diff --git a/program/source/grid/examples_ug_optics.cc b/program/source/grid/examples_ug_optics.cc
index e658989be3f5decbc5709634e77b27328461f224..1e5fc7233368a9a5bfed24820171983aca1f8ed3 100644
--- a/program/source/grid/examples_ug_optics.cc
+++ b/program/source/grid/examples_ug_optics.cc
@@ -111,6 +111,12 @@ D3vector transform_right_lens_diag_NW_quad ( double t1, double t2, double* point
     x = x*t2;
     double y = R_global_data*(cos ( t1*0.5*M_PI )- ( 1-t1 )) ;
     y = y*t2;
+
+//    if (t1 == 0.75 && t2 == 1.0)
+//    {
+//        std::cout << "break";
+//    }
+
     double actualX = 0             +  r_global_data * t1 + 0                             * t2 + (R_global_data-r_global_data) * t1 * t2;
     double actualY = r_global_data -  r_global_data * t1 + (R_global_data-r_global_data) * t2 - (R_global_data-r_global_data) * t1 * t2;
 
@@ -279,6 +285,8 @@ D3vector transform_right_lens_diag_SW_quad ( double t1, double t2, double* point
     double temp = t1;
     t1 = t2;
     t2 = temp;
+    //test
+    t1 = 1.0 - t1;
     double t = t2;
     double x = -R_global_data *( sin ( t1*0.5*M_PI )-t1);
     x = x*t2;
@@ -317,6 +325,8 @@ D3vector transform_left_lens_diag_SW_quad ( double t1, double t2, double* pointe
     t1 = t2;
     t2 = temp;
     double t = t2;
+    //test
+    t1 = 1.0 - t1;
     double x = -R_global_data *( sin ( t1*0.5*M_PI )-t1);
     x = x*t2;
     double y = -R_global_data *(cos ( t1*0.5*M_PI )- ( 1-t1 )) ;
@@ -353,6 +363,9 @@ D3vector transform_left_lens_diag_SE_quad ( double t1, double t2, double* pointe
     t1 = t2;
     t2 = temp;
     double t = t2;
+
+    //test
+    t1 = 1.0 - t1;
     double x =R_global_data * ( sin ( t1*0.5*M_PI )-t1);
     x = x*t2;
     double y = -R_global_data *(cos ( t1*0.5*M_PI )- ( 1-t1 )) ;
@@ -361,7 +374,7 @@ D3vector transform_left_lens_diag_SE_quad ( double t1, double t2, double* pointe
     double actualX = 0             +  r_global_data * t1 + 0                             * t2 + (R_global_data-r_global_data) * t1 * t2;
     double actualY = r_global_data -  r_global_data * t1 + (R_global_data-r_global_data) * t2 - (R_global_data-r_global_data) * t1 * t2;
     actualY = -actualY;
-
+    //actualX = -actualX;
     double sign = (curvatureLeft_global_data > 0) ? 1 : ((curvatureLeft_global_data < 0) ? -1 : 0)  ;
     double radiusSquared = ((x+actualX)*(x+actualX)+(y+actualY)*(y+actualY));
 
@@ -370,6 +383,9 @@ D3vector transform_left_lens_diag_SE_quad ( double t1, double t2, double* pointe
      if (std::isnan(z))
      {z = 0;}
 
+//     temp = x;
+//     x = y;
+//     y = temp;
      return D3vector ( x,y,z);
 }
 
@@ -388,14 +404,21 @@ D3vector transform_right_lens_diag_SE_quad ( double t1, double t2, double* point
     t1 = t2;
     t2 = temp;
     double t = t2;
+    //test
+    t1 = 1.0 - t1;
     double x =R_global_data * ( sin ( t1*0.5*M_PI )-t1);
     x = x*t2;
     double y = -R_global_data *(cos ( t1*0.5*M_PI )- ( 1-t1 )) ;
     y = y*t2;
 
+//    if (t1 == 0.75 && t2 == 1.0)
+//    {
+//        std::cout << "break";
+//    }
     double actualX = 0             +  r_global_data * t1 + 0                             * t2 + (R_global_data-r_global_data) * t1 * t2;
     double actualY = r_global_data -  r_global_data * t1 + (R_global_data-r_global_data) * t2 - (R_global_data-r_global_data) * t1 * t2;
     actualY = -actualY;
+    //actualX = -actualX;
     double sign = (curvatureRight_global_data > 0) ? 1 : ((curvatureRight_global_data < 0) ? -1 : 0)  ;
 
     double z = offsetZ_global_data+
@@ -403,10 +426,13 @@ D3vector transform_right_lens_diag_SE_quad ( double t1, double t2, double* point
                            ((x+actualX)*(x+actualX)+(y+actualY)*(y+actualY)))
                       + sign*(-curvatureRight_global_data +( (1-t)*(thickness_global_data-z_right_inner_global_data) + t * (thickness_global_data-z_right_outer_global_data)))));
 
-
     if (std::isnan(z))
     {
     z = 0;}
+//    temp = x;
+//    x = y;
+//    y = temp;
+
     return D3vector ( x,y,z);
 
 }
@@ -427,6 +453,7 @@ D3vector transform_left_lens_diag_NE_quad ( double t1, double t2, double* pointe
     t1 = t2;
     t2 = temp;
     double t = t2;
+    t1 = 1.0 - t1;
 
     double x = R_global_data * ( sin ( t1*0.5*M_PI )-t1);
 
@@ -641,7 +668,7 @@ D3vector transform_right_lens_diag_NE_quad ( double t1, double t2, double* point
     t1 = t2;
     t2 = temp;
     double t = t2;
-
+    t1 = 1.0 - t1;
     double x = R_global_data * ( sin ( t1*0.5*M_PI )-t1);
 
     x = x*t2;
@@ -1167,15 +1194,7 @@ D3vector transform_right_lens_diag_NE_quad_cut ( double t1, double t2, double* p
     if (std::isnan(x) || std::isnan(y) || std::isnan(z))
     {   z = 0;}
 
-//    std::cout << "transform_right_lens_diag_NE_quad_cut ";
-//    D3vector ( x,y,z).Print();
-//    std::cout << std::endl;
-//    double actualZ =  offsetZ_global_data+
-//            sign*(  ( sqrt(pow(curvatureRight_global_data,2)-
-//                           radiusSquared)
-//                      + sign*(-curvatureRight_global_data))) ;
-//    return D3vector (actualX, actualY,actualZ );
-    //return D3vector ( xT,yT,z);
+
     return D3vector ( x,y,z);
     //return D3vector ( (1-t2) * xAdd,(1-t2) * yAdd,z);
     return D3vector ( 0,0,z);
@@ -1726,6 +1745,7 @@ Lens_Geometry_Quad::Lens_Geometry_Quad(double Radius, double thickness, double c
   Set_transformation_face(4,5,12,13,transform_diag_inner_faces_NE_quad);
   Set_transformation_face(3,5,11,13,transform_outer_boundary_NW); //transform_outer_boundary_NW
   Set_transformation_face(10,11,12,13,transform_right_lens_diag_NW_quad); //transform_right_lens_diag_NW_quad
+  //Set_transformation_face(10,11,12,13,transform_quadrangle_NULL); //transform_right_lens_diag_NW_quad
 
   //bottom-west block: corner ids: 4 5 6 7 12 13 14 15
   //eher: S-W-BLOCK
@@ -1744,7 +1764,7 @@ Lens_Geometry_Quad::Lens_Geometry_Quad(double Radius, double thickness, double c
   Set_transformation_face(6,7,14,15,transform_diag_inner_faces_NE_quad);
   Set_transformation_face(1,7,9,15,transform_outer_boundary_SE);
   Set_transformation_face(8,9,14,15,transform_right_lens_diag_SE_quad);
-
+  //Set_transformation_face(8,9,14,15,transform_quadrangle_NULL);
 
 
   construction_done();
@@ -1764,6 +1784,9 @@ Lens_Geometry_cutted_edges::Lens_Geometry_cutted_edges(double RadiusLeft, double
     {
         cutRight = true;
     }
+
+    assert(!cutLeft || (curvatureLeft < 0 && cutLeft)  && "Assertion failed! If left side of lens is cutted, its curvature must be negative (convex)!");
+    assert(!cutRight || (curvatureRight < 0 && cutRight)  && "Assertion failed! If right side of lens is cutted, its curvature must be negative (convex)!");
     if (MechanicalRadiusLeft < RadiusLeft)
     {
         std::cout << "warning : mech radius < radius\n set to radiusLeft";
diff --git a/program/source/math_lib/math_lib.h b/program/source/math_lib/math_lib.h
index d66cdcd5230857ed15fa152f92632a4e7323f85a..7c33b36de681d6aa08b2f210cd23f67fb4ab0eb7 100644
--- a/program/source/math_lib/math_lib.h
+++ b/program/source/math_lib/math_lib.h
@@ -567,8 +567,10 @@ inline void D3vector::Print() {
 }
 
 inline void D3vector::PrintCoordinatesOnly() {
+
   std::cout << x << ", " << y << ", " << z;
 }
+
 inline void D3vector::Print(std::ofstream *Datei) {
   *Datei  << x << " " << y << " " << z;
 }
diff --git a/program2D/source/extemp/cellvar2D.h b/program2D/source/extemp/cellvar2D.h
index 4b1d54fc6fcf601d0dda0d158f06964adfc4f13c..539bf23f73b21dbb8d7f69e13a228fc36ace58cd 100644
--- a/program2D/source/extemp/cellvar2D.h
+++ b/program2D/source/extemp/cellvar2D.h
@@ -188,6 +188,12 @@ double L_infty_cell(const Expr2D<A>& a, Marker2D& marker);
 
 template <class A>
 double L_infty_cell(const Expr2D<A>& a);
+
+template <class A>
+double Maximum_cell(const Expr2D<A>& ao);
+
+template <class A>
+double Minimum_cell(const Expr2D<A>& ao);
 /* @} */
 
 
diff --git a/program2D/source/grid/interpolation2D_cc.h b/program2D/source/grid/interpolation2D_cc.h
index 62aa2f7c55f2df1614b6990c679cc4b866f8dc7b..c9fd360c5994ead6fd77c92d34805cfc7223e910 100644
--- a/program2D/source/grid/interpolation2D_cc.h
+++ b/program2D/source/grid/interpolation2D_cc.h
@@ -30,10 +30,11 @@
 #else
   #ifdef WIN32
     #include <array>
+    using std::array;
   #else
     #include <tr1/array>
+using std::tr1::array;
   #endif
-  using std::tr1::array;
 #endif
   
 #endif // _NOARRAYLIB  
diff --git a/program2D/source/interpol/interpolTwoD.cc b/program2D/source/interpol/interpolTwoD.cc
index dcd172562a900c3f9312bd88060b0d2c120c282e..9b898877f40d5c334ec270306ec52126dc1cb308 100644
--- a/program2D/source/interpol/interpolTwoD.cc
+++ b/program2D/source/interpol/interpolTwoD.cc
@@ -77,7 +77,7 @@ Interpolate_on_structured_2Dgrid::Interpolate_on_structured_2Dgrid(int nx_, int
 }
 
 
-Interpolate_on_structured_2Dgrid::Interpolate_on_structured_2Dgrid(Blockgrid2D* blockgrid_) {
+Interpolate_on_structured_2Dgrid::Interpolate_on_structured_2Dgrid(Blockgrid2D* blockgrid_, double factorIncrease) {
   blockgrid = blockgrid_;
   ug = blockgrid->Give_unstructured_grid();  
     
@@ -122,8 +122,9 @@ Interpolate_on_structured_2Dgrid::Interpolate_on_structured_2Dgrid(Blockgrid2D*
 	  }
   }
   
-  nx = Nmax*4;
-  ny = Nmax*4;  
+  nx = Nmax*factorIncrease;
+  ny = Nmax*factorIncrease;  
+  
   
   pWS = boxWS;
   pEN = boxEN;
diff --git a/program2D/source/interpol/interpolTwoD.h b/program2D/source/interpol/interpolTwoD.h
index 326f2bdd5dd4533be002ba7c01ed34ec597897f0..0ecdbc20f3793c0bf792e8447734ce5d26890879 100644
--- a/program2D/source/interpol/interpolTwoD.h
+++ b/program2D/source/interpol/interpolTwoD.h
@@ -76,7 +76,7 @@ class Interpolate_on_structured_2Dgrid {
  * preparation for interpolation
  @param  blockgrid_ of unstructured grid
 **/
-  Interpolate_on_structured_2Dgrid(Blockgrid2D* blockgrid_);  
+  Interpolate_on_structured_2Dgrid(Blockgrid2D* blockgrid_, double factorIncrease = 4);  
   
   
 /**
@@ -129,7 +129,7 @@ class Interpolate_on_structured_2Dgrid_with_data : protected Interpolate_on_stru
     Interpolate_on_structured_2Dgrid_with_data(int nx_, int ny_,
 				               D2vector pWS, D2vector pEN,
 				               Blockgrid2D& blockgrid_);
-    Interpolate_on_structured_2Dgrid_with_data(Blockgrid2D& blockgrid_);    
+    Interpolate_on_structured_2Dgrid_with_data(Blockgrid2D& blockgrid_, double factorIncrease = 4);    
     
     void setData(Variable2D<DTyp>& u, DTyp defaultInterpolation);
     
@@ -361,8 +361,8 @@ Interpolate_on_structured_2Dgrid_with_data<DTyp>::Interpolate_on_structured_2Dgr
 }
 
 template <class DTyp>
-Interpolate_on_structured_2Dgrid_with_data<DTyp>::Interpolate_on_structured_2Dgrid_with_data(Blockgrid2D& blockgrid_) 
-   : Interpolate_on_structured_2Dgrid(&blockgrid_) {
+Interpolate_on_structured_2Dgrid_with_data<DTyp>::Interpolate_on_structured_2Dgrid_with_data(Blockgrid2D& blockgrid_, double factorIncrease) 
+   : Interpolate_on_structured_2Dgrid(&blockgrid_, factorIncrease) {
    data = new DTyp[nx*ny];
    for(int i=0;i<nx*ny;++i) data[i] = 0.0; 
 }