Add option to set object origin to the center of mass

This uses the weighted average of polygon centroids based on area
It work well in most cases but will be slightly wrong when polygons have 
many vertices.

source/blender/blenkernel/BKE_mesh.h

@@ -292,6 +292,7 @@ void create_vert_edge_map(MeshElemMap **map, int **mem,
 int BKE_mesh_minmax(struct Mesh *me, float r_min[3], float r_max[3]);
 int BKE_mesh_center_median(struct Mesh *me, float cent[3]);
 int BKE_mesh_center_bounds(struct Mesh *me, float cent[3]);
+int BKE_mesh_center_centroid(struct Mesh *me, float cent[3]);
 void BKE_mesh_translate(struct Mesh *me, float offset[3], int do_keys);
 
 /* mesh_validate.c */

source/blender/blenkernel/intern/mesh.c

@@ -3175,6 +3175,32 @@ int BKE_mesh_center_bounds(Mesh *me, float cent[3])
 	return 0;
 }
 
+int BKE_mesh_center_centroid(Mesh *me, float cent[3])
+{
+	int i = me->totpoly;
+	MPoly *mpoly;
+	float poly_area;
+	float total_area = 0.0f;
+	float poly_cent[3];
+	
+	zero_v3(cent);
+	
+	/* calculate a weighted average of polygon centroids */
+	for (mpoly = me->mpoly; i--; mpoly++) {
+		BKE_mesh_calc_poly_center(mpoly, me->mloop + mpoly->loopstart, me->mvert, poly_cent);
+		poly_area = BKE_mesh_calc_poly_area(mpoly, me->mloop + mpoly->loopstart, me->mvert, NULL);
+		
+		madd_v3_v3fl(cent, poly_cent, poly_area);
+		total_area += poly_area;
+	}
+	/* otherwise we get NAN for 0 polys */
+	if (me->totpoly) {
+		mul_v3_fl(cent, 1.0f / total_area);
+	}
+
+	return (me->totpoly != 0);
+}
+
 void BKE_mesh_translate(Mesh *me, float offset[3], int do_keys)
 {
 	int i = me->totvert;

source/blender/editors/object/object_transform.c

@@ -654,7 +654,8 @@ void OBJECT_OT_transform_apply(wmOperatorType *ot)
 enum {
 	GEOMETRY_TO_ORIGIN = 0,
 	ORIGIN_TO_GEOMETRY,
-	ORIGIN_TO_CURSOR
+	ORIGIN_TO_CURSOR,
+	ORIGIN_TO_CENTER_OF_MASS
 };
 
 static int object_origin_set_exec(bContext *C, wmOperator *op)
@@ -785,6 +786,7 @@ static int object_origin_set_exec(bContext *C, wmOperator *op)
 				Mesh *me = ob->data;
 
 				if (centermode == ORIGIN_TO_CURSOR) { /* done */ }
+				else if (centermode == ORIGIN_TO_CENTER_OF_MASS) { BKE_mesh_center_centroid(me, cent); }
 				else if (around == V3D_CENTROID) { BKE_mesh_center_median(me, cent); }
 				else { BKE_mesh_center_bounds(me, cent); }
 
@@ -980,6 +982,8 @@ void OBJECT_OT_origin_set(wmOperatorType *ot)
 		                     "Move object origin to center of object geometry"},
 		{ORIGIN_TO_CURSOR, "ORIGIN_CURSOR", 0, "Origin to 3D Cursor",
 		                   "Move object origin to position of the 3D cursor"},
+		{ORIGIN_TO_CENTER_OF_MASS, "ORIGIN_CENTER_OF_MASS", 0, "Origin to Center of Mass",
+		                           "Move object origin to the object center of mass (assuming uniform density)"},
 		{0, NULL, 0, NULL, NULL}
 	};
 	
@@ -1006,4 +1010,3 @@ void OBJECT_OT_origin_set(wmOperatorType *ot)
 	ot->prop = RNA_def_enum(ot->srna, "type", prop_set_center_types, 0, "Type", "");
 	RNA_def_enum(ot->srna, "center", prop_set_bounds_types, V3D_CENTROID, "Center", "");
 }
-