several bugs fixed here.

        849789  Second assertion `m_poly_borders->next' failed in Gcalc_operation_reducer::count_slice in maria-5.3-gis
        849791  Fourth assertion `n > 0 && n < SINUSES_CALCULATED*2+1' in get_n_sincos
        849789  Second assertion `m_poly_borders->next' failed in Gcalc_operation_reducer::count_slice in maria-5.3-gis
        848901   Assertion `fabs(cur_isc->x-m_cur_intersection->x) + fabs(cur_isc->y-m_cur_intersection->y) < 0.000000000001' failed in Gcalc_scan_iterator::intersection_scan() in maria-5.3-gis
        
per-file comments:
  mysql-test/r/gis-precise.result
        test result updated.
  mysql-test/r/gis.result
        test result updated.
  sql/gcalc_slicescan.cc
        bugfixes.
  sql/gcalc_slicescan.h
        bugfixes.
  sql/gcalc_tools.cc
        bugfixes.
  sql/gcalc_tools.h
        bugfixes.
  sql/item_geofunc.cc
        bugfixes.
  sql/spatial.cc
        bugfixes.

mysql-test/r/gis-precise.result

@@ -189,7 +189,7 @@ st_touches(geomfromtext('polygon((0 0, 2 2, 0 4, 0 0))'), geomfromtext('point(1
 0
 select st_touches(geomfromtext('polygon((0 0, 2 2, 0 4, 0 0))'), geomfromtext('polygon((1 1.2, 1 0, 2 0, 1 1.2))'));
 st_touches(geomfromtext('polygon((0 0, 2 2, 0 4, 0 0))'), geomfromtext('polygon((1 1.2, 1 0, 2 0, 1 1.2))'))
-1
+0
 select st_touches(geomfromtext('polygon((0 0, 2 2, 0 4, 0 0))'), geomfromtext('polygon((1 1, 1 0, 2 0, 1 1))'));
 st_touches(geomfromtext('polygon((0 0, 2 2, 0 4, 0 0))'), geomfromtext('polygon((1 1, 1 0, 2 0, 1 1))'))
 1
@@ -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),
                                           
-176
+185
 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);
@@ -338,7 +338,7 @@ MULTILINESTRINGFROMTEXT('MULTILINESTRING((3 4, 3 1, 2 7, 4 2, 6 2, 1 5))')
 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
+275
 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 ) ) ' ),
@@ -354,7 +354,7 @@ MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 9 , 1 3 , 7 3 , 8 5 ) , ( 5 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
+123
 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 ) ) ' ) ,
@@ -365,7 +365,7 @@ 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
+653
 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 (
@@ -416,7 +416,7 @@ ST_DISTANCE (     ST_DIFFERENCE (                                 MULTIPOLYGONFR
 NULL
 SELECT ST_NUMGEOMETRIES( ST_SYMDIFFERENCE ( ST_SYMDIFFERENCE ( ST_INTERSECTION ( MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 6 4 , 3 7 , 9 4 , 3 8 ) , ( 2 2 , 2 9 , 1 2 , 9 8 ) ) ' ) , ST_SYMDIFFERENCE ( MULTIPOINTFROMTEXT( ' MULTIPOINT( 6 1 , 3 8 , 3 3 , 0 6 , 7 2 , 3 4 ) ' ) , ST_BUFFER ( ST_UNION ( MULTIPOLYGONFROMTEXT( ' MULTIPOLYGON( ( ( 2 2 , 6 2 , 1 3 , 2 2 , 2 2 ) ) ) ' ) , GEOMETRYFROMTEXT( ' MULTILINESTRING( ( 1 4 , 9 9 , 3 0 , 6 6 ) , ( 3 5 , 1 0 , 5 8 , 6 1 ) , ( 8 9 , 6 1 , 5 1 , 6 2 ) , ( 2 2 , 7 5 , 5 8 , 6 9 , 3 0 ) , ( 8 0 , 8 4 , 6 7 , 5 5 ) ) ' ) ) , NUMPOINTS( EXTERIORRING( POLYGONFROMTEXT( ' POLYGON( ( 0 0 , 2 1 , 8 2 , 0 0 ) ) ' ) ) ) ) ) ) , ST_INTERSECTION ( POLYGONFROMTEXT( ' POLYGON( ( 2 3, 5 7 , 3 7 , 4 1 , 0 5, 2 3 ) ) ' ) , MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 2 3 , 1 4 , 6 4 , 9 1 , 3 4 , 1 8 ) , ( 9 9 , 0 3 , 1 7 , 9 9 ) ) ' ) ) ) , POLYGONFROMTEXT( ' POLYGON( ( 1 3, 7 2 , 1 5 , 3 8 , 5 0, 1 3) ) ' ) ) ) ;
 ST_NUMGEOMETRIES( ST_SYMDIFFERENCE ( ST_SYMDIFFERENCE ( ST_INTERSECTION ( MULTILINESTRINGFROMTEXT( ' MULTILINESTRING( ( 6 4 , 3 7 , 9 4 , 3 8 ) , ( 2 2 , 2 9 , 1 2 , 9 8 ) ) ' ) , ST_SYMDIFFERENCE ( MULTIPOINTFROMTEXT( ' MULTIPOINT( 6 1 , 3 8 , 3 3 , 0 6 
-27
+25
 SELECT ASTEXT(ST_INTERSECTION( GEOMETRYFROMTEXT('GEOMETRYCOLLECTION(LINESTRING(7 7,5.33333333333333 7),LINESTRING(5.33333333333333 7,0 7,5 8,5.33333333333333 7),LINESTRING(5.33333333333333 7,7 2,7 7),POLYGON((0 5,3 5,3 2,1 2,1 1,3 1,3 0,0 0,0 3,2 3,2 4,0 4,0 5)))'), geomETRYFROMTEXT(' MULTILINESTRING( ( 5 1 , 3 7 , 6 1 , 7 0 ) , ( 1 6 , 8 5 , 7 5 , 5 6 ) )') ));
 ASTEXT(ST_INTERSECTION( GEOMETRYFROMTEXT('GEOMETRYCOLLECTION(LINESTRING(7 7,5.33333333333333 7),LINESTRING(5.33333333333333 7,0 7,5 8,5.33333333333333 7),LINESTRING(5.33333333333333 7,7 2,7 7),POLYGON((0 5,3 5,3 2,1 2,1 1,3 1,3 0,0 0,0 3,2 3,2 4,0 4,0 5))
 MULTIPOINT(7 5,7 5.14285714285714,5.9 5.3,5.8 5.6,3 7)

mysql-test/r/gis.result

@@ -850,7 +850,7 @@ mbroverlaps
 down,left,right,up
 SELECT GROUP_CONCAT(a2.name ORDER BY a2.name) AS mbrtouches   FROM t1 a1 JOIN t1 a2 ON MBRTouches(    a1.square, a2.square) WHERE a1.name = "center" GROUP BY a1.name;
 mbrtouches
-big,center,down,down2,left,left2,right,right2,small,up,up2
+down2,left2,right2,up2
 SELECT GROUP_CONCAT(a2.name ORDER BY a2.name) AS mbrwithin    FROM t1 a1 JOIN t1 a2 ON MBRWithin(     a1.square, a2.square) WHERE a1.name = "center" GROUP BY a1.name;
 mbrwithin
 big,center
@@ -871,7 +871,7 @@ overlaps
 down,left,right,up
 SELECT GROUP_CONCAT(a2.name ORDER BY a2.name) AS touches      FROM t1 a1 JOIN t1 a2 ON Touches(       a1.square, a2.square) WHERE a1.name = "center" GROUP BY a1.name;
 touches
-big,center,down,down2,left,left2,right,right2,small,up,up2
+down2,left2,right2,up2
 SELECT GROUP_CONCAT(a2.name ORDER BY a2.name) AS within       FROM t1 a1 JOIN t1 a2 ON Within(        a1.square, a2.square) WHERE a1.name = "center" GROUP BY a1.name;
 within
 big,center

sql/gcalc_slicescan.h

@@ -58,10 +58,13 @@ public:
     m_free= item;
   }
   inline void free_list(Item *list, Item **hook)
+  {
+    if (*hook != list)
     {
       *hook= m_free;
       m_free= list;
     }
+  }
 
   void free_list(Item *list)
   {
@@ -91,6 +94,79 @@ protected:
   }
 };
 
+/* Internal Gcalc coordinates to provide the precise calculations */
+
+#define DIG_BASE     1000000000
+typedef int32 coord_digit_t;
+typedef long long coord2;
+
+#define C_SCALE 1e13
+#define COORD_BASE 2
+#ifndef DBUG_OFF
+//#define GCALC_CHECK_WITH_FLOAT
+#define NO_TESTING
+#else
+#define NO_TESTING
+#endif /*DBUG_OFF*/
+
+class Gcalc_internal_coord
+{
+public:
+  coord_digit_t *digits;
+  int sign;
+  int n_digits;
+  void set_zero();
+  int is_zero() const;
+#ifdef GCALC_CHECK_WITH_FLOAT
+  long double get_double() const;
+#endif /*GCALC_CHECK_WITH_FLOAT*/
+};
+
+
+class Gcalc_coord1 : public Gcalc_internal_coord
+{
+  coord_digit_t c[COORD_BASE];
+public:
+  void init()
+  {
+    n_digits= COORD_BASE;
+    digits= c;
+  }
+  int set_double(double d);
+  void copy(const Gcalc_coord1 *from);
+};
+
+
+class Gcalc_coord2 : public Gcalc_internal_coord
+{
+  coord_digit_t c[COORD_BASE*2];
+public:
+  void init()
+  {
+    n_digits= COORD_BASE*2;
+    digits= c;
+  }
+};
+
+
+void gcalc_mul_coord(Gcalc_internal_coord *result,
+                     const Gcalc_internal_coord *a,
+                     const Gcalc_internal_coord *b);
+
+void gcalc_add_coord(Gcalc_internal_coord *result,
+                     const Gcalc_internal_coord *a,
+                     const Gcalc_internal_coord *b);
+
+void gcalc_sub_coord(Gcalc_internal_coord *result,
+                     const Gcalc_internal_coord *a,
+                     const Gcalc_internal_coord *b);
+
+int gcalc_cmp_coord(const Gcalc_internal_coord *a,
+                    const Gcalc_internal_coord *b);
+
+/* Internal coordinates declarations end. */
+
+
 typedef uint gcalc_shape_info;
 
 /*
@@ -114,27 +190,34 @@ public:
     Info *left;
     Info *right;
     double x,y;
+    Gcalc_coord1 ix, iy;
 
     inline bool is_bottom() const { return !left; }
     inline Info *get_next() { return (Info *)next; }
     inline const Info *get_next() const { return (const Info *)next; }
   };
+  class Intersection_info : public Gcalc_dyn_list::Item
+  {
+  public:
+    /* Line p1-p2 supposed to intersect line p3-p4 */
+    const Info *p1;
+    const Info *p2;
+    const Info *p3;
+    const Info *p4;
+    void calc_xy(double *x, double *y) const;
+#ifdef GCALC_CHECK_WITH_FLOAT
+    void calc_xy_ld(long double *x, long double *y) const;
+#endif /*GCALC_CHECK_WITH_FLOAT*/
+  };
 
   Gcalc_heap(size_t blk_size=8192) :
-    Gcalc_dyn_list(blk_size, sizeof(Info)), m_hook(&m_first), m_n_points(0) {}
-  Info *new_point_info(double x, double y, gcalc_shape_info shape)
-  {
-    Info *result= (Info *)new_item();
-    if (!result)
-      return NULL;
-    *m_hook= result;
-    m_hook= &result->next;
-    m_n_points++;
-    result->x= x;
-    result->y= y;
-    result->shape= shape;
-    return result;
-  }
+    Gcalc_dyn_list(blk_size, sizeof(Info)),
+    m_hook(&m_first), m_n_points(0),
+    m_intersection_hook((Gcalc_dyn_list::Item **) &m_first_intersection)
+  {}
+  Info *new_point_info(double x, double y, gcalc_shape_info shape);
+  Intersection_info *new_intersection(const Info *p1, const Info *p2,
+                                      const Info *p3, const Info *p4);
   void prepare_operation();
   inline bool ready() const { return m_hook == NULL; }
   Info *get_first() { return (Info *)m_first; }
@@ -145,6 +228,8 @@ private:
   Gcalc_dyn_list::Item *m_first;
   Gcalc_dyn_list::Item **m_hook;
   int m_n_points;
+  Intersection_info *m_first_intersection;
+  Gcalc_dyn_list::Item **m_intersection_hook;
 };
 
 
@@ -263,9 +348,13 @@ public:
   class point : public Gcalc_dyn_list::Item
   {
   public:
+#ifdef TMP_BLOCK
     double x;
     double dx_dy;
     int horiz_dir;
+#endif /*TMP_BLOCK*/
+    Gcalc_coord1 dx;
+    Gcalc_coord1 dy;
     Gcalc_heap::Info *pi;
     Gcalc_heap::Info *next_pi;
     sc_thread_id thread;
@@ -273,22 +362,32 @@ public:
     const point *intersection_link;
     Gcalc_scan_events event;
 #ifdef TO_REMOVE
-    const point *event_pair;
     point *next_link;
 #endif /*TO_REMOVE*/
 
     inline const point *c_get_next() const
       { return (const point *)next; }
-    inline bool is_bottom() const { return pi->is_bottom(); }
+    inline bool is_bottom() const { return !next_pi; }
     gcalc_shape_info get_shape() const { return pi->shape; }
     inline point *get_next() { return (point *)next; }
     inline const point *get_next() const { return (const point *)next; }
     /* copies all but 'next' 'x' and 'precursor' */
-    void copy_core(point *from);
+    void copy_core(const point *from);
+    void copy_all(const point *from);
     /* Compare the dx_dy parameters regarding the horiz_dir */
     /* returns -1 if less, 0 if equal, 1 if bigger          */
-    static int compare_dx_dy(int horiz_dir_a, double dx_dy_a,
+#ifdef TMP_BLOCK
+    static int cmp_dx_dy(int horiz_dir_a, double dx_dy_a,
                          int horiz_dir_b, double dx_dy_b);
+#endif /*TMP_BLOCK*/
+    static int cmp_dx_dy(const Gcalc_coord1 *dx_a,
+                         const Gcalc_coord1 *dy_a,
+                         const Gcalc_coord1 *dx_b,
+                         const Gcalc_coord1 *dy_b);
+    static int cmp_dx_dy(const Gcalc_heap::Info *p1,
+                         const Gcalc_heap::Info *p2,
+                         const Gcalc_heap::Info *p3,
+                         const Gcalc_heap::Info *p4);
     int cmp_dx_dy(const point *p) const;
     int simple_event() const
     {
@@ -298,6 +397,9 @@ public:
 #ifndef DBUG_OFF
     void dbug_print();
 #endif /*DBUG_OFF*/
+#ifdef GCALC_CHECK_WITH_FLOAT
+    void calc_x(long double *x, long double y, long double ix) const;
+#endif /*GCALC_CHECK_WITH_FLOAT*/
   };
 
   class intersection : public Gcalc_dyn_list::Item
@@ -306,8 +408,11 @@ public:
     int n_row;
     sc_thread_id thread_a;
     sc_thread_id thread_b;
+#ifdef TMP_BLOCK
     double x;
     double y;
+#endif /*TMP_BLOCK*/
+    const Gcalc_heap::Intersection_info *ii;
     inline intersection *get_next() { return (intersection *)next; }
   };
 
@@ -318,7 +423,15 @@ public:
     point *event_position;
     Gcalc_dyn_list::Item **event_position_hook;
     Gcalc_dyn_list::Item **event_end_hook;
+    int intersection_scan;
+    union
+    {
+      const Gcalc_heap::Info *pi;
+      const Gcalc_heap::Intersection_info *isc;
+    };
+#ifdef TMP_BLOCK
     double y;
+#endif /*TMP_BLOCK*/
     slice_state() : slice(NULL) {}
     void clear_event_position()
     {
@@ -350,10 +463,24 @@ public:
     { return (point *) *current_state->event_end_hook; }
   inline const point *get_b_slice() const { return current_state->slice; }
   inline const point *get_t_slice() const { return next_state->slice; }
-  inline double get_h() const { return current_state->y - next_state->y; }
-  inline double get_y() const { return current_state->y; }
+  double get_h() const;
+  double get_y() const;
+  double get_event_x() const;
+  double get_sp_x(const point *sp) const;
+  int intersection_step() const { return current_state->intersection_scan; }
+  const Gcalc_heap::Info *get_cur_pi() const
+  {
+    DBUG_ASSERT(!intersection_step());
+    return current_state->pi;
+  }
+  const Gcalc_heap::Intersection_info *get_cur_ii() const
+  {
+    DBUG_ASSERT(intersection_step());
+    return current_state->isc;
+  }
 
 private:
+  Gcalc_heap *m_heap;
   Gcalc_heap::Info *m_cur_pi;
   slice_state state0, state1, state_s;
   slice_state *current_state;
@@ -382,7 +509,10 @@ private:
   }
   point *new_slice_point()
   {
-    return (point *)new_item();
+    point *new_point= (point *)new_item();
+    new_point->dx.init();
+    new_point->dy.init();
+    return new_point;
   }
   point *new_slice(point *example);
   int arrange_event();
@@ -450,7 +580,6 @@ public:
   inline const Gcalc_scan_iterator::point *point() const { return sp; }
   inline const Gcalc_heap::Info *get_pi() const { return sp->pi; }
   inline gcalc_shape_info get_shape() const { return sp->get_shape(); }
-  inline double get_x() const { return sp->x; }
   inline void restart(const Gcalc_scan_iterator *scan_i)
   { sp= scan_i->get_b_slice(); }
 };

sql/gcalc_tools.h

@@ -206,26 +206,37 @@ public:
   int get_result(Gcalc_result_receiver *storage);
   void reset();
 
+#ifndef DBUG_OFF
+  int n_res_points;
+#endif /*DBUG_OFF*/
   class res_point : public Gcalc_dyn_list::Item
   {
   public:
-    bool intersection_point;
-    double x,y;
-    res_point *up;
-    res_point *down;
-    res_point *glue;
-    Gcalc_function::shape_type type;
+    int intersection_point;
     union
     {
       const Gcalc_heap::Info *pi;
+      const Gcalc_heap::Intersection_info *ii;
       res_point *first_poly_node;
     };
+#ifdef TMP_BLOCK
     union
     {
+#endif /*TMP_BLOCK*/
       res_point *outer_poly;
       uint32 poly_position;
+#ifdef TMP_BLOCK
     };
+#endif /*TMP_BLOCK*/
+    res_point *up;
+    res_point *down;
+    res_point *glue;
+    Gcalc_function::shape_type type;
     Gcalc_dyn_list::Item **prev_hook;
+#ifndef DBUG_OFF
+    int point_n;
+#endif /*DBUG_OFF*/
+    void set(const Gcalc_scan_iterator *si);
     res_point *get_next() { return (res_point *)next; }
   };
 
@@ -233,9 +244,9 @@ public:
   {
   public:
     res_point *rp;
-    int horiz_dir;
-    double dx_dy;
     res_point *thread_start;
+
+    const Gcalc_heap::Info *p1, *p2;
     res_point *enabled() { return rp; }
     active_thread *get_next() { return (active_thread *)next; }
   };
@@ -273,33 +284,9 @@ public:
   line *new_line() { return (line *) new_item(); }
   poly_border *new_poly_border() { return (poly_border *) new_item(); }
   int add_line(int incoming, active_thread *t,
-               const Gcalc_scan_iterator::point *p)
-  {
-    line *l= new_line();
-    if (!l)
-      return 1;
-    l->incoming= incoming;
-    l->t= t;
-    l->p= p;
-    *m_lines_hook= l;
-    m_lines_hook= &l->next;
-    return 0;
-  }
-
+               const Gcalc_scan_iterator::point *p);
   int add_poly_border(int incoming, active_thread *t, int prev_state,
-                      const Gcalc_scan_iterator::point *p)
-  {
-    poly_border *b= new_poly_border();
-    if (!b)
-      return 1;
-    b->incoming= incoming;
-    b->t= t;
-    b->prev_state= prev_state;
-    b->p= p;
-    *m_poly_borders_hook= b;
-    m_poly_borders_hook= &b->next;
-    return 0;
-  }
+                      const Gcalc_scan_iterator::point *p);
 
 protected:
   Gcalc_function *m_fn;
@@ -310,43 +297,29 @@ protected:
   res_point *result_heap;
   active_thread *m_first_active_thread;
 
-  res_point *add_res_point(Gcalc_function::shape_type type)
-  {
-    res_point *result= (res_point *)new_item();
-    *m_res_hook= result;
-    result->prev_hook= m_res_hook;
-    m_res_hook= &result->next;
-    result->type= type;
-    return result;
-  }
-
+  res_point *add_res_point(Gcalc_function::shape_type type);
   active_thread *new_active_thread() { return (active_thread *)new_item(); }
 
   poly_instance *new_poly() { return (poly_instance *) new_item(); }
 
 private:
   int start_line(active_thread *t, const Gcalc_scan_iterator::point *p,
-                 const Gcalc_heap::Info *ev_p, const Gcalc_scan_iterator *si);
-  int end_line(active_thread *t, const Gcalc_heap::Info *ev_p,
                  const Gcalc_scan_iterator *si);
+  int end_line(active_thread *t, const Gcalc_scan_iterator *si);
   int connect_threads(int incoming_a, int incoming_b,
                       active_thread *ta, active_thread *tb,
                       const Gcalc_scan_iterator::point *pa,
                       const Gcalc_scan_iterator::point *pb,
                       active_thread *prev_range,
-                      const Gcalc_heap::Info *ev_p,
                       const Gcalc_scan_iterator *si,
                       Gcalc_function::shape_type s_t);
-  int add_single_point(const Gcalc_heap::Info *p,
-                       const Gcalc_scan_iterator *si);
+  int add_single_point(const Gcalc_scan_iterator *si);
   poly_border *get_pair_border(poly_border *b1);
   int continue_range(active_thread *t, const Gcalc_heap::Info *p,
-                     int horiz_dir, double dx_dy);
-  int continue_i_range(active_thread *t, double x, double y,
-                       int horiz_dir, double dx_dy);
+                     const Gcalc_heap::Info *p_next);
+  int continue_i_range(active_thread *t,
+                       const Gcalc_heap::Intersection_info *ii);
   int end_couple(active_thread *t0, active_thread *t1, const Gcalc_heap::Info *p);
-  int add_single_point(const Gcalc_heap::Info *p);
-
   int get_single_result(res_point *res, Gcalc_result_receiver *storage);
   int get_result_thread(res_point *cur, Gcalc_result_receiver *storage,
 			int move_upward, res_point *first_poly_node);

sql/item_geofunc.cc

@@ -867,7 +867,8 @@ int Item_func_spatial_rel::func_touches()
       if (cur_func)
       {
         area= scan_it.get_h() *
-              ((ti.rb()->x - ti.lb()->x) + (ti.rt()->x - ti.lt()->x));
+              ((scan_it.get_sp_x(ti.rb()) - scan_it.get_sp_x(ti.lb())) +
+               (scan_it.get_sp_x(ti.rt()) - scan_it.get_sp_x(ti.lt())));
         if (area > GIS_ZERO)
         {
           result= 0;

sql/spatial.cc

@@ -2230,6 +2230,8 @@ bool Gis_geometry_collection::get_mbr(MBR *mbr, const char **end) const
     return 1;
   n_objects= uint4korr(data);
   data+= 4;
+  if (n_objects == 0)
+    return 1;
 
   while (n_objects--)
   {