From 23ff77ef2e67bce357a15e2d952ac026c3219d91 Mon Sep 17 00:00:00 2001
From: 3Davydov <davydovdaniil501@gmail.com>
Date: Fri, 4 Aug 2023 03:51:02 +0700
Subject: [PATCH] Created some tests for contains and overlap operations to
 check DE-9IM compliance

---
 Makefile              |    5 +-
 expected/contains.out |  233 ++++++++++
 expected/overlaps.out | 1017 +++++++++++++++++++++++++++++++++++++++++
 sql/contains.sql      |  123 +++++
 sql/overlaps.sql      |  484 ++++++++++++++++++++
 5 files changed, 1860 insertions(+), 2 deletions(-)
 create mode 100644 expected/contains.out
 create mode 100644 expected/overlaps.out
 create mode 100644 sql/contains.sql
 create mode 100644 sql/overlaps.sql

diff --git a/Makefile b/Makefile
index dca3b7d..5bd53f7 100644
--- a/Makefile
+++ b/Makefile
@@ -31,7 +31,8 @@ DATA_built  = $(RELEASE_SQL) \
 
 DOCS        = README.pg_sphere COPYRIGHT.pg_sphere
 REGRESS     = init tables points euler circle line ellipse poly path box index \
-              contains_ops contains_ops_compat bounding_box_gist gnomo epochprop
+              contains_ops contains_ops_compat bounding_box_gist gnomo epochprop \
+              contains overlaps
 
 ifneq ($(USE_HEALPIX),0)
 REGRESS    += healpix moc mocautocast
@@ -41,7 +42,7 @@ REGRESS_9_5 = index_9.5 # experimental for spoint3
 
 TESTS       = init_test tables points euler circle line ellipse poly path box \
               index contains_ops contains_ops_compat bounding_box_gist gnomo \
-              epochprop
+              epochprop contains overlaps
 
 ifneq ($(USE_HEALPIX),0)
 TESTS      += healpix moc mocautocast
diff --git a/expected/contains.out b/expected/contains.out
new file mode 100644
index 0000000..e86fcad
--- /dev/null
+++ b/expected/contains.out
@@ -0,0 +1,233 @@
+/*
+This set of tests is designed to verify the compliance of the contain operation with the DE-9IM model
+*/
+-- sline vs spoint
+-- the point lies far beyond the line
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(0d, 50d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline ~ spoint | f        | f
+(1 row)
+
+-- the point lies in the boundary of line
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(270d, 10d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the interior of line
+select 'sline ~ spoint', 't' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(270d, 20d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline ~ spoint | t        | t
+(1 row)
+
+-- the point and line that degenerated into the point coincide
+select 'sline ~ spoint', 't' as expected, sline(spoint'(270d,10d)', spoint'(270d,10d)') ~ spoint'(270d, 10d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline ~ spoint | t        | t
+(1 row)
+
+-- the point and line that degenerated into the point do not coincide
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,10d)') ~ spoint'(270d, 20d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline ~ spoint | f        | f
+(1 row)
+
+-- spoint vs scircle
+-- the point lies far beyond the circle
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,0d)' @ scircle'<(0d,90d),50d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoint @ scircle | f        | f
+(1 row)
+
+-- the point lies in the boundary of circle
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,80d)' @ scircle'<(0d,90d),10d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoint @ scircle | f        | t
+(1 row)
+
+-- the point lies in the interior of circle
+select 'spoint @ scircle', 't' as expected, spoint'(0d,80d)' @ scircle'<(0d,90d),50d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoint @ scircle | t        | t
+(1 row)
+
+-- the point and circle that degenerated into the point coincide
+select 'spoint @ scircle', 't' as expected, spoint'(0d,90d)' @ scircle'<(0d,90d),0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoint @ scircle | t        | t
+(1 row)
+
+-- the point and circle that degenerated into the point do not coincide
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,50d)' @ scircle'<(0d,90d),0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoint @ scircle | f        | f
+(1 row)
+
+-- sellipse vs spoint
+-- the point lies far beyond the ellipse
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(0d, 0d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | f        | f
+(1 row)
+
+-- the point lies in the boundary of ellipse
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(0d, 70d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the interior of ellipse
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(90d, 65d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | t        | t
+(1 row)
+
+-- the point lies in the boundary of ellipse that degenerated into the line
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 10d , 0d }, (0d , 0d) , 0d>' ~ spoint'(10d, 0d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | t        | t
+(1 row)
+
+-- the point lies in the interior of ellipse that degenerated into the line
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 10d , 0d }, (0d , 0d) , 0d>' ~ spoint'(0d, 0d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | t        | t
+(1 row)
+
+-- the point and ellipse that degenerated into the point coincide
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 0d , 0d }, (0d , 90d) , 0d>' ~ spoint'(0d, 90d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | t        | t
+(1 row)
+
+-- the point and ellipse that degenerated into the point do not coincide
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 90d) , 0d>' ~ spoint'(0d, 91d)' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ sellipse ~ spoint | f        | f
+(1 row)
+
+-- spath vs spoint
+-- the point lies far beyond the opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(0d, 90d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath ~ spoint | f        | f
+(1 row)
+
+-- the point lies in the boundary of opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(-10d, 0d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the boundary of unsimple opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d),(-5d, 0d) }' ~ spoint'(-5d, 0d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the interior of opened path
+select 'spath ~ spoint', 't' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(9d, 0d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath ~ spoint | t        | t
+(1 row)
+
+-- the point lies in the interior of closed path
+select 'spath ~ spoint', 't' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d),(-10d, 0d) }' ~ spoint'(-10d, 0d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath ~ spoint | t        | t
+(1 row)
+
+-- spoly vs spoint
+-- the point lies far beyond the polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(0d, 90d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly ~ spoint | f        | f
+(1 row)
+
+-- the point lies in the boundary of polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(5d, 0d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the boundary of polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(20d, 20d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the interior of polygon
+select 'spoly ~ spoint', 't' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(5d, 5d)' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly ~ spoint | t        | t
+(1 row)
+
+-- sbox vs spoint
+--  the point lies far beyond the box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 90d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | f        | f
+(1 row)
+
+-- the point lies in the boundary of box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 5d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the boundary of box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 0d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | f        | t
+(1 row)
+
+-- the point lies in the interior of box
+select 'sbox ~ spoint', 't' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(5d, 5d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | t        | t
+(1 row)
+
+-- the point and box that degenerated into the point coincide
+select 'sbox ~ spoint', 't' as expected, sbox'( (0d,0d), (0d,0d) )' ~ spoint'(0d, 0d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | t        | t
+(1 row)
+
+-- the point and box that degenerated into the point do not coincide
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (0d,0d) )' ~ spoint'(0d, 1d)' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox ~ spoint | f        | f
+(1 row)
+
diff --git a/expected/overlaps.out b/expected/overlaps.out
new file mode 100644
index 0000000..5a7625f
--- /dev/null
+++ b/expected/overlaps.out
@@ -0,0 +1,1017 @@
+/*
+This set of tests is designed to verify the compliance of the overlap operation with the DE-9IM model
+*/
+-- sline vs sline
+-- the lines have no common points
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(20d,0d)', spoint'(30d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | f
+(1 row)
+
+-- the point of intersection of the lines is the boundary for both
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(10d,0d)', spoint'(20d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- one line intersects the other at the boundary point of the latter
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,90d)', spoint'(0d,-10d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- the interiors of the lines intersect at one point
+select 'sline && sline', 'f' as expected, sline( spoint'(-10d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,90d)', spoint'(0d,-10d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- the lines match
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(10d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- one line lies completely in the other and they have an intersection at the boundary point
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(5d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- one line lies completely in the other and they have no intersection at the boundary point
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(2d,0d)', spoint'(5d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- one line partially lies in the other
+select 'sline && sline', 't' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(5d,0d)', spoint'(20d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | t        | t
+(1 row)
+
+-- the line degenerated into the point lies on the boundary of another
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(0d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- the line degenerated into the point lies in the interior of another
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(5d,0d)', spoint'(5d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- both lines are degenerated into the point and coincide
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(0d,0d)') && sline( spoint'(0d,0d)', spoint'(0d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | t
+(1 row)
+
+-- both lines are degenerated into the point and do not coincide, but lie close to each other
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(0d,0d)') && sline( spoint'(1d,0d)', spoint'(1d,0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ sline && sline | f        | f
+(1 row)
+
+-- scircle vs scircle
+-- the circles have no common points
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(30d , 0d) , 5d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | f
+(1 row)
+
+-- the point of intersection of the circles is the boundary for both
+select 'scircle && scircle', 'f' as expected, scircle'<(-10d , 0d) , 10d>' && scircle'<(10d , 0d) , 10d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- the circles match
+select 'scircle && scircle', 'f' as expected, scircle'<(-10d , 0d) , 10d>' && scircle'<(-10d , 0d) , 10d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- one circle lies completely in the other and they have an intersection at the boundary point
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(-10d , 0d) , 10d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- one circle lies completely in the other and they have no intersection at the boundary point
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(0d , 0d) , 5d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- one circle partially lies in the other
+select 'scircle && scircle', 't' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(10d , 0d) , 20d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | t        | t
+(1 row)
+
+-- the circle degenerated into the point lies on the boundary of another
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(20d , 0d) , 0d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- the circle degenerated into the point lies in the interior of another
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(0d , 0d) , 0d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- both circles are degenerated into the point and coincide
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | t
+(1 row)
+
+-- both circles are degenerated into the point and do not coincide, but lie close to each other
+select 'scircle && scircle', 'f' as expected, scircle'<(1d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+      ?column?      | expected | actual 
+--------------------+----------+--------
+ scircle && scircle | f        | f
+(1 row)
+
+-- sellipse vs sellipse
+-- the ellipses have no common points
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (50 , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- the point of intersection of the ellipses is the boundary for both
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (45d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | f
+(1 row)
+
+-- the ellipses match
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- one ellipse lies completely in the other and they have an intersection at the boundary point
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 5d }, (-20d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- one ellipse lies completely in the other and they have no intersection at the boundary point
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 10d , 5d }, (-20d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- one ellipse partially lies in the other
+select 'sellipse && sellipse', 't' as expected, sellipse'<{ 45d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 5d }, (30d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | t        | t
+(1 row)
+
+-- the ellipse degenerated into the line lies completely in the interior of another (non-degenerate) ellipse
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 10d , 0d }, (10d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the line partially lies in the interior of another (non-degenerate) ellipse
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 0d }, (30d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies on the boundary of another
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (30d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies in the interior of another
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (40d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- both ellipses are degenerated into the point and coincide
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | t
+(1 row)
+
+-- both ellipses are degenerated into the point and do not coincide, but lie close to each other
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (1d , 0d) , 0d>' as actual;
+       ?column?       | expected | actual 
+----------------------+----------+--------
+ sellipse && sellipse | f        | f
+(1 row)
+
+-- sellipse vs scircle
+-- the ellipse and circle have no common points
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(30d , 0d) , 5d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | f
+(1 row)
+
+-- the point of intersection of the ellipse and circle is the boundary for both
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(30d , 0d) , 10d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | f
+(1 row)
+
+-- the ellipse and circle match
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 10d , 10d }, (30d , 0d) , 0d>' && scircle'<(30d , 0d) , 10d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse lies completely in the circle and they have an intersection at the boundary point
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(20d , 0d) , 40d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse lies completely in the circle and they have no intersection at the boundary point
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (20d , 0d) , 0d>' && scircle'<(20d , 0d) , 40d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the circle lies completely in the ellipse
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 5d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the circle partially lies in the ellipse
+select 'sellipse && scircle', 't' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(20d , 0d) , 15d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | t        | t
+(1 row)
+
+-- the ellipse degenerated into the line lies completely in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 0d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 20d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse degenerated into the line partially lies in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 0d }, (10d , 0d) , 0d>' && scircle'<(0d , 0d) , 20d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies on the boundary of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (10d , 0d) , 0d>' && scircle'<(0d , 0d) , 10d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (5d , 0d) , 0d>' && scircle'<(0d , 0d) , 10d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipse and circle are degenerated into the point and coincide
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | t
+(1 row)
+
+-- the ellipses are degenerated into the point and do not coincide, but lie close to each other
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && scircle'<(1d , 0d) , 0d>' as actual;
+      ?column?       | expected | actual 
+---------------------+----------+--------
+ sellipse && scircle | f        | f
+(1 row)
+
+-- spath vs spath
+-- the opened paths have no common points
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d) }' && spath'{ (60d, 15d),(70d, 20d),(75d, 20d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | f
+(1 row)
+
+-- the points of intersection of the opened paths is the boundary for both
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-10d, 0d),(0d, 10d),(45d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- one opened path intersects the other at the boundary point of the latter
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-20d, -10d),(-10d, 0d),(0d, 10d),(45d, 15d),(60d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- the interiors of the opened paths intersect at one point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (0d, 10d),(0d, -10d),(10d, -10d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- the interiors of the opened paths intersect at two points
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (0d, 10d),(0d, -10d),(5d, 0d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- the opened paths match
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- the closed paths match
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- one opened path lies completely in the other and they have an intersection at the boundary point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 15d),(70d, 20d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- one opened path lies completely in the other and they have no intersection at the boundary point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 15d),(70d, 20d) }' && spath'{ (10d, 0d),(45d, 15d),(60d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | f        | t
+(1 row)
+
+-- one opened path partially lies in the other
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | t        | t
+(1 row)
+
+-- one closed path partially lies in the other
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d),(45d, 15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | t        | t
+(1 row)
+
+-- the opened path partially lies in the closed path
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && spath | t        | t
+(1 row)
+
+-- spath vs sline
+-- the opened path and line have no common points
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(20d, 0d)', spoint'(30d, 0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | f
+(1 row)
+
+-- the points of intersection of the opened path and line is the boundary for both
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(-10d, 0d)', spoint'(45d, 15d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the interiors of the opened path and line intersect at one point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(0d, 10d)', spoint'(0d, -10d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the path and line match
+select 'spath && sline', 'f' as expected, spath'{ (0d, 10d),(0d, -10d) }' && sline( spoint'(0d, 10d)', spoint'(0d, -10d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the line lies completely in the opened path and they have an intersection at the boundary point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 20d) }' && sline( spoint'(-10d, 0d)', spoint'(10d, 0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the line lies completely in the opened path and they have no intersection at the boundary point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 20d) }' && sline( spoint'(10d, 0d)', spoint'(45d, 15d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the line partially lies in the open path
+select 'spath && sline', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(5d, 0d)', spoint'(20d, 0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | t        | t
+(1 row)
+
+-- the line degenerated into the point lies in the boundary of open path
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(-10d, 0d)', spoint'(-10d, 0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- the line degenerated into the point lies in the interior of open path
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(0d, 0d)', spoint'(0d, 0d)') as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spath && sline | f        | t
+(1 row)
+
+-- spoly vs spoly
+-- the polygons have no common points
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (10d, 0d),(20d, 0d),(10d, 10d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | f
+(1 row)
+
+-- the point of intersection of the polygons is the boundary for both
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (10d, 0d),(20d, 0d),(0d, 10d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | t
+(1 row)
+
+-- the interiors of the polygons intersect at one line
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (0d, 0d),(20d, 0d),(0d, 10d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | t
+(1 row)
+
+-- the polygons matches
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | t
+(1 row)
+
+-- one polygon lies completely in the other and they have an intersection at the boundary line
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | t
+(1 row)
+
+-- one polygon lies completely in the other and they have no intersection at the boundary line or point
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && spoly'{ (5d, 5d),(15d, 5d),(15d, 15d),(5d,15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | f        | t
+(1 row)
+
+-- one polygon partially lies in the other
+select 'spoly && spoly', 't' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (5d, 5d),(30d, 5d),(30d, 15d),(5d,15d) }' as actual;
+    ?column?    | expected | actual 
+----------------+----------+--------
+ spoly && spoly | t        | f
+(1 row)
+
+-- spoly vs scircle
+-- the polygon and circle have no common points
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 90d) , 10d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | f
+(1 row)
+
+-- the point of intersection of the polygon and circle is the boundary for both
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 90d) , 80d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- the circle lies completely in the polygon and they have an intersection at the boundary point
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(5d , 1d) , 1d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- the circle lies completely in the polygon and they have no intersection at the boundary point
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(5d , 2d) , 1d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- the polygon lies completely in the circle
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 15d) , 20d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- the polygon partially lies in the circle
+select 'spoly && scircle', 't' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 5d) , 5d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | t        | t
+(1 row)
+
+-- the circle degenerated into the point lies in the boundary of polygon
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 0d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- the circle degenerated into the point lies in the interior of polygon
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(2d , 2d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ spoly && scircle | f        | t
+(1 row)
+
+-- spoly vs sellipse
+-- the polygon and ellipse have no common points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | f
+(1 row)
+
+-- the point of intersection of the polygon and ellipse is the boundary for both
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 80d , 20d }, (0d , 90d) , 90d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse lies completely in the polygon and they have an intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && sellipse'<{ 10d , 5d }, (10d , 10d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse lies completely in the polygon and they have no intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && sellipse'<{ 7d , 5d }, (10d , 10d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the polygon lies completely in the ellipse and they have an intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 5d),(10d, 10d),(20d, 5d),(10d, 0d) }' && sellipse'<{ 10d , 5d }, (10d , 5d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the polygon lies completely in the ellipse and they have no intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (1d, 5d),(10d, 9d),(19d, 5d),(10d, 1d) }' && sellipse'<{ 10d , 5d }, (10d , 10d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse partially lies in the polygon
+select 'spoly && sellipse', 't' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 10d , 2d }, (0d , 5d) , 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | t        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies in the boundary of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 0d , 0d }, (0d , 0d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the point lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 0d , 0d }, (5d , 2d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the line lies in the boundary of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 5d , 0d }, (5d , 0d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the line lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 2d , 0d }, (1d , 4d), 90d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- the ellipse degenerated into the line partially lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 10d , 0d }, (1d , 4d), 0d>' as actual;
+     ?column?      | expected | actual 
+-------------------+----------+--------
+ spoly && sellipse | f        | t
+(1 row)
+
+-- sbox vs sbox
+-- the boxes have no common points
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((30d , 30d), (50d , 50d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | f
+(1 row)
+
+-- the point of intersection of the boxes is the boundary for both
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((20d , 20d), (50d , 50d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- the boundaries of the boxes intersect at one line
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((20d , 0d), (50d , 20d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- the boxes matches
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 10d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- one box lies completely in the other and they have no intersection at the boundary line or point
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 10d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- one box partially lies in the other
+select 'sbox && sbox', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((10d , 10d), (30d , 30d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | t        | t
+(1 row)
+
+-- one box degenerated into the line lies in the boundary of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((0d , 0d), (20d , 0d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- one box degenerated into the line lies in the interior of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 5d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- one box degenerated into the point lies in the boundary of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((0d , 0d), (0d , 0d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- one box degenerated into the point lies in the interior of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (5d , 5d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- the boxes are degenerated into the point and coincide
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sbox'((0d , 0d), (0d , 0d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | t
+(1 row)
+
+-- the boxes are degenerated into the point and not coincide
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sbox'((10d , 10d), (10d , 10d))' as actual;
+   ?column?   | expected | actual 
+--------------+----------+--------
+ sbox && sbox | f        | f
+(1 row)
+
+-- sbox vs scircle
+-- the box and circle have no common points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(0d , 90d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | f
+(1 row)
+
+-- the point of intersection of the box and circle is the boundary for both
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(30d , 0d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the circle lies completely in the box and they have an intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the circle lies completely in the box and they have no intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 5d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the box lies completely in the circle and they have an intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((-4d , -3d), (3d , 4d))' && scircle'<(0d , 0d) , 5d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the box lies completely in the circle and they have no intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((-4d , -3d), (3d , 4d))' && scircle'<(0d , 0d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the box degenerated into the line intersects circle
+select 'sbox && scircle', 'f' as expected, sbox'((-20d , 0d), (20d , 0d))' && scircle'<(0d , 0d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | f
+(1 row)
+
+-- the circle partially lies in the box
+select 'sbox && scircle', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(15d , 15d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | t        | t
+(1 row)
+
+-- the circle degenerated into the point lies in the boundary of box
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(0d , 10d) , 0d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the circle degenerated into the point lies in the interior of box
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 0d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the box degenerated into the point lies in the boundary of circle
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(10d , 0d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | f
+(1 row)
+
+-- the box degenerated into the point lies in the interior of circle
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(0d , 0d) , 10d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | f
+(1 row)
+
+-- the box and circle are degenerated into the point and coincide
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(0d , 0d) , 0d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | t
+(1 row)
+
+-- the box and circle are degenerated into the point and not coincide
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(5d , 5d) , 0d>' as actual;
+    ?column?     | expected | actual 
+-----------------+----------+--------
+ sbox && scircle | f        | f
+(1 row)
+
+-- sbox vs spoly
+-- the box and polygon have no common points
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (30d, 0d),(40d, 0d),(30d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | f
+(1 row)
+
+-- the point of intersection of the box and polygon is the boundary for both
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (30d, 0d),(40d, 0d),(30d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | f
+(1 row)
+
+-- the boundaries of the boxes intersect at one line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (20d, 0d),(30d, 0d),(20d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box and circle matches
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the polygon lies completely in the box and they have an intersection at the boundary line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the polygon lies completely in the box and they have no intersection at the boundary
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (1d, 1d),(11d, 1d),(1d, 19d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box lies completely in the polygon and they have an intersection at the boundary line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (10d , 10d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box lies completely in the polygon and they have no intersection at the boundary
+select 'sbox && spoly', 'f' as expected, sbox'((1d , 1d), (2d , 2d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the polygon partially lies in the box
+select 'sbox && spoly', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (15d, 0d),(35d, 0d),(15d, 35d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | t        | t
+(1 row)
+
+-- the box degenerated into the line lies in the boundary of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 0d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box degenerated into the line lies in the interior of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 5d), (10d , 5d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box degenerated into the point lies in the boundary of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- the box degenerated into the point lies in the interior of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((5d , 5d), (5d , 5d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+   ?column?    | expected | actual 
+---------------+----------+--------
+ sbox && spoly | f        | t
+(1 row)
+
+-- sbox vs sellipse
+-- the box and ellipse have no common points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 20d , 10d }, (0d, 90d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | f
+(1 row)
+
+-- the point of intersection of the box and ellipse is the boundary for both
+select 'sbox && sellipse', 'f' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 80d , 10d }, (0d, 90d) , 90d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | f
+(1 row)
+
+-- the ellipse lies completely in the box and they have an intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 10d , 5d }, (10d, 10d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
+-- the ellipse lies completely in the box and they have no intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 9d , 5d }, (10d, 10d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
+-- the box lies completely in the ellipse and they have no intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
+-- the ellipse partially lies in the box
+select 'sbox && sellipse', 't' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 10d , 5d }, (10d, 10d) , 90d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | t        | t
+(1 row)
+
+-- the box degenerated into the point lies in the boundary of ellipse
+select 'sbox && sellipse', 'f' as expected, sbox'((30d , 0d), (30d , 0d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
+-- the box degenerated into the point lies in the interior of ellipse
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (10d , 0d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
+-- the box and ellipse are degenerated into the point and coincide
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sellipse'<{ 0d , 0d }, (0d, 0d) , 0d>' as actual;
+     ?column?     | expected | actual 
+------------------+----------+--------
+ sbox && sellipse | f        | t
+(1 row)
+
diff --git a/sql/contains.sql b/sql/contains.sql
new file mode 100644
index 0000000..4e348cc
--- /dev/null
+++ b/sql/contains.sql
@@ -0,0 +1,123 @@
+/*
+This set of tests is designed to verify the compliance of the contain operation with the DE-9IM model
+*/
+
+
+-- sline vs spoint
+
+
+-- the point lies far beyond the line
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(0d, 50d)' as actual;
+
+-- the point lies in the boundary of line
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(270d, 10d)' as actual;
+
+-- the point lies in the interior of line
+select 'sline ~ spoint', 't' as expected, sline(spoint'(270d,10d)', spoint'(270d,30d)') ~ spoint'(270d, 20d)' as actual;
+
+-- the point and line that degenerated into the point coincide
+select 'sline ~ spoint', 't' as expected, sline(spoint'(270d,10d)', spoint'(270d,10d)') ~ spoint'(270d, 10d)' as actual;
+
+-- the point and line that degenerated into the point do not coincide
+select 'sline ~ spoint', 'f' as expected, sline(spoint'(270d,10d)', spoint'(270d,10d)') ~ spoint'(270d, 20d)' as actual;
+
+
+-- spoint vs scircle
+
+
+-- the point lies far beyond the circle
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,0d)' @ scircle'<(0d,90d),50d>' as actual;
+
+-- the point lies in the boundary of circle
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,80d)' @ scircle'<(0d,90d),10d>' as actual;
+
+-- the point lies in the interior of circle
+select 'spoint @ scircle', 't' as expected, spoint'(0d,80d)' @ scircle'<(0d,90d),50d>' as actual;
+
+-- the point and circle that degenerated into the point coincide
+select 'spoint @ scircle', 't' as expected, spoint'(0d,90d)' @ scircle'<(0d,90d),0d>' as actual;
+
+-- the point and circle that degenerated into the point do not coincide
+select 'spoint @ scircle', 'f' as expected, spoint'(0d,50d)' @ scircle'<(0d,90d),0d>' as actual;
+
+
+-- sellipse vs spoint
+
+
+-- the point lies far beyond the ellipse
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(0d, 0d)' as actual;
+
+-- the point lies in the boundary of ellipse
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(0d, 70d)' as actual;
+
+-- the point lies in the interior of ellipse
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' ~ spoint'(90d, 65d)' as actual;
+
+-- the point lies in the boundary of ellipse that degenerated into the line
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 10d , 0d }, (0d , 0d) , 0d>' ~ spoint'(10d, 0d)' as actual;
+
+-- the point lies in the interior of ellipse that degenerated into the line
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 10d , 0d }, (0d , 0d) , 0d>' ~ spoint'(0d, 0d)' as actual;
+
+-- the point and ellipse that degenerated into the point coincide
+select 'sellipse ~ spoint', 't' as expected, sellipse'<{ 0d , 0d }, (0d , 90d) , 0d>' ~ spoint'(0d, 90d)' as actual;
+
+-- the point and ellipse that degenerated into the point do not coincide
+select 'sellipse ~ spoint', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 90d) , 0d>' ~ spoint'(0d, 91d)' as actual;
+
+
+-- spath vs spoint
+
+
+-- the point lies far beyond the opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(0d, 90d)' as actual;
+
+-- the point lies in the boundary of opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(-10d, 0d)' as actual;
+
+-- the point lies in the boundary of unsimple opened path
+select 'spath ~ spoint', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d),(-5d, 0d) }' ~ spoint'(-5d, 0d)' as actual;
+
+-- the point lies in the interior of opened path
+select 'spath ~ spoint', 't' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d) }' ~ spoint'(9d, 0d)' as actual;
+
+-- the point lies in the interior of closed path
+select 'spath ~ spoint', 't' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d),(80d,30d),(-10d, 0d) }' ~ spoint'(-10d, 0d)' as actual;
+
+
+-- spoly vs spoint
+
+
+-- the point lies far beyond the polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(0d, 90d)' as actual;
+
+-- the point lies in the boundary of polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(5d, 0d)' as actual;
+
+-- the point lies in the boundary of polygon
+select 'spoly ~ spoint', 'f' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(20d, 20d)' as actual;
+
+-- the point lies in the interior of polygon
+select 'spoly ~ spoint', 't' as expected, spoly'{ (0d,0d), (10d,0d), (20d,20d) }' ~ spoint'(5d, 5d)' as actual;
+
+
+-- sbox vs spoint
+
+
+--  the point lies far beyond the box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 90d)' as actual;
+
+-- the point lies in the boundary of box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 5d)' as actual;
+
+-- the point lies in the boundary of box
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(0d, 0d)' as actual;
+
+-- the point lies in the interior of box
+select 'sbox ~ spoint', 't' as expected, sbox'( (0d,0d), (20d,10d) )' ~ spoint'(5d, 5d)' as actual;
+
+-- the point and box that degenerated into the point coincide
+select 'sbox ~ spoint', 't' as expected, sbox'( (0d,0d), (0d,0d) )' ~ spoint'(0d, 0d)' as actual;
+
+-- the point and box that degenerated into the point do not coincide
+select 'sbox ~ spoint', 'f' as expected, sbox'( (0d,0d), (0d,0d) )' ~ spoint'(0d, 1d)' as actual;
diff --git a/sql/overlaps.sql b/sql/overlaps.sql
new file mode 100644
index 0000000..82db270
--- /dev/null
+++ b/sql/overlaps.sql
@@ -0,0 +1,484 @@
+/*
+This set of tests is designed to verify the compliance of the overlap operation with the DE-9IM model
+*/
+
+
+-- sline vs sline
+
+
+-- the lines have no common points
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(20d,0d)', spoint'(30d,0d)') as actual;
+
+-- the point of intersection of the lines is the boundary for both
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(10d,0d)', spoint'(20d,0d)') as actual;
+
+-- one line intersects the other at the boundary point of the latter
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,90d)', spoint'(0d,-10d)') as actual;
+
+-- the interiors of the lines intersect at one point
+select 'sline && sline', 'f' as expected, sline( spoint'(-10d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,90d)', spoint'(0d,-10d)') as actual;
+
+-- the lines match
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(10d,0d)') as actual;
+
+-- one line lies completely in the other and they have an intersection at the boundary point
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(5d,0d)') as actual;
+
+-- one line lies completely in the other and they have no intersection at the boundary point
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(2d,0d)', spoint'(5d,0d)') as actual;
+
+-- one line partially lies in the other
+select 'sline && sline', 't' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(5d,0d)', spoint'(20d,0d)') as actual;
+
+-- the line degenerated into the point lies on the boundary of another
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(0d,0d)', spoint'(0d,0d)') as actual;
+
+-- the line degenerated into the point lies in the interior of another
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(10d,0d)') && sline( spoint'(5d,0d)', spoint'(5d,0d)') as actual;
+
+-- both lines are degenerated into the point and coincide
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(0d,0d)') && sline( spoint'(0d,0d)', spoint'(0d,0d)') as actual;
+
+-- both lines are degenerated into the point and do not coincide, but lie close to each other
+select 'sline && sline', 'f' as expected, sline( spoint'(0d,0d)', spoint'(0d,0d)') && sline( spoint'(1d,0d)', spoint'(1d,0d)') as actual;
+
+
+-- scircle vs scircle
+
+
+-- the circles have no common points
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(30d , 0d) , 5d>' as actual;
+
+-- the point of intersection of the circles is the boundary for both
+select 'scircle && scircle', 'f' as expected, scircle'<(-10d , 0d) , 10d>' && scircle'<(10d , 0d) , 10d>' as actual;
+
+-- the circles match
+select 'scircle && scircle', 'f' as expected, scircle'<(-10d , 0d) , 10d>' && scircle'<(-10d , 0d) , 10d>' as actual;
+
+-- one circle lies completely in the other and they have an intersection at the boundary point
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(-10d , 0d) , 10d>' as actual;
+
+-- one circle lies completely in the other and they have no intersection at the boundary point
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(0d , 0d) , 5d>' as actual;
+
+-- one circle partially lies in the other
+select 'scircle && scircle', 't' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(10d , 0d) , 20d>' as actual;
+
+-- the circle degenerated into the point lies on the boundary of another
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(20d , 0d) , 0d>' as actual;
+
+-- the circle degenerated into the point lies in the interior of another
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 20d>' && scircle'<(0d , 0d) , 0d>' as actual;
+
+-- both circles are degenerated into the point and coincide
+select 'scircle && scircle', 'f' as expected, scircle'<(0d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+
+-- both circles are degenerated into the point and do not coincide, but lie close to each other
+select 'scircle && scircle', 'f' as expected, scircle'<(1d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+
+
+-- sellipse vs sellipse
+
+
+-- the ellipses have no common points
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (50 , 0d) , 0d>' as actual;
+
+-- the point of intersection of the ellipses is the boundary for both
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (45d , 0d) , 0d>' as actual;
+
+-- the ellipses match
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' && sellipse'<{ 45d , 20d }, (-45d , 0d) , 0d>' as actual;
+
+-- one ellipse lies completely in the other and they have an intersection at the boundary point
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 5d }, (-20d , 0d) , 0d>' as actual;
+
+-- one ellipse lies completely in the other and they have no intersection at the boundary point
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 10d , 5d }, (-20d , 0d) , 0d>' as actual;
+
+-- one ellipse partially lies in the other
+select 'sellipse && sellipse', 't' as expected, sellipse'<{ 45d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 5d }, (30d , 0d) , 0d>' as actual;
+
+-- the ellipse degenerated into the line lies completely in the interior of another (non-degenerate) ellipse
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 10d , 0d }, (10d , 0d) , 0d>' as actual;
+
+-- the ellipse degenerated into the line partially lies in the interior of another (non-degenerate) ellipse
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 20d , 0d }, (30d , 0d) , 0d>' as actual;
+
+-- the ellipse degenerated into the point lies on the boundary of another
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (30d , 0d) , 0d>' as actual;
+
+-- the ellipse degenerated into the point lies in the interior of another
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 40d , 30d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (40d , 0d) , 0d>' as actual;
+
+-- both ellipses are degenerated into the point and coincide
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' as actual;
+
+-- both ellipses are degenerated into the point and do not coincide, but lie close to each other
+select 'sellipse && sellipse', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && sellipse'<{ 0d , 0d }, (1d , 0d) , 0d>' as actual;
+
+
+-- sellipse vs scircle
+
+
+-- the ellipse and circle have no common points
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(30d , 0d) , 5d>' as actual;
+
+-- the point of intersection of the ellipse and circle is the boundary for both
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(30d , 0d) , 10d>' as actual;
+
+-- the ellipse and circle match
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 10d , 10d }, (30d , 0d) , 0d>' && scircle'<(30d , 0d) , 10d>' as actual;
+
+-- the ellipse lies completely in the circle and they have an intersection at the boundary point
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(20d , 0d) , 40d>' as actual;
+
+-- the ellipse lies completely in the circle and they have no intersection at the boundary point
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (20d , 0d) , 0d>' && scircle'<(20d , 0d) , 40d>' as actual;
+
+-- the circle lies completely in the ellipse
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 5d>' as actual;
+
+-- the circle partially lies in the ellipse
+select 'sellipse && scircle', 't' as expected, sellipse'<{ 20d , 10d }, (0d , 0d) , 0d>' && scircle'<(20d , 0d) , 15d>' as actual;
+
+-- the ellipse degenerated into the line lies completely in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 0d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 20d>' as actual;
+
+-- the ellipse degenerated into the line partially lies in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 20d , 0d }, (10d , 0d) , 0d>' && scircle'<(0d , 0d) , 20d>' as actual;
+
+-- the ellipse degenerated into the point lies on the boundary of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (10d , 0d) , 0d>' && scircle'<(0d , 0d) , 10d>' as actual;
+
+-- the ellipse degenerated into the point lies in the interior of circle
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (5d , 0d) , 0d>' && scircle'<(0d , 0d) , 10d>' as actual;
+
+-- the ellipse and circle are degenerated into the point and coincide
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && scircle'<(0d , 0d) , 0d>' as actual;
+
+-- the ellipses are degenerated into the point and do not coincide, but lie close to each other
+select 'sellipse && scircle', 'f' as expected, sellipse'<{ 0d , 0d }, (0d , 0d) , 0d>' && scircle'<(1d , 0d) , 0d>' as actual;
+
+
+-- spath vs spath
+
+
+-- the opened paths have no common points
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d,0d),(45d,15d) }' && spath'{ (60d, 15d),(70d, 20d),(75d, 20d) }' as actual;
+
+-- the points of intersection of the opened paths is the boundary for both
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-10d, 0d),(0d, 10d),(45d, 15d) }' as actual;
+
+-- one opened path intersects the other at the boundary point of the latter
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-20d, -10d),(-10d, 0d),(0d, 10d),(45d, 15d),(60d, 15d) }' as actual;
+
+-- the interiors of the opened paths intersect at one point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (0d, 10d),(0d, -10d),(10d, -10d) }' as actual;
+
+-- the interiors of the opened paths intersect at two points
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (0d, 10d),(0d, -10d),(5d, 0d) }' as actual;
+
+-- the opened paths match
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' as actual;
+
+-- the closed paths match
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' as actual;
+
+-- one opened path lies completely in the other and they have an intersection at the boundary point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 15d),(70d, 20d) }' && spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' as actual;
+
+-- one opened path lies completely in the other and they have no intersection at the boundary point
+select 'spath && spath', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 15d),(70d, 20d) }' && spath'{ (10d, 0d),(45d, 15d),(60d, 15d) }' as actual;
+
+-- one opened path partially lies in the other
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d) }' as actual;
+
+-- one closed path partially lies in the other
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d),(45d, 15d) }' as actual;
+
+-- the opened path partially lies in the closed path
+select 'spath && spath', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(-10d, 0d) }' && spath'{ (45d, 15d),(60d, 15d),(70d, 20d) }' as actual;
+
+
+-- spath vs sline
+
+
+-- the opened path and line have no common points
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(20d, 0d)', spoint'(30d, 0d)') as actual;
+
+-- the points of intersection of the opened path and line is the boundary for both
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(-10d, 0d)', spoint'(45d, 15d)') as actual;
+
+-- the interiors of the opened path and line intersect at one point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(0d, 10d)', spoint'(0d, -10d)') as actual;
+
+-- the path and line match
+select 'spath && sline', 'f' as expected, spath'{ (0d, 10d),(0d, -10d) }' && sline( spoint'(0d, 10d)', spoint'(0d, -10d)') as actual;
+
+-- the line lies completely in the opened path and they have an intersection at the boundary point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 20d) }' && sline( spoint'(-10d, 0d)', spoint'(10d, 0d)') as actual;
+
+-- the line lies completely in the opened path and they have no intersection at the boundary point
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d),(60d, 20d) }' && sline( spoint'(10d, 0d)', spoint'(45d, 15d)') as actual;
+
+-- the line partially lies in the open path
+select 'spath && sline', 't' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(5d, 0d)', spoint'(20d, 0d)') as actual;
+
+-- the line degenerated into the point lies in the boundary of open path
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(-10d, 0d)', spoint'(-10d, 0d)') as actual;
+
+-- the line degenerated into the point lies in the interior of open path
+select 'spath && sline', 'f' as expected, spath'{ (-10d, 0d),(10d, 0d),(45d, 15d) }' && sline( spoint'(0d, 0d)', spoint'(0d, 0d)') as actual;
+
+
+-- spoly vs spoly
+
+
+-- the polygons have no common points
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (10d, 0d),(20d, 0d),(10d, 10d) }' as actual;
+
+-- the point of intersection of the polygons is the boundary for both
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (10d, 0d),(20d, 0d),(0d, 10d) }' as actual;
+
+-- the interiors of the polygons intersect at one line
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (0d, 0d),(20d, 0d),(0d, 10d) }' as actual;
+
+-- the polygons matches
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' as actual;
+
+-- one polygon lies completely in the other and they have an intersection at the boundary line
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- one polygon lies completely in the other and they have no intersection at the boundary line or point
+select 'spoly && spoly', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && spoly'{ (5d, 5d),(15d, 5d),(15d, 15d),(5d,15d) }' as actual;
+
+-- one polygon partially lies in the other
+select 'spoly && spoly', 't' as expected, spoly'{ (0d, 0d),(-10d, 0d),(0d, 10d) }' && spoly'{ (5d, 5d),(30d, 5d),(30d, 15d),(5d,15d) }' as actual;
+
+
+-- spoly vs scircle
+
+
+-- the polygon and circle have no common points
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 90d) , 10d>' as actual;
+
+-- the point of intersection of the polygon and circle is the boundary for both
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 90d) , 80d>' as actual;
+
+-- the circle lies completely in the polygon and they have an intersection at the boundary point
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(5d , 1d) , 1d>' as actual;
+
+-- the circle lies completely in the polygon and they have no intersection at the boundary point
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(5d , 2d) , 1d>' as actual;
+
+-- the polygon lies completely in the circle
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 15d) , 20d>' as actual;
+
+-- the polygon partially lies in the circle
+select 'spoly && scircle', 't' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 5d) , 5d>' as actual;
+
+-- the circle degenerated into the point lies in the boundary of polygon
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(0d , 0d) , 0d>' as actual;
+
+-- the circle degenerated into the point lies in the interior of polygon
+select 'spoly && scircle', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && scircle'<(2d , 2d) , 0d>' as actual;
+
+
+-- spoly vs sellipse
+
+
+-- the polygon and ellipse have no common points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 30d , 20d }, (0d , 90d) , 0d>' as actual;
+
+-- the point of intersection of the polygon and ellipse is the boundary for both
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 80d , 20d }, (0d , 90d) , 90d>' as actual;
+
+-- the ellipse lies completely in the polygon and they have an intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && sellipse'<{ 10d , 5d }, (10d , 10d), 0d>' as actual;
+
+-- the ellipse lies completely in the polygon and they have no intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' && sellipse'<{ 7d , 5d }, (10d , 10d), 0d>' as actual;
+
+-- the polygon lies completely in the ellipse and they have an intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 5d),(10d, 10d),(20d, 5d),(10d, 0d) }' && sellipse'<{ 10d , 5d }, (10d , 5d), 0d>' as actual;
+
+-- the polygon lies completely in the ellipse and they have no intersection at the boundary points
+select 'spoly && sellipse', 'f' as expected, spoly'{ (1d, 5d),(10d, 9d),(19d, 5d),(10d, 1d) }' && sellipse'<{ 10d , 5d }, (10d , 10d), 0d>' as actual;
+
+-- the ellipse partially lies in the polygon
+select 'spoly && sellipse', 't' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 10d , 2d }, (0d , 5d) , 0d>' as actual;
+
+-- the ellipse degenerated into the point lies in the boundary of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 0d , 0d }, (0d , 0d), 0d>' as actual;
+
+-- the ellipse degenerated into the point lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 0d , 0d }, (5d , 2d), 0d>' as actual;
+
+-- the ellipse degenerated into the line lies in the boundary of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 5d , 0d }, (5d , 0d), 0d>' as actual;
+
+-- the ellipse degenerated into the line lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 2d , 0d }, (1d , 4d), 90d>' as actual;
+
+-- the ellipse degenerated into the line partially lies in the interior of polygon
+select 'spoly && sellipse', 'f' as expected, spoly'{ (0d, 0d),(10d, 0d),(0d, 10d) }' && sellipse'<{ 10d , 0d }, (1d , 4d), 0d>' as actual;
+
+
+-- sbox vs sbox
+
+
+-- the boxes have no common points
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((30d , 30d), (50d , 50d))' as actual;
+
+-- the point of intersection of the boxes is the boundary for both
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((20d , 20d), (50d , 50d))' as actual;
+
+-- the boundaries of the boxes intersect at one line
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((20d , 0d), (50d , 20d))' as actual;
+
+-- the boxes matches
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 10d))' as actual;
+
+-- one box lies completely in the other and they have no intersection at the boundary line or point
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 10d))' as actual;
+
+-- one box partially lies in the other
+select 'sbox && sbox', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((10d , 10d), (30d , 30d))' as actual;
+
+-- one box degenerated into the line lies in the boundary of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((0d , 0d), (20d , 0d))' as actual;
+
+-- one box degenerated into the line lies in the interior of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (10d , 5d))' as actual;
+
+-- one box degenerated into the point lies in the boundary of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((0d , 0d), (0d , 0d))' as actual;
+
+-- one box degenerated into the point lies in the interior of other
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sbox'((5d , 5d), (5d , 5d))' as actual;
+
+-- the boxes are degenerated into the point and coincide
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sbox'((0d , 0d), (0d , 0d))' as actual;
+
+-- the boxes are degenerated into the point and not coincide
+select 'sbox && sbox', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sbox'((10d , 10d), (10d , 10d))' as actual;
+
+
+-- sbox vs scircle
+
+
+-- the box and circle have no common points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(0d , 90d) , 10d>' as actual;
+
+-- the point of intersection of the box and circle is the boundary for both
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(30d , 0d) , 10d>' as actual;
+
+-- the circle lies completely in the box and they have an intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 10d>' as actual;
+
+-- the circle lies completely in the box and they have no intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 5d>' as actual;
+
+-- the box lies completely in the circle and they have an intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((-4d , -3d), (3d , 4d))' && scircle'<(0d , 0d) , 5d>' as actual;
+
+-- the box lies completely in the circle and they have no intersection at the boundary points
+select 'sbox && scircle', 'f' as expected, sbox'((-4d , -3d), (3d , 4d))' && scircle'<(0d , 0d) , 10d>' as actual;
+
+-- the box degenerated into the line intersects circle
+select 'sbox && scircle', 'f' as expected, sbox'((-20d , 0d), (20d , 0d))' && scircle'<(0d , 0d) , 10d>' as actual;
+
+-- the circle partially lies in the box
+select 'sbox && scircle', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(15d , 15d) , 10d>' as actual;
+
+-- the circle degenerated into the point lies in the boundary of box
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(0d , 10d) , 0d>' as actual;
+
+-- the circle degenerated into the point lies in the interior of box
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && scircle'<(10d , 10d) , 0d>' as actual;
+
+-- the box degenerated into the point lies in the boundary of circle
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(10d , 0d) , 10d>' as actual;
+
+-- the box degenerated into the point lies in the interior of circle
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(0d , 0d) , 10d>' as actual;
+
+-- the box and circle are degenerated into the point and coincide
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(0d , 0d) , 0d>' as actual;
+
+-- the box and circle are degenerated into the point and not coincide
+select 'sbox && scircle', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && scircle'<(5d , 5d) , 0d>' as actual;
+
+
+-- sbox vs spoly
+
+
+-- the box and polygon have no common points
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (30d, 0d),(40d, 0d),(30d, 20d) }' as actual;
+
+-- the point of intersection of the box and polygon is the boundary for both
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (30d, 0d),(40d, 0d),(30d, 20d) }' as actual;
+
+-- the boundaries of the boxes intersect at one line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (20d, 0d),(30d, 0d),(20d, 20d) }' as actual;
+
+-- the box and circle matches
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (0d, 0d),(20d, 0d),(20d, 20d),(0d, 20d) }' as actual;
+
+-- the polygon lies completely in the box and they have an intersection at the boundary line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the polygon lies completely in the box and they have no intersection at the boundary
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (1d, 1d),(11d, 1d),(1d, 19d) }' as actual;
+
+-- the box lies completely in the polygon and they have an intersection at the boundary line
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (10d , 10d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the box lies completely in the polygon and they have no intersection at the boundary
+select 'sbox && spoly', 'f' as expected, sbox'((1d , 1d), (2d , 2d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the polygon partially lies in the box
+select 'sbox && spoly', 't' as expected, sbox'((0d , 0d), (20d , 20d))' && spoly'{ (15d, 0d),(35d, 0d),(15d, 35d) }' as actual;
+
+-- the box degenerated into the line lies in the boundary of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (20d , 0d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the box degenerated into the line lies in the interior of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 5d), (10d , 5d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the box degenerated into the point lies in the boundary of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+-- the box degenerated into the point lies in the interior of polygon
+select 'sbox && spoly', 'f' as expected, sbox'((5d , 5d), (5d , 5d))' && spoly'{ (0d, 0d),(20d, 0d),(0d, 20d) }' as actual;
+
+
+-- sbox vs sellipse
+
+
+-- the box and ellipse have no common points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 20d , 10d }, (0d, 90d) , 0d>' as actual;
+
+-- the point of intersection of the box and ellipse is the boundary for both
+select 'sbox && sellipse', 'f' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 80d , 10d }, (0d, 90d) , 90d>' as actual;
+
+-- the ellipse lies completely in the box and they have an intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 10d , 5d }, (10d, 10d) , 0d>' as actual;
+
+-- the ellipse lies completely in the box and they have no intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (20d , 20d))' && sellipse'<{ 9d , 5d }, (10d, 10d) , 0d>' as actual;
+
+-- the box lies completely in the ellipse and they have no intersection at the boundary points
+select 'sbox && sellipse', 'f' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+
+-- the ellipse partially lies in the box
+select 'sbox && sellipse', 't' as expected, sbox'((-10d , -10d), (10d , 10d))' && sellipse'<{ 10d , 5d }, (10d, 10d) , 90d>' as actual;
+
+-- the box degenerated into the point lies in the boundary of ellipse
+select 'sbox && sellipse', 'f' as expected, sbox'((30d , 0d), (30d , 0d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+
+-- the box degenerated into the point lies in the interior of ellipse
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (10d , 0d))' && sellipse'<{ 30d , 20d }, (0d, 0d) , 0d>' as actual;
+
+-- the box and ellipse are degenerated into the point and coincide
+select 'sbox && sellipse', 'f' as expected, sbox'((0d , 0d), (0d , 0d))' && sellipse'<{ 0d , 0d }, (0d, 0d) , 0d>' as actual;