Fix for few similar bugs:

  #841622 Assertion `t->rp->type == Gcalc_function::shape_line' failed in Gcalc_operation_reducer::end_line in maria-5.3-gi
  #841625 Assertion `m_poly_borders->next' failed in Gcalc_operation_reducer::count_slice in maria-5.3-gis
  #841638 Assertion `!m_prev || m_prev->x != x || m_prev->y != y' failed in Gcalc_shape_transporter::int_add_point in maria-5.3-gis
  #841662 Third assertion `n > 0 && n < SINUSES_CALCULATED*2+1' in get_n_sincos
  #841745 Assertion `!sp0->is_bottom()' failed in Gcalc_scan_iterator::find_intersections in maria-5.3-gis

  They mostly was caused by inprecision of double arithmetic.
  Fixed by changes in how to handle multiple intersections to keep their order right.

  Also ST_DISTANCE(GEOM, EMPTY_GEOM) was defined as NULL.


per-file comments:
  mysql-test/r/gis-precise.result
   GIS bugfixes.
        test result updated.
  mysql-test/t/gis-precise.test
   GIS bugfixes.
        test cases added.
  sql/gcalc_slicescan.cc
   GIS bugfixes.
        If intersections are close, add order checks to cope with the
        double calcualtions imprecision.
  sql/gcalc_slicescan.h
   GIS bugfixes.
        n_row parameter added to intersection to check their order.
  sql/item_geofunc.cc
   GIS bugfixes.
        ST_DISTANCE(GEOM, EMPTY_GEOM) returns NULL.

mysql-test/r/gis-precise.result

@@ -214,7 +214,7 @@ astext(ST_BUFFER(LineStringFromText('LINESTRING(0 0,1 1)'),0))
 LINESTRING(0 0,1 1)
 SELECT Round(ST_Area(ST_BUFFER(MultipointFromText('MULTIPOINT(7 7,3 7,7 2,7 4 ,7 7)'), 3)), 5);
 Round(ST_Area(ST_BUFFER(MultipointFromText('MULTIPOINT(7 7,3 7,7 2,7 4 ,7 7)'), 3)), 5)
-78.68303
+78.68426
 SELECT ST_INTERSECTION(NULL, NULL);
 ST_INTERSECTION(NULL, NULL)
 NULL
@@ -257,7 +257,7 @@ ST_NUMGEOMETRIES((ST_UNION(ST_UNION(
 MULTILINESTRINGFROMTEXT('MULTILINESTRING((2 0,4 2,0 2,1 5,0 3,7 0,8 5,5 8),
                                                  (6 2,4 0,3 5,3 6,4 3,6 4,3 9,0 7,3 7,8 4,2 9,5 0),
                                           
-183
+176
 SELECT Round(ST_AREA(ST_BUFFER( ST_UNION(
 POLYGONFROMTEXT('POLYGON((7 7, 7 7, 7 4, 7 7, 7 7))'),
 POLYGONFROMTEXT('POLYGON((7 7, 4 7, 2 9, 7 6, 7 7))')), 1)), 6);
@@ -331,3 +331,86 @@ ST_DISTANCE(POINTFROMTEXT('POINT(7 1)'),MULTILINESTRINGFROMTEXT('MULTILINESTRING
 SELECT AsText(ST_UNION(POLYGONFROMTEXT('POLYGON((12 9, 3 6, 3 0, 12 9))'), POLYGONFROMTEXT('POLYGON((2 2, 7 2, 4 2, 2 0, 2 2))')));
 AsText(ST_UNION(POLYGONFROMTEXT('POLYGON((12 9, 3 6, 3 0, 12 9))'), POLYGONFROMTEXT('POLYGON((2 2, 7 2, 4 2, 2 0, 2 2))')))
 GEOMETRYCOLLECTION(POLYGON((2 0,2 2,3 2,3 6,12 9,3 0,3 1,2 0)),LINESTRING(5 2,7 2))
+SELECT ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER(ST_UNION(
+MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 2 5, 7 6, 1 8),(0 0 ,1 6 ,0 1, 8 9, 2 4, 6 1, 3 5, 4 8), (9 3, 5 4, 1 8, 4 2, 5 8, 3 0))' ) ,
+MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 3 1, 2 7, 4 2, 6 2, 1 5))')
+), 16)));
+ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER(ST_UNION(
+MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 2 5, 7 6, 1 8),(0 0 ,1 6 ,0 1, 8 9, 2 4, 6 1, 3 5, 4 8), (9 3, 5 4, 1 8, 4 2, 5 8, 3 0))' ) ,
+MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 3 1, 2 7, 4 2, 6 2
+280
+SELECT ST_NUMGEOMETRIES(ST_DIFFERENCE (
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 4 , 5 0 , 2 9 , 6 2 , 0 2 ) , ( 4 3 , 5 6 , 9 4 , 0 7 , 7 2 , 2 0 , 8 2 ) , ( 5 0 , 1 5 , 3 7 , 7 7 ) , ( 2 3 , 9 5 , 2 0 , 8 1 ) , ( 0 9 , 9 3 , 2 8 , 8 1 , 9 4 ) ) ' ),
+ST_UNION (
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 7 2 , 6 2 , 2 6 , 2 2 ) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,
+ENVELOPE(
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' )
+)
+)
+),
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 9 , 1 3 , 7 3 , 8 5 ) , ( 5 0 , 8 1 , 2 0 , 7 4 , 1 0 ) , ( 9 2 , 5 2 , 6 5 , 8 8 , 0 2 ) , ( 0 8 , 3 9 , 4 0 , 1 0 ) , ( 0 0 , 7 6 , 8 3 , 0 0 ) ) ' )
+));
+ST_NUMGEOMETRIES(ST_DIFFERENCE (
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 4 , 5 0 , 2 9 , 6 2 , 0 2 ) , ( 4 3 , 5 6 , 9 4 , 0 7 , 7 2 , 2 0 , 8 2 ) , ( 5 0 , 1 5 , 3 7 , 7 7 ) , ( 2 3 , 9 5 , 2 0 , 8 1 ) , ( 0 9 , 9 3 , 2 8 , 8 1 , 9 4 )
+126
+SELECT ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER (
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 7 3 , 1 8 , 4 0 , 7 9 ) , ( 5 4 , 9 8 , 7 4 , 3 7 ) , ( 5 8 , 5 4 , 9 2 , 5 6 ) , ( 4 0 , 3 2 , 0 1 , 3 9 ) , ( 2 0 , 3 5 , 9 5 , 0 9 ) ) ' ) ,
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 4 5 , 3 0 , 3 1 , 4 7 , 4 2 ) , ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) ' )
+) , 1
+)));
+ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER (
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 7 3 , 1 8 , 4 0 , 7 9 ) , ( 5 4 , 9 8 , 7 4 , 3 7 ) , ( 5 8 , 5 4 , 9 2 , 5 6 ) , ( 4 0 , 3 2 , 0 1 , 3 9 ) , ( 2 0 , 3 5 , 9 5 , 0 9 ) ) ' ) ,
+MULTILINESTRI
+659
+SELECT ASTEXT(ST_DIFFERENCE (
+POLYGONFROMTEXT( ' POLYGON( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) ' ) ,
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( (3 5, 2 5, 2 4, 3 4, 3 5) ) ' ) ,
+ST_SYMDIFFERENCE (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 3 8 , 0 8 , 6 6 , 6 1 , 0 5 , 6 7 , 3 7 ) , ( 5 8 , 7 7 , 9 0 , 8 7 ) , ( 1 5 , 1 8 , 2 3 , 3 9 ) , ( 1 3 , 9 7 , 5 5 , 0 8 , 6 9 ) , ( 3 6 , 6 9 , 8 7 , 0 2 , 4 6 , 9 5 ) ) ' ) ,
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 9 4 , 2 0 , 2 2 , 7 2 , 6 2 ) , ( 5 2 , 8 2 , 4 8 , 3 4 ) , ( 1 0 , 1 4 , 2 7 , 7 0 , 1 5 ) , ( 2 8 , 4 4 , 5 0 , 7 0 , 4 0 ) ) ' ) ,
+GEOMETRYFROMTEXT( ' MULTILINESTRING( ( 3 7 , 7 3 , 5 8 , 4 8 ) , ( 3 2 , 5 0 , 9 3 , 4 4 ) , ( 6 0 , 4 2 , 7 8 , 1 3 ) ) ' )
+)
+)
+)
+));
+ASTEXT(ST_DIFFERENCE (
+POLYGONFROMTEXT( ' POLYGON( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) ' ) ,
+ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( (3 5, 2 5, 2 4, 3 4, 3 5) ) ' ) ,
+ST_SYMDIFFERENCE (
+MULTILINESTRINGFROMTEX
+POLYGON((2 2,2 8,8 8,8 2,2 2),(4 4,4 6,6 6,6 4,4 4))
+SELECT ST_NUMGEOMETRIES(ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 0 8 , 1 9 , 5 7 , 2 8 , 5 8 , 6 7 ) , ( 4 5 , 8 4 , 0 3 , 5 1 ) , ( 6 8 , 2 7 , 1 6 , 9 9 , 7 2 ) , ( 9 5 , 2 8 , 1 2 , 9 6 , 2 0 ) ) ' ) ,
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 7 7 , 2 7, 6 8, 7 1 , 7 7 ) ) ) ' )
+));
+ST_NUMGEOMETRIES(ST_UNION (
+MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 0 8 , 1 9 , 5 7 , 2 8 , 5 8 , 6 7 ) , ( 4 5 , 8 4 , 0 3 , 5 1 ) , ( 6 8 , 2 7 , 1 6 , 9 9 , 7 2 ) , ( 9 5 , 2 8 , 1 2 , 9 6 , 2 0 ) ) ' ) ,
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (
+50
+SELECT ST_BUFFER (
+LINESTRINGFROMTEXT( ' LINESTRING( 5 4 , 3 8 , 2 6 , 5 5 , 7 9 ) ' ) ,
+ST_DISTANCE (
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 4, 2 5, 3 5) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) , ( ( 0 0 , 8 3 , 9 5 , 0 0 ) ) ) ' ) ,
+ST_DIFFERENCE (
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) , ( ( 0 0 , 3 8 , 9 4 , 0 0 ) ) ) ' )
+)
+)
+) ;
+ST_BUFFER (
+LINESTRINGFROMTEXT( ' LINESTRING( 5 4 , 3 8 , 2 6 , 5 5 , 7 9 ) ' ) ,
+ST_DISTANCE (
+MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 4, 2 5, 3 5) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) , ( ( 0 0 , 8 3 , 9 5 , 0 0 ) ) ) ' ) ,
+ST_DIFFERENCE (
+MULTIPOL
+NULL
+SELECT   ST_DISTANCE (     ST_DIFFERENCE (                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) , ( ( 0 0 , 3 8 , 9 4 , 0 0 ) ) ) ' )                         ),                         MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 4, 2 5, 3 5) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) , ( ( 0 0 , 8 3 , 9 5 , 0 0 ) ) ) ' ) )  ;
+ST_DISTANCE (     ST_DIFFERENCE (                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 ,
+NULL

mysql-test/t/gis-precise.test

@@ -214,4 +214,69 @@ SELECT ST_DISTANCE(POINTFROMTEXT('POINT(7 1)'),MULTILINESTRINGFROMTEXT('MULTILIN
 #bug 839327 Crash in Gcalc_operation_reducer::end_couple with ST_UNION and MULTIPOLYGONs in 5.3-gis
 SELECT AsText(ST_UNION(POLYGONFROMTEXT('POLYGON((12 9, 3 6, 3 0, 12 9))'), POLYGONFROMTEXT('POLYGON((2 2, 7 2, 4 2, 2 0, 2 2))')));
 
+#bug 841622 Assertion `t->rp->type == Gcalc_function::shape_line' failed in Gcalc_operation_reducer::end_line in maria-5.3-gis
+
+SELECT ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER(ST_UNION(
+  MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 2 5, 7 6, 1 8),(0 0 ,1 6 ,0 1, 8 9, 2 4, 6 1, 3 5, 4 8), (9 3, 5 4, 1 8, 4 2, 5 8, 3 0))' ) ,
+  MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 3 1, 2 7, 4 2, 6 2, 1 5))')
+  ), 16)));
+
+#bug 841625 Assertion `m_poly_borders->next' failed in Gcalc_operation_reducer::count_slice in maria-5.3-gis
+
+SELECT ST_NUMGEOMETRIES(ST_DIFFERENCE (
+        ST_UNION (
+                MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 4 , 5 0 , 2 9 , 6 2 , 0 2 ) , ( 4 3 , 5 6 , 9 4 , 0 7 , 7 2 , 2 0 , 8 2 ) , ( 5 0 , 1 5 , 3 7 , 7 7 ) , ( 2 3 , 9 5 , 2 0 , 8 1 ) , ( 0 9 , 9 3 , 2 8 , 8 1 , 9 4 ) ) ' ),
+                ST_UNION (
+                        MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 7 2 , 6 2 , 2 6 , 2 2 ) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,
+                        ENVELOPE(
+                                MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' )
+                        )
+                )
+        ),
+        MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 9 , 1 3 , 7 3 , 8 5 ) , ( 5 0 , 8 1 , 2 0 , 7 4 , 1 0 ) , ( 9 2 , 5 2 , 6 5 , 8 8 , 0 2 ) , ( 0 8 , 3 9 , 4 0 , 1 0 ) , ( 0 0 , 7 6 , 8 3 , 0 0 ) ) ' )
+));
+
+
+#bug 841638 Assertion `!m_prev || m_prev->x != x || m_prev->y != y' failed in Gcalc_shape_transporter::int_add_point in maria-5.3-gis
+SELECT ST_NUMPOINTS(ST_EXTERIORRING(ST_BUFFER (
+         ST_UNION (
+                MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 7 3 , 1 8 , 4 0 , 7 9 ) , ( 5 4 , 9 8 , 7 4 , 3 7 ) , ( 5 8 , 5 4 , 9 2 , 5 6 ) , ( 4 0 , 3 2 , 0 1 , 3 9 ) , ( 2 0 , 3 5 , 9 5 , 0 9 ) ) ' ) ,
+                MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 4 5 , 3 0 , 3 1 , 4 7 , 4 2 ) , ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) ' )
+        ) , 1
+)));
+
+#bug 841745 ssertion `!sp0->is_bottom()' failed in Gcalc_scan_iterator::find_intersections in maria-5.3-gis
+SELECT ASTEXT(ST_DIFFERENCE (
+        POLYGONFROMTEXT( ' POLYGON( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) ' ) ,
+        ST_UNION (
+                MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( (3 5, 2 5, 2 4, 3 4, 3 5) ) ' ) ,
+                ST_SYMDIFFERENCE (
+                        MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 3 8 , 0 8 , 6 6 , 6 1 , 0 5 , 6 7 , 3 7 ) , ( 5 8 , 7 7 , 9 0 , 8 7 ) , ( 1 5 , 1 8 , 2 3 , 3 9 ) , ( 1 3 , 9 7 , 5 5 , 0 8 , 6 9 ) , ( 3 6 , 6 9 , 8 7 , 0 2 , 4 6 , 9 5 ) ) ' ) ,
+                        ST_UNION (
+                                MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 9 4 , 2 0 , 2 2 , 7 2 , 6 2 ) , ( 5 2 , 8 2 , 4 8 , 3 4 ) , ( 1 0 , 1 4 , 2 7 , 7 0 , 1 5 ) , ( 2 8 , 4 4 , 5 0 , 7 0 , 4 0 ) ) ' ) ,
+                                GEOMETRYFROMTEXT( ' MULTILINESTRING( ( 3 7 , 7 3 , 5 8 , 4 8 ) , ( 3 2 , 5 0 , 9 3 , 4 4 ) , ( 6 0 , 4 2 , 7 8 , 1 3 ) ) ' )
+                        )
+                )
+        )
+));
+
+#bug 841773 Assertion `t0->rp->type == t1->rp->type' failed in Gcalc_operation_reducer::end_couple in maria-5.3-gis
+SELECT ST_NUMGEOMETRIES(ST_UNION (
+        MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 0 8 , 1 9 , 5 7 , 2 8 , 5 8 , 6 7 ) , ( 4 5 , 8 4 , 0 3 , 5 1 ) , ( 6 8 , 2 7 , 1 6 , 9 9 , 7 2 ) , ( 9 5 , 2 8 , 1 2 , 9 6 , 2 0 ) ) ' ) ,
+        MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 7 7 , 2 7, 6 8, 7 1 , 7 7 ) ) ) ' )
+));
+
+#bug 841662 Third assertion `n > 0 && n < SINUSES_CALCULATED*2+1' in get_n_sincos 
+SELECT ST_BUFFER (
+                LINESTRINGFROMTEXT( ' LINESTRING( 5 4 , 3 8 , 2 6 , 5 5 , 7 9 ) ' ) ,
+                ST_DISTANCE (
+                        MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 4, 2 5, 3 5) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) , ( ( 0 0 , 8 3 , 9 5 , 0 0 ) ) ) ' ) ,
+                        ST_DIFFERENCE (
+                                MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,
+                                MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) , ( ( 0 0 , 3 8 , 9 4 , 0 0 ) ) ) ' )
+                        )
+                )
+ ) ;
+SELECT   ST_DISTANCE (     ST_DIFFERENCE (                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 5, 2 4, 3 4, 3 5) ) ) ' ) ,                                 MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 2 8 , 8 8 , 8 2 , 2 2 ) , ( 4 4 , 4 6 , 6 6 , 6 4 , 4 4 ) ) , ( ( 0 0 , 3 8 , 9 4 , 0 0 ) ) ) ' )                         ),                         MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( (3 5, 2 4, 2 5, 3 5) ) , ( (3 5, 2 5, 2 4, 3 4, 3 5) ) , ( ( 0 0 , 8 3 , 9 5 , 0 0 ) ) ) ' ) )  ;
+
 

sql/gcalc_slicescan.cc

@@ -683,7 +683,8 @@ int Gcalc_scan_iterator::normal_scan()
 
 #define INTERSECTION_ZERO 0.000000000001
 
-int Gcalc_scan_iterator::add_intersection(const point *a, const point *b,
+int Gcalc_scan_iterator::add_intersection(int n_row,
+                                          const point *a, const point *b,
 		                          Gcalc_dyn_list::Item ***p_hook)
 {
   intersection *isc= new_intersection();
@@ -693,6 +694,7 @@ int Gcalc_scan_iterator::add_intersection(const point *a, const point *b,
   m_n_intersections++;
   **p_hook= isc;
   *p_hook= &isc->next;
+  isc->n_row= n_row;
   isc->thread_a= a->thread;
   isc->thread_b= b->thread;
 
@@ -703,13 +705,22 @@ int Gcalc_scan_iterator::add_intersection(const point *a, const point *b,
 
   if (!a0->horiz_dir && !b0->horiz_dir)
   {
-    double dk= a0->dx_dy - b0->dx_dy;
-    double dy= (b0->x - a0->x)/dk;
+    double b0_x= a0->next_pi->x - a0->pi->x;
+    double b0_y= a0->next_pi->y - a0->pi->y;
+    double b1_x= b0->next_pi->x - b0->pi->x;
+    double b1_y= b0->next_pi->y - b0->pi->y;
+    double b1xb0= b1_x * b0_y - b1_y * b0_x;
+    double t= (a0->pi->x - b0->pi->x) * b0_y - (a0->pi->y - b0->pi->y) * b0_x;
+    if (fabs(b1xb0) < INTERSECTION_ZERO)
+    {
+      isc->y= current_state->y;
+      isc->x= a0->x;
+      return 0;
+    }
 
-    if (fabs(dk) < INTERSECTION_ZERO)
-      dy= 0.0;
-    isc->y= current_state->y + dy;
-    isc->x= a0->x + dy*a0->dx_dy;
+    t/= b1xb0;
+    isc->x= b0->pi->x + b1_x*t;
+    isc->y= b0->pi->y + b1_y*t;
     return 0;
   }
   isc->y= next_state->y;
@@ -720,13 +731,13 @@ int Gcalc_scan_iterator::add_intersection(const point *a, const point *b,
 
 int Gcalc_scan_iterator::find_intersections()
 {
-  point *sp1= next_state->slice;
   Gcalc_dyn_list::Item **hook;
 
   m_n_intersections= 0;
   {
     /* Set links between slicepoints */
     point *sp0= current_state->slice;
+    point *sp1= next_state->slice;
     for (; sp1; sp0= sp0->get_next(),sp1= sp1->get_next())
     {
       DBUG_ASSERT(!sp0->is_bottom());
@@ -737,30 +748,34 @@ int Gcalc_scan_iterator::find_intersections()
 
   hook= (Gcalc_dyn_list::Item **)&m_intersections;
   bool intersections_found;
+  int n_row= 0;
 
-  point *last_possible_isc= NULL;
   do
   {
     point **pprev_s1= &next_state->slice;
     intersections_found= false;
-    sp1= next_state->slice->get_next();
-    point *cur_possible_isc= NULL;
-    for (; sp1 != last_possible_isc;
-	 pprev_s1= (point **)(&(*pprev_s1)->next), sp1= sp1->get_next())
+    n_row++;
+    for (;;)
     {
       point *prev_s1= *pprev_s1;
-      if (prev_s1->x <= sp1->x)
-	continue;
+      point *s1= prev_s1->get_next();
+      if (!s1)
+        break;
+      if (prev_s1->x <= s1->x)
+      {
+        pprev_s1= (point **) &prev_s1->next;
+        continue;
+      }
       intersections_found= true;
-      if (add_intersection(prev_s1, sp1, &hook))
+      if (add_intersection(n_row, prev_s1, s1, &hook))
 	return 1;
-      *pprev_s1= sp1;
-      prev_s1->next= sp1->next;
-      sp1->next= prev_s1;
-      sp1= prev_s1;
-      cur_possible_isc= sp1;
-    }
-    last_possible_isc= cur_possible_isc;
+      *pprev_s1= s1;
+      prev_s1->next= s1->next;
+      s1->next= prev_s1;
+      pprev_s1= (point **) &prev_s1->next;
+      if (!*pprev_s1)
+        break;
+    };
   } while (intersections_found);
 
   *hook= NULL;
@@ -772,7 +787,13 @@ static int compare_intersections(const void *e0, const void *e1)
 {
   Gcalc_scan_iterator::intersection *i0= (Gcalc_scan_iterator::intersection *)e0;
   Gcalc_scan_iterator::intersection *i1= (Gcalc_scan_iterator::intersection *)e1;
-  if (i0->y != i1->y)
+
+  if (fabs(i0->y - i1->y) > 0.00000000000001)
+    return i0->y > i1->y;
+
+  if (i0->n_row != i1->n_row)
+    return i0->n_row > i1->n_row;
+  if (!coord_eq(i0->y, i1->y))
     return i0->y > i1->y;
   return i0->x > i1->x;
 }
@@ -810,7 +831,8 @@ int Gcalc_scan_iterator::intersection_scan()
 {
   point *sp0, *sp1;
   Gcalc_dyn_list::Item **hook;
-  intersection *next_intersection;
+  intersection *next_intersection= NULL;
+  int met_equal= 0;
 
   if (m_cur_intersection != m_intersections)
   {
@@ -860,7 +882,6 @@ int Gcalc_scan_iterator::intersection_scan()
 
   next_state->y= m_cur_intersection->y;
 
-found_equal_intersection:
   sp0= current_state->slice;
   hook= (Gcalc_dyn_list::Item **) &next_state->slice;
   sp1= next_state->slice;
@@ -872,6 +893,10 @@ int Gcalc_scan_iterator::intersection_scan()
     if (sp0->thread == m_cur_intersection->thread_a ||
         sp0->thread == m_cur_intersection->thread_b)
     {
+#ifdef REACTIVATE_THIS
+      DBUG_ASSERT(sp0->thread != m_cur_intersection->thread_a ||
+        sp0->get_next()->thread == m_cur_intersection->thread_b);
+#endif /*REACTIVATE_THIS*/
       sp1->copy_core(sp0);
       sp1->x= m_cur_intersection->x;
       sp1->event= scev_intersection;
@@ -888,6 +913,7 @@ int Gcalc_scan_iterator::intersection_scan()
       {
         sp1->event= scev_intersection;
         mark_event_position1(sp1, hook);
+        met_equal= 1;
       }
       else
         sp1->event= scev_none;
@@ -900,13 +926,64 @@ int Gcalc_scan_iterator::intersection_scan()
     *hook= NULL;
   }
 
-  next_intersection= m_cur_intersection->get_next();
-  if (next_intersection &&
-      coord_eq(next_intersection->x, m_cur_intersection->x) &&
-      coord_eq(next_intersection->y, m_cur_intersection->y))
+  if (met_equal)
   {
-    m_cur_intersection= next_intersection;
-    goto found_equal_intersection;
+    /* Remove superfluous intersections. */
+    /* Double operations can produce unexact result, so it's needed. */
+    for (sp0= next_state->event_position;
+        sp0 != *next_state->event_end_hook;
+        sp0= sp0->get_next())
+    {
+      for (sp1= sp0->get_next();
+          sp1 != *next_state->event_end_hook;
+          sp1= sp1->get_next())
+      {
+        intersection *isc= m_cur_intersection;
+        while (isc->get_next())
+        {
+          intersection *cur_isc= isc->get_next();
+          if ((cur_isc->thread_a == sp0->thread &&
+                cur_isc->thread_b == sp1->thread) ||
+              (cur_isc->thread_a == sp1->thread &&
+               cur_isc->thread_b == sp0->thread))
+          {
+            /* The superfluous intersection should be close to the current. */
+            DBUG_ASSERT(fabs(cur_isc->x-m_cur_intersection->x) +
+                        fabs(cur_isc->y-m_cur_intersection->y) <
+                        INTERSECTION_ZERO);
+            isc->next= isc->next->next;
+            free_item(cur_isc);
+          }
+          else
+            isc= isc->get_next();
+        }
+      }
+    }
+  }
+
+  for (next_intersection= m_cur_intersection->get_next();
+       next_intersection &&
+         coord_eq(next_intersection->x, m_cur_intersection->x) &&
+         coord_eq(next_intersection->y, m_cur_intersection->y);
+       next_intersection= next_intersection->get_next())
+  {
+    /* Handle equal intersections. We only need to set proper events */
+    sp0= current_state->slice;
+    hook= (Gcalc_dyn_list::Item **) &next_state->slice;
+    sp1= next_state->slice;
+    next_state->clear_event_position();
+
+    for (; sp0;
+        hook= &sp1->next, sp1= sp1->get_next(), sp0= sp0->get_next())
+    {
+      if (sp0->thread == next_intersection->thread_a ||
+          sp0->thread == next_intersection->thread_b ||
+          sp1->event == scev_intersection)
+      {
+        sp1->event= scev_intersection;
+        mark_event_position1(sp1, hook);
+      }
+    }
   }
   m_cur_intersection= next_intersection;
 

sql/gcalc_slicescan.h

@@ -303,6 +303,7 @@ class Gcalc_scan_iterator : public Gcalc_dyn_list
   class intersection : public Gcalc_dyn_list::Item
   {
   public:
+    int n_row;
     sc_thread_id thread_a;
     sc_thread_id thread_b;
     double x;
@@ -371,7 +372,7 @@ class Gcalc_scan_iterator : public Gcalc_dyn_list
   void sort_intersections();
   int handle_intersections();
   int insert_top_point();
-  int add_intersection(const point *a, const point *b,
+  int add_intersection(int n_row, const point *a, const point *b,
 		       Gcalc_dyn_list::Item ***p_hook);
   int find_intersections();
 

sql/item_geofunc.cc

@@ -1789,6 +1789,14 @@ double Item_func_distance::val_real()
   if (g2->store_shapes(&trn) || func.alloc_states())
     goto mem_error;
 
+  if (obj2_si == 0 || func.get_nshapes() == obj2_si)
+  {
+    distance= 0.0;
+    null_value= 1;
+    goto exit;
+  }
+
+
   collector.prepare_operation();
   scan_it.init(&collector);