5,-12) | ((0,1),(0,1)) | 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 -----+--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ((-3,0),(-2.59807621135076,1.50000000000442),(-1.49999999999116,2.59807621135842),(1.53102359017709e-11,3),(1.50000000001768,2.59807621134311),(2.59807621136607,1.4999999999779),(3,-3.06204718035418e-11),(2.59807621133545,-1.50000000003094),(1.49999999996464,-2.59807621137373),(-4.59307077053127e-11,-3),(-1.5000000000442,-2.5980762113278),(-2.59807621138139,-1.49999999995138)) | ((-99,2),(-85.6025403783588,52.0000000001473),(-48.9999999997054,88.602540378614),(1.00000000051034,102),(51.0000000005893,88.6025403781036),(87.6025403788692,51.9999999992634),(101,1.99999999897932),(87.6025403778485,-48.0000000010313),(50.9999999988214,-84.6025403791243),(0.999999998468976,-98),(-49.0000000014732,-84.6025403775933),(-85.6025403793795,-47.9999999983794)) | ((-4,3),(-3.33012701891794,5.50000000000737),(-1.49999999998527,7.3301270189307),(1.00000000002552,8),(3.50000000002946,7.33012701890518),(5.33012701894346,5.49999999996317),(6,2.99999999994897),(5.33012701889242,0.499999999948437),(3.49999999994107,-1.33012701895622),(0.999999999923449,-2),(-1.50000000007366,-1.33012701887967),(-3.33012701896897,0.500000000081028)) | ((-2,2),(-1.59807621135076,3.50000000000442),(-0.499999999991161,4.59807621135842),(1.00000000001531,5),(2.50000000001768,4.59807621134311),(3.59807621136607,3.4999999999779),(4,1.99999999996938),(3.59807621133545,0.499999999969062),(2.49999999996464,-0.59807621137373),(0.999999999954069,-1),(-0.500000000044197,-0.598076211327799),(-1.59807621138139,0.500000000048617)) | ((90,200),(91.3397459621641,205.000000000015),(95.0000000000295,208.660254037861),(100.000000000051,210),(105.000000000059,208.66025403781),(108.660254037887,204.999999999926),(110,199.999999999898),(108.660254037785,194.999999999897),(104.999999999882,191.339745962088),(99.9999999998469,190),(94.9999999998527,191.339745962241),(91.3397459620621,195.000000000162)) | ((0,0),(13.3974596216412,50.0000000001473),(50.0000000002946,86.602540378614),(100.00000000051,100),(150.000000000589,86.6025403781036),(186.602540378869,49.9999999992634),(200,-1.02068239345139e-09),(186.602540377848,-50.0000000010313),(149.999999998821,-86.6025403791243),(99.999999998469,-100),(49.9999999985268,-86.6025403775933),(13.3974596206205,-49.9999999983794)) (6 rows) -- convert the circle to an 8-point polygon SELECT '' AS six, polygon(8, f1) FROM CIRCLE_TBL; six | polygon -----+------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ((-3,0),(-2.12132034355423,2.12132034356506),(1.53102359017709e-11,3),(2.12132034357588,2.1213203435434),(3,-3.06204718035418e-11),(2.12132034353258,-2.12132034358671),(-4.59307077053127e-11,-3),(-2.12132034359753,-2.12132034352175)) | ((-99,2),(-69.7106781184743,72.7106781188352),(1.00000000051034,102),(71.7106781191961,72.7106781181135),(101,1.99999999897932),(71.7106781177526,-68.7106781195569),(0.999999998468976,-98),(-69.7106781199178,-68.7106781173917)) | ((-4,3),(-2.53553390592372,6.53553390594176),(1.00000000002552,8),(4.5355339059598,6.53553390590567),(6,2.99999999994897),(4.53553390588763,-0.535533905977846),(0.999999999923449,-2),(-2.53553390599589,-0.535533905869586)) | ((-2,2),(-1.12132034355423,4.12132034356506),(1.00000000001531,5),(3.12132034357588,4.1213203435434),(4,1.99999999996938),(3.12132034353258,-0.121320343586708),(0.999999999954069,-1),(-1.12132034359753,-0.121320343521752)) | ((90,200),(92.9289321881526,207.071067811884),(100.000000000051,210),(107.07106781192,207.071067811811),(110,199.999999999898),(107.071067811775,192.928932188044),(99.9999999998469,190),(92.9289321880082,192.928932188261)) | ((0,0),(29.2893218815257,70.7106781188352),(100.00000000051,100),(170.710678119196,70.7106781181135),(200,-1.02068239345139e-09),(170.710678117753,-70.7106781195569),(99.999999998469,-100),(29.2893218800822,-70.7106781173917)) (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),1.4142135623731> | <(2,2),1.4142135623731> | <(2.5,3),0.5> | <(3,3),0> (4 rows) SELECT '' AS two, circle(f1) FROM POLYGON_TBL WHERE (# f1) >= 3; two | circle -----+-------------------------------------------------------- | <(1.33333333333333,1.33333333333333),2.04168905063636> | <(2.33333333333333,1.33333333333333),1.47534300379185> (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, circle, point using <<; twentyfour | circle | point | distance ------------+----------------+------------+------------------ | <(100,0),100> | (5.1,34.5) | 0.97653192697797 | <(1,2),3> | (-3,4) | 1.47213595499958 | <(0,0),3> | (-3,4) | 2 | <(100,0),100> | (-3,4) | 3.07764064044152 | <(100,0),100> | (-5,-12) | 5.68348972285122 | <(1,3),5> | (-10,0) | 6.40175425099138 | <(1,3),5> | (10,10) | 6.40175425099138 | <(0,0),3> | (-10,0) | 7 | <(1,2),3> | (-10,0) | 8.18033988749895 | <(1,2),3> | (10,10) | 9.0415945787923 | <(0,0),3> | (-5,-12) | 10 | <(100,0),100> | (-10,0) | 10 | <(0,0),3> | (10,10) | 11.142135623731 | <(1,3),5> | (-5,-12) | 11.1554944214035 | <(1,2),3> | (-5,-12) | 12.2315462117278 | <(1,3),5> | (5.1,34.5) | 26.7657047773223 | <(1,2),3> | (5.1,34.5) | 29.757594539282 | <(0,0),3> | (5.1,34.5) | 31.8749193547455 | <(100,200),10> | (5.1,34.5) | 180.778038568384 | <(100,200),10> | (10,10) | 200.237960416286 | <(100,200),10> | (-3,4) | 211.415898254845 | <(100,200),10> | (0,0) | 213.606797749979 | <(100,200),10> | (-10,0) | 218.254244210267 | <(100,200),10> | (-5,-12) | 226.577682802077 (24 rows)