MDEV-12915 ST_Centroid does not return the same result than MySQL.

        Calculation of the polygon's centroid fixed.

mysql-test/r/gis.result

@@ -333,8 +333,8 @@ fid	IsClosed(g)
 116	0
 SELECT fid, AsText(Centroid(g)) FROM gis_multi_polygon;
 fid	AsText(Centroid(g))
-117	POINT(55.58852775304245 17.426536064113982)
-118	POINT(55.58852775304245 17.426536064113982)
+117	POINT(57.98031067576927 17.854754130800433)
+118	POINT(57.98031067576927 17.854754130800433)
 119	POINT(2 2)
 SELECT fid, Area(g) FROM gis_multi_polygon;
 fid	Area(g)
@@ -684,11 +684,11 @@ insert into t1 values ('85984',GeomFromText('MULTIPOLYGON(((-115.006363
 select object_id, geometrytype(geo), ISSIMPLE(GEO), ASTEXT(centroid(geo)) from
 t1 where object_id=85998;
 object_id	geometrytype(geo)	ISSIMPLE(GEO)	ASTEXT(centroid(geo))
-85998	MULTIPOLYGON	1	POINT(115.31877315203187 -36.23747282102153)
+85998	MULTIPOLYGON	1	POINT(115.2970604672862 -36.23335610879993)
 select object_id, geometrytype(geo), ISSIMPLE(GEO), ASTEXT(centroid(geo)) from
 t1 where object_id=85984;
 object_id	geometrytype(geo)	ISSIMPLE(GEO)	ASTEXT(centroid(geo))
-85984	MULTIPOLYGON	1	POINT(-114.87787186923313 36.33101763469059)
+85984	MULTIPOLYGON	1	POINT(-114.86854472054372 36.34725218253213)
 drop table t1;
 create table t1 (fl geometry not null);
 insert into t1 values (1);

mysql-test/suite/archive/archive_gis.result

@@ -326,8 +326,8 @@ fid	IsClosed(g)
 116	0
 SELECT fid, AsText(Centroid(g)) FROM gis_multi_polygon ORDER by fid;
 fid	AsText(Centroid(g))
-117	POINT(55.58852775304245 17.426536064113982)
-118	POINT(55.58852775304245 17.426536064113982)
+117	POINT(57.98031067576927 17.854754130800433)
+118	POINT(57.98031067576927 17.854754130800433)
 119	POINT(2 2)
 SELECT fid, Area(g) FROM gis_multi_polygon ORDER by fid;
 fid	Area(g)

mysql-test/suite/innodb/r/innodb_gis.result

@@ -326,8 +326,8 @@ fid	IsClosed(g)
 116	0
 SELECT fid, AsText(Centroid(g)) FROM gis_multi_polygon ORDER by fid;
 fid	AsText(Centroid(g))
-117	POINT(55.58852775304245 17.426536064113982)
-118	POINT(55.58852775304245 17.426536064113982)
+117	POINT(57.98031067576927 17.854754130800433)
+118	POINT(57.98031067576927 17.854754130800433)
 119	POINT(2 2)
 SELECT fid, Area(g) FROM gis_multi_polygon ORDER by fid;
 fid	Area(g)

sql/spatial.cc

@@ -1150,8 +1150,8 @@ int Gis_polygon::centroid_xy(double *x, double *y) const
     uint32 n_points, org_n_points;
     double prev_x, prev_y;
     double cur_area= 0;
-    double cur_cx= 0;
-    double cur_cy= 0;
+    double cur_cx= 0, cur_cy= 0;
+    double sum_cx= 0, sum_cy= 0;
 
     if (no_data(data, 4))
       return 1;
@@ -1165,17 +1165,32 @@ int Gis_polygon::centroid_xy(double *x, double *y) const
     while (--n_points)				// One point is already read
     {
       double tmp_x, tmp_y;
+      double loc_area;
       get_point(&tmp_x, &tmp_y, data);
       data+= POINT_DATA_SIZE;
-      cur_area+= (prev_x + tmp_x) * (prev_y - tmp_y);
+      loc_area= prev_x * tmp_y - tmp_x * prev_y;
+      cur_area+= loc_area;
       cur_cx+= tmp_x;
       cur_cy+= tmp_y;
+      sum_cx+= (prev_x + tmp_x) * loc_area;
+      sum_cy+= (prev_y + tmp_y) * loc_area;
+
       prev_x= tmp_x;
       prev_y= tmp_y;
     }
-    cur_area= fabs(cur_area) / 2;
+
+    if (fabs(cur_area) > 1e-10)
+    {
+      cur_cx= sum_cx / cur_area / 3.0;
+      cur_cy= sum_cy / cur_area / 3.0;
+    }
+    else
+    {
       cur_cx= cur_cx / (org_n_points - 1);
       cur_cy= cur_cy / (org_n_points - 1);
+    }
+
+    cur_area= fabs(cur_area);
 
     if (!first_loop)
     {