add a centroid calculation using tetrahedral decomposition. tested.

src/wings_we.erl

@@ -34,7 +34,7 @@
 	 visible/1,visible/2,visible_vs/1,visible_vs/2,
 	 visible_edges/1,visible_edges/2,fully_visible_edges/2,
 	 validate_mirror/1,mirror_flatten/2,mirror_projection/1,
-	 create_mirror/2,freeze_mirror/1,break_mirror/1]).
+	 create_mirror/2,freeze_mirror/1,break_mirror/1,centroid/1]).
 
 -include("wings.hrl").
 -include("e3d.hrl").
@@ -1204,3 +1204,30 @@ validate_vertex_tab(#we{es=Etab,vc=Vct}) ->
 			#edge{ve=V} -> ok
 		    end
 	    end, array:sparse_to_orddict(Vct)).
+
+
+%% Geometric center by weighted tetrahedrons
+centroid( #we{}=_We ) ->
+    We = wings_tesselation:triangulate(_We),
+    #we{fs=Ftab}=We,
+    MyAcc = fun(Fi, {{ Tx, Ty, Tz }, VTotal } ) ->
+        { _A, Vol, { CX, CY, CZ }  }  = centroid_parts(Fi,We),
+        { { Tx+Vol*CX,  Ty+Vol*CY,  Tz+Vol*CZ },  Vol + VTotal } 
+    end,
+
+    {{ X, Y, Z }, VolumeT }  = lists:foldl(MyAcc, {{ 0.0, 0.0, 0.0 } , 0.0 } , gb_trees:keys(Ftab)  ),
+    { X/VolumeT, Y/VolumeT,  Z/VolumeT }.
+
+
+centroid_parts(Face, We) ->
+    [V1,V2,V3] = wings_face:vertex_positions(Face, We),
+    E1 = e3d_vec:sub(V1, V2),
+    E2 = e3d_vec:sub(V3, V2),
+    Cp = e3d_vec:cross(E1, E2),
+    Bc = e3d_vec:cross(V2, V3),
+    Area = e3d_vec:len(Cp)/2.0,
+    Volume = e3d_vec:dot(V1, Bc)/6.0,
+
+    Centroid = e3d_vec:average(   [ V1, V2, V3, {0.0, 0.0, 0.0} ]   ),
+
+    {Area, Volume, Centroid}.