diff --git a/program/source/grid/examples_ug_optics.cc b/program/source/grid/examples_ug_optics.cc
index f16199a28221b44b57c18ee5555feb7f47a306e0..e658989be3f5decbc5709634e77b27328461f224 100644
--- a/program/source/grid/examples_ug_optics.cc
+++ b/program/source/grid/examples_ug_optics.cc
@@ -2053,25 +2053,16 @@ Lens_Geometry_cutted_edges::Lens_Geometry_cutted_edges(double RadiusLeft, double
   //1,16,3,17,1+8,16+4,3+8,17+4
   Set_transformation_face(1,16,3,17,transform_left_lens_diag_NE_quad_cut);
   Set_transformation_face(1,16,9,20,transform_diag_inner_faces_NE_quad_cut);
-  //Set_transformation_face(1,3,9,11,transform_quadrangle_NULL); // inner face : no transform necessary
   Set_transformation_face(1,3,9,11,transform_outer_boundary_NE); // inner face :
   Set_transformation_face(3,17,11,21,transform_diag_inner_faces_NE_quad_cut);
   Set_transformation_face(16,17,20,21,transform_outer_boundary_NE_cut); //
   Set_transformation_face(9,20,11,21,transform_right_lens_diag_NE_quad_cut);
-  //all set to zero!!!
-//  Set_transformation_face(1,16,3,17,transform_quadrangle_NULL);
-//  Set_transformation_face(1,16,9,20,transform_diag_inner_faces_NE_quad_cut);
-//  Set_transformation_face(1,3,9,11,transform_quadrangle_NULL); // inner face :
-//  Set_transformation_face(3,17,11,21,transform_diag_inner_faces_NE_quad_cut);
-//  Set_transformation_face(16,17,20,21,transform_outer_boundary_NE_cut); //
-//  Set_transformation_face(9,20,11,21,transform_quadrangle_NULL);
 
   //north-west outer block: corner ids: 2 3  4 5  10 11 12 13
   //north-west outer block: corner ids: 3 17 5 18 11 21 13 22
   //3,17,5,18,3+8,17+4,5+8,18+4
   Set_transformation_face(3,17,5,18,transform_left_lens_diag_NW_quad_cut);//transform_left_lens_diag_NW_quad
   Set_transformation_face(3,17,11,21,transform_diag_inner_faces_NE_quad_cut);
-  //Set_transformation_face(3,5,11,13,transform_quadrangle_NULL); // inner face : no transform necessary
   Set_transformation_face(3,5,11,13,transform_outer_boundary_NW); // inner face : no transform necessary
   Set_transformation_face(5,18,13,22,transform_diag_inner_faces_NE_quad_cut);
   Set_transformation_face(17,18,21,22,transform_outer_boundary_NW_cut); //transform_outer_boundary_NW
@@ -2082,7 +2073,6 @@ Lens_Geometry_cutted_edges::Lens_Geometry_cutted_edges(double RadiusLeft, double
   //5,18,7,19,5+8,18+4,7+8,19+4
   Set_transformation_face(5,18,7,19,transform_left_lens_diag_SW_quad_cut);
   Set_transformation_face(5,18,13,22,transform_diag_inner_faces_NE_quad_cut);
-  //Set_transformation_face(5,7,13,15,transform_quadrangle_NULL); // inner face : no transform necessary
   Set_transformation_face(5,7,13,15,transform_outer_boundary_SW); // inner face : no transform necessary
   Set_transformation_face(7,19,15,23,transform_diag_inner_faces_NE_quad_cut);
   Set_transformation_face(18,19,22,23,transform_outer_boundary_SW_cut); //
@@ -2093,7 +2083,6 @@ Lens_Geometry_cutted_edges::Lens_Geometry_cutted_edges(double RadiusLeft, double
   //7,19,1,16,7+8,19+4,1+8,16+4
   Set_transformation_face(1,16,7,19,transform_left_lens_diag_SE_quad_cut);
   Set_transformation_face(1,16,9,20,transform_diag_inner_faces_NE_quad_cut);
-  //Set_transformation_face(1,7,9,15,transform_quadrangle_NULL); // inner face : no transform necessary
   Set_transformation_face(1,7,9,15,transform_outer_boundary_SE); // inner face : no transform necessary
   Set_transformation_face(7,19,15,23,transform_diag_inner_faces_NE_quad_cut);
   Set_transformation_face(16,19,20,23,transform_outer_boundary_SE_cut);
diff --git a/program/source/math_lib/math_lib.h b/program/source/math_lib/math_lib.h
index 419718c880637f7c911d26eefd369ceb5505c723..d66cdcd5230857ed15fa152f92632a4e7323f85a 100644
--- a/program/source/math_lib/math_lib.h
+++ b/program/source/math_lib/math_lib.h
@@ -54,6 +54,7 @@ class D3vector {
   D3vector() : x(0), y(0), z(0) {};
   ~D3vector(){};
   void Print();
+  void PrintCoordinatesOnly();
   void Print(std::ofstream *Datei);
   void operator=(const D3vector& v) { x=v.x; y=v.y; z=v.z; }
   void operator+=(const D3vector& v) { x+=v.x; y+=v.y; z+=v.z; }
@@ -565,6 +566,9 @@ inline void D3vector::Print() {
   std::cout << "Coordinate: " << x << ", " << y << ", " << z << ";\n";
 }
 
+inline void D3vector::PrintCoordinatesOnly() {
+  std::cout << x << ", " << y << ", " << z;
+}
 inline void D3vector::Print(std::ofstream *Datei) {
   *Datei  << x << " " << y << " " << z;
 }