508 lines
14 KiB
SQL
508 lines
14 KiB
SQL
--
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-- GEOMETRY
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--
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-- Back off displayed precision a little bit to reduce platform-to-platform
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-- variation in results.
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SET extra_float_digits TO -3;
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--
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-- Points
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--
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SELECT '' AS four, center(f1) AS center
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FROM BOX_TBL;
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SELECT '' AS four, (@@ f1) AS center
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FROM BOX_TBL;
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SELECT '' AS six, point(f1) AS center
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FROM CIRCLE_TBL;
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SELECT '' AS six, (@@ f1) AS center
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FROM CIRCLE_TBL;
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SELECT '' AS two, (@@ f1) AS center
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FROM POLYGON_TBL
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WHERE (# f1) > 2;
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-- "is horizontal" function
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SELECT '' AS two, p1.f1
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FROM POINT_TBL p1
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WHERE ishorizontal(p1.f1, point '(0,0)');
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-- "is horizontal" operator
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SELECT '' AS two, p1.f1
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FROM POINT_TBL p1
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WHERE p1.f1 ?- point '(0,0)';
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-- "is vertical" function
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SELECT '' AS one, p1.f1
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FROM POINT_TBL p1
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WHERE isvertical(p1.f1, point '(5.1,34.5)');
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-- "is vertical" operator
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SELECT '' AS one, p1.f1
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FROM POINT_TBL p1
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WHERE p1.f1 ?| point '(5.1,34.5)';
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-- Slope
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SELECT p1.f1, p2.f1, slope(p1.f1, p2.f1) FROM POINT_TBL p1, POINT_TBL p2;
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-- Add point
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SELECT p1.f1, p2.f1, p1.f1 + p2.f1 FROM POINT_TBL p1, POINT_TBL p2;
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-- Subtract point
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SELECT p1.f1, p2.f1, p1.f1 - p2.f1 FROM POINT_TBL p1, POINT_TBL p2;
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-- Multiply with point
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SELECT p1.f1, p2.f1, p1.f1 * p2.f1 FROM POINT_TBL p1, POINT_TBL p2 WHERE p1.f1[0] BETWEEN 1 AND 1000;
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-- Underflow error
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SELECT p1.f1, p2.f1, p1.f1 * p2.f1 FROM POINT_TBL p1, POINT_TBL p2 WHERE p1.f1[0] < 1;
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-- Divide by point
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SELECT p1.f1, p2.f1, p1.f1 / p2.f1 FROM POINT_TBL p1, POINT_TBL p2 WHERE p2.f1[0] BETWEEN 1 AND 1000;
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-- Overflow error
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SELECT p1.f1, p2.f1, p1.f1 / p2.f1 FROM POINT_TBL p1, POINT_TBL p2 WHERE p2.f1[0] > 1000;
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-- Division by 0 error
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SELECT p1.f1, p2.f1, p1.f1 / p2.f1 FROM POINT_TBL p1, POINT_TBL p2 WHERE p2.f1 ~= '(0,0)'::point;
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-- Distance to line
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SELECT p.f1, l.s, p.f1 <-> l.s FROM POINT_TBL p, LINE_TBL l;
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-- Distance to line segment
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SELECT p.f1, l.s, p.f1 <-> l.s FROM POINT_TBL p, LSEG_TBL l;
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-- Distance to box
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SELECT p.f1, b.f1, p.f1 <-> b.f1 FROM POINT_TBL p, BOX_TBL b;
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-- Distance to path
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SELECT p.f1, p1.f1, p.f1 <-> p1.f1 FROM POINT_TBL p, PATH_TBL p1;
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-- Distance to polygon
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SELECT p.f1, p1.f1, p.f1 <-> p1.f1 FROM POINT_TBL p, POLYGON_TBL p1;
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-- Closest point to line
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SELECT p.f1, l.s, p.f1 ## l.s FROM POINT_TBL p, LINE_TBL l;
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-- Closest point to line segment
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SELECT p.f1, l.s, p.f1 ## l.s FROM POINT_TBL p, LSEG_TBL l;
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-- Closest point to box
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SELECT p.f1, b.f1, p.f1 ## b.f1 FROM POINT_TBL p, BOX_TBL b;
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-- On line
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SELECT p.f1, l.s FROM POINT_TBL p, LINE_TBL l WHERE p.f1 <@ l.s;
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-- On line segment
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SELECT p.f1, l.s FROM POINT_TBL p, LSEG_TBL l WHERE p.f1 <@ l.s;
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-- On path
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SELECT p.f1, p1.f1 FROM POINT_TBL p, PATH_TBL p1 WHERE p.f1 <@ p1.f1;
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--
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-- Lines
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--
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-- Vertical
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SELECT s FROM LINE_TBL WHERE ?| s;
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-- Horizontal
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SELECT s FROM LINE_TBL WHERE ?- s;
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-- Same as line
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SELECT l1.s, l2.s FROM LINE_TBL l1, LINE_TBL l2 WHERE l1.s = l2.s;
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-- Parallel to line
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SELECT l1.s, l2.s FROM LINE_TBL l1, LINE_TBL l2 WHERE l1.s ?|| l2.s;
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-- Perpendicular to line
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SELECT l1.s, l2.s FROM LINE_TBL l1, LINE_TBL l2 WHERE l1.s ?-| l2.s;
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-- Distance to line
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SELECT l1.s, l2.s, l1.s <-> l2.s FROM LINE_TBL l1, LINE_TBL l2;
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-- Distance to box
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SELECT l.s, b.f1, l.s <-> b.f1 FROM LINE_TBL l, BOX_TBL b;
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-- Intersect with line
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SELECT l1.s, l2.s FROM LINE_TBL l1, LINE_TBL l2 WHERE l1.s ?# l2.s;
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-- Intersect with box
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SELECT l.s, b.f1 FROM LINE_TBL l, BOX_TBL b WHERE l.s ?# b.f1;
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-- Intersection point with line
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SELECT l1.s, l2.s, l1.s # l2.s FROM LINE_TBL l1, LINE_TBL l2;
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-- Closest point to line segment
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SELECT l.s, l1.s, l.s ## l1.s FROM LINE_TBL l, LSEG_TBL l1;
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-- Closest point to box
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SELECT l.s, b.f1, l.s ## b.f1 FROM LINE_TBL l, BOX_TBL b;
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--
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-- Line segments
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--
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-- intersection
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SELECT '' AS count, p.f1, l.s, l.s # p.f1 AS intersection
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FROM LSEG_TBL l, POINT_TBL p;
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-- Length
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SELECT s, @-@ s FROM LSEG_TBL;
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-- Vertical
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SELECT s FROM LSEG_TBL WHERE ?| s;
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-- Horizontal
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SELECT s FROM LSEG_TBL WHERE ?- s;
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-- Center
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SELECT s, @@ s FROM LSEG_TBL;
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-- To point
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SELECT s, s::point FROM LSEG_TBL;
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-- Has points less than line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s < l2.s;
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-- Has points less than or equal to line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s <= l2.s;
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-- Has points equal to line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s = l2.s;
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-- Has points greater than or equal to line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s >= l2.s;
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-- Has points greater than line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s > l2.s;
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-- Has points not equal to line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s != l2.s;
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-- Parallel with line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s ?|| l2.s;
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-- Perpendicular with line segment
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SELECT l1.s, l2.s FROM LSEG_TBL l1, LSEG_TBL l2 WHERE l1.s ?-| l2.s;
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-- Distance to line
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SELECT l.s, l1.s, l.s <-> l1.s FROM LSEG_TBL l, LINE_TBL l1;
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-- Distance to line segment
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SELECT l1.s, l2.s, l1.s <-> l2.s FROM LSEG_TBL l1, LSEG_TBL l2;
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-- Distance to box
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SELECT l.s, b.f1, l.s <-> b.f1 FROM LSEG_TBL l, BOX_TBL b;
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-- Intersect with line segment
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SELECT l.s, l1.s FROM LSEG_TBL l, LINE_TBL l1 WHERE l.s ?# l1.s;
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-- Intersect with box
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SELECT l.s, b.f1 FROM LSEG_TBL l, BOX_TBL b WHERE l.s ?# b.f1;
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-- Intersection point with line segment
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SELECT l1.s, l2.s, l1.s # l2.s FROM LSEG_TBL l1, LSEG_TBL l2;
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-- Closest point to line
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SELECT l.s, l1.s, l.s ## l1.s FROM LSEG_TBL l, LINE_TBL l1;
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-- Closest point to line segment
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SELECT l1.s, l2.s, l1.s ## l2.s FROM LSEG_TBL l1, LSEG_TBL l2;
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-- Closest point to box
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SELECT l.s, b.f1, l.s ## b.f1 FROM LSEG_TBL l, BOX_TBL b;
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-- On line
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SELECT l.s, l1.s FROM LSEG_TBL l, LINE_TBL l1 WHERE l.s <@ l1.s;
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-- On box
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SELECT l.s, b.f1 FROM LSEG_TBL l, BOX_TBL b WHERE l.s <@ b.f1;
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--
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-- Boxes
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--
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SELECT '' as six, box(f1) AS box FROM CIRCLE_TBL;
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-- translation
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SELECT '' AS twentyfour, b.f1 + p.f1 AS translation
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FROM BOX_TBL b, POINT_TBL p;
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SELECT '' AS twentyfour, b.f1 - p.f1 AS translation
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FROM BOX_TBL b, POINT_TBL p;
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-- Multiply with point
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SELECT b.f1, p.f1, b.f1 * p.f1 FROM BOX_TBL b, POINT_TBL p WHERE p.f1[0] BETWEEN 1 AND 1000;
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-- Overflow error
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SELECT b.f1, p.f1, b.f1 * p.f1 FROM BOX_TBL b, POINT_TBL p WHERE p.f1[0] > 1000;
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-- Divide by point
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SELECT b.f1, p.f1, b.f1 / p.f1 FROM BOX_TBL b, POINT_TBL p WHERE p.f1[0] BETWEEN 1 AND 1000;
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-- To box
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SELECT f1::box
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FROM POINT_TBL;
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SELECT bound_box(a.f1, b.f1)
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FROM BOX_TBL a, BOX_TBL b;
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-- Below box
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SELECT b1.f1, b2.f1, b1.f1 <^ b2.f1 FROM BOX_TBL b1, BOX_TBL b2;
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-- Above box
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SELECT b1.f1, b2.f1, b1.f1 >^ b2.f1 FROM BOX_TBL b1, BOX_TBL b2;
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-- Intersection point with box
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SELECT b1.f1, b2.f1, b1.f1 # b2.f1 FROM BOX_TBL b1, BOX_TBL b2;
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-- Diagonal
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SELECT f1, diagonal(f1) FROM BOX_TBL;
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-- Distance to box
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SELECT b1.f1, b2.f1, b1.f1 <-> b2.f1 FROM BOX_TBL b1, BOX_TBL b2;
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--
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-- Paths
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--
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-- Points
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SELECT f1, npoints(f1) FROM PATH_TBL;
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-- Area
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SELECT f1, area(f1) FROM PATH_TBL;
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-- Length
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SELECT f1, @-@ f1 FROM PATH_TBL;
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-- Center
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SELECT f1, @@ f1 FROM PATH_TBL;
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-- To polygon
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SELECT f1, f1::polygon FROM PATH_TBL WHERE isclosed(f1);
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-- Open path cannot be converted to polygon error
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SELECT f1, f1::polygon FROM PATH_TBL WHERE isopen(f1);
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-- Has points less than path
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SELECT p1.f1, p2.f1 FROM PATH_TBL p1, PATH_TBL p2 WHERE p1.f1 < p2.f1;
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-- Has points less than or equal to path
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SELECT p1.f1, p2.f1 FROM PATH_TBL p1, PATH_TBL p2 WHERE p1.f1 <= p2.f1;
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-- Has points equal to path
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SELECT p1.f1, p2.f1 FROM PATH_TBL p1, PATH_TBL p2 WHERE p1.f1 = p2.f1;
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-- Has points greater than or equal to path
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SELECT p1.f1, p2.f1 FROM PATH_TBL p1, PATH_TBL p2 WHERE p1.f1 >= p2.f1;
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-- Has points greater than path
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SELECT p1.f1, p2.f1 FROM PATH_TBL p1, PATH_TBL p2 WHERE p1.f1 > p2.f1;
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-- Add path
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SELECT p1.f1, p2.f1, p1.f1 + p2.f1 FROM PATH_TBL p1, PATH_TBL p2;
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-- Add point
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SELECT p.f1, p1.f1, p.f1 + p1.f1 FROM PATH_TBL p, POINT_TBL p1;
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-- Subtract point
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SELECT p.f1, p1.f1, p.f1 - p1.f1 FROM PATH_TBL p, POINT_TBL p1;
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-- Multiply with point
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SELECT p.f1, p1.f1, p.f1 * p1.f1 FROM PATH_TBL p, POINT_TBL p1;
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-- Divide by point
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SELECT p.f1, p1.f1, p.f1 / p1.f1 FROM PATH_TBL p, POINT_TBL p1 WHERE p1.f1[0] BETWEEN 1 AND 1000;
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-- Division by 0 error
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SELECT p.f1, p1.f1, p.f1 / p1.f1 FROM PATH_TBL p, POINT_TBL p1 WHERE p1.f1 ~= '(0,0)'::point;
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-- Distance to path
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SELECT p1.f1, p2.f1, p1.f1 <-> p2.f1 FROM PATH_TBL p1, PATH_TBL p2;
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--
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-- Polygons
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--
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-- containment
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SELECT '' AS twentyfour, p.f1, poly.f1, poly.f1 @> p.f1 AS contains
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FROM POLYGON_TBL poly, POINT_TBL p;
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SELECT '' AS twentyfour, p.f1, poly.f1, p.f1 <@ poly.f1 AS contained
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FROM POLYGON_TBL poly, POINT_TBL p;
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SELECT '' AS four, npoints(f1) AS npoints, f1 AS polygon
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FROM POLYGON_TBL;
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SELECT '' AS four, polygon(f1)
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FROM BOX_TBL;
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SELECT '' AS four, polygon(f1)
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FROM PATH_TBL WHERE isclosed(f1);
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SELECT '' AS four, f1 AS open_path, polygon( pclose(f1)) AS polygon
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FROM PATH_TBL
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WHERE isopen(f1);
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-- To box
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SELECT f1, f1::box FROM POLYGON_TBL;
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-- To path
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SELECT f1, f1::path FROM POLYGON_TBL;
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-- Same as polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 ~= p2.f1;
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-- Contained by polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 <@ p2.f1;
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-- Contains polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 @> p2.f1;
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-- Overlap with polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 && p2.f1;
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-- Left of polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 << p2.f1;
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-- Overlap of left of polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 &< p2.f1;
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-- Right of polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 >> p2.f1;
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-- Overlap of right of polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 &> p2.f1;
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-- Below polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 <<| p2.f1;
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-- Overlap or below polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 &<| p2.f1;
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-- Above polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 |>> p2.f1;
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-- Overlap or above polygon
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SELECT p1.f1, p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2 WHERE p1.f1 |&> p2.f1;
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-- Distance to polygon
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SELECT p1.f1, p2.f1, p1.f1 <-> p2.f1 FROM POLYGON_TBL p1, POLYGON_TBL p2;
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--
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-- Circles
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--
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SELECT '' AS six, circle(f1, 50.0)
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FROM POINT_TBL;
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SELECT '' AS four, circle(f1)
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FROM BOX_TBL;
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SELECT '' AS two, circle(f1)
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FROM POLYGON_TBL
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WHERE (# f1) >= 3;
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SELECT '' AS twentyfour, c1.f1 AS circle, p1.f1 AS point, (p1.f1 <-> c1.f1) AS distance
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FROM CIRCLE_TBL c1, POINT_TBL p1
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WHERE (p1.f1 <-> c1.f1) > 0
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ORDER BY distance, area(c1.f1), p1.f1[0];
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-- To polygon
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SELECT f1, f1::polygon FROM CIRCLE_TBL WHERE f1 >= '<(0,0),1>';
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-- To polygon with less points
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SELECT f1, polygon(8, f1) FROM CIRCLE_TBL WHERE f1 >= '<(0,0),1>';
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-- Too less points error
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SELECT f1, polygon(1, f1) FROM CIRCLE_TBL WHERE f1 >= '<(0,0),1>';
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-- Zero radius error
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SELECT f1, polygon(10, f1) FROM CIRCLE_TBL WHERE f1 < '<(0,0),1>';
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-- Same as circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 ~= c2.f1;
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-- Overlap with circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 && c2.f1;
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-- Overlap or left of circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 &< c2.f1;
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-- Left of circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 << c2.f1;
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-- Right of circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 >> c2.f1;
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-- Overlap or right of circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 &> c2.f1;
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-- Contained by circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 <@ c2.f1;
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-- Contain by circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 @> c2.f1;
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-- Below circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 <<| c2.f1;
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-- Above circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 |>> c2.f1;
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-- Overlap or below circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 &<| c2.f1;
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-- Overlap or above circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 |&> c2.f1;
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-- Area equal with circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 = c2.f1;
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-- Area not equal with circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 != c2.f1;
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-- Area less than circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 < c2.f1;
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-- Area greater than circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 > c2.f1;
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-- Area less than or equal circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 <= c2.f1;
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-- Area greater than or equal circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 >= c2.f1;
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-- Area less than circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 < c2.f1;
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-- Area greater than circle
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SELECT c1.f1, c2.f1 FROM CIRCLE_TBL c1, CIRCLE_TBL c2 WHERE c1.f1 < c2.f1;
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-- Add point
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SELECT c.f1, p.f1, c.f1 + p.f1 FROM CIRCLE_TBL c, POINT_TBL p;
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-- Subtract point
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SELECT c.f1, p.f1, c.f1 - p.f1 FROM CIRCLE_TBL c, POINT_TBL p;
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-- Multiply with point
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SELECT c.f1, p.f1, c.f1 * p.f1 FROM CIRCLE_TBL c, POINT_TBL p;
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-- Divide by point
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SELECT c.f1, p.f1, c.f1 / p.f1 FROM CIRCLE_TBL c, POINT_TBL p WHERE p.f1[0] BETWEEN 1 AND 1000;
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-- Overflow error
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SELECT c.f1, p.f1, c.f1 / p.f1 FROM CIRCLE_TBL c, POINT_TBL p WHERE p.f1[0] > 1000;
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-- Division by 0 error
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SELECT c.f1, p.f1, c.f1 / p.f1 FROM CIRCLE_TBL c, POINT_TBL p WHERE p.f1 ~= '(0,0)'::point;
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-- Distance to polygon
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SELECT c.f1, p.f1, c.f1 <-> p.f1 FROM CIRCLE_TBL c, POLYGON_TBL p;
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