Mapping of Zaglmayr QuadBasis to fit Gmsh Ref Space

FunctionSpace/QuadEdgeBasis.cpp

@@ -201,6 +201,33 @@ QuadEdgeBasis::QuadEdgeBasis(int order){
   }
 
 
+  // Mapping to Gmsh Quad //
+  // x = (u + 1) / 2
+  // y = (v + 1) / 2
+  //
+  // (x, y) = Zaglmayr Ref Quad
+  // (u, v) = Gmsh     Ref Quad
+
+  Polynomial  mapX(Polynomial(0.5, 1, 0, 0) + 
+		   Polynomial(0.5, 0, 0, 0));
+
+  Polynomial  mapY(Polynomial(0.5, 0, 1, 0) + 
+		   Polynomial(0.5, 0, 0, 0));
+
+  for(int i = 0; i < nEdgeClosure; i++){
+    for(int j = 0; j < nEdge; j++){
+      (*(*edge)[i])[j]->at(0) = (*(*edge)[i])[j]->at(0).compose(mapX, mapY);
+      (*(*edge)[i])[j]->at(1) = (*(*edge)[i])[j]->at(1).compose(mapX, mapY);
+      (*(*edge)[i])[j]->at(2) = (*(*edge)[i])[j]->at(2).compose(mapX, mapY);
+    }
+  }
+
+  for(int i = 0; i < nCell; i++){
+    (*cell)[i]->at(0) = (*cell)[i]->at(0).compose(mapX, mapY);
+    (*cell)[i]->at(1) = (*cell)[i]->at(1).compose(mapX, mapY);
+    (*cell)[i]->at(2) = (*cell)[i]->at(2).compose(mapX, mapY);
+  }
+
   // Free Temporary Sapce //
   delete[] legendre;
   delete[] intLegendre;

FunctionSpace/QuadEdgeBasis.h

@@ -10,9 +10,13 @@
    This class can instantiate an Edge-Based Basis 
    (high or low order) for Quads.@n
    
-   It uses 
+   It uses a variation of
    <a href="http://www.hpfem.jku.at/publications/szthesis.pdf">Zaglmayr's</a>  
    Basis for @em high @em order Polynomial%s generation.@n
+
+   The following mapping has been applied to Zaglmayr's Basis for Quads:
+   @li @f$x = \frac{u + 1}{2}@f$
+   @li @f$y = \frac{v + 1}{2}@f$ 
 */
 
 class QuadEdgeBasis: public BasisVector{

FunctionSpace/QuadNodeBasis.cpp

@@ -127,6 +127,30 @@ QuadNodeBasis::QuadNodeBasis(int order){
   }
 
 
+  // Mapping to Gmsh Quad //
+  // x = (u + 1) / 2
+  // y = (v + 1) / 2
+  //
+  // (x, y) = Zaglmayr Ref Quad
+  // (u, v) = Gmsh     Ref Quad
+
+  Polynomial  mapX(Polynomial(0.5, 1, 0, 0) + 
+		   Polynomial(0.5, 0, 0, 0));
+
+  Polynomial  mapY(Polynomial(0.5, 0, 1, 0) + 
+		   Polynomial(0.5, 0, 0, 0));
+
+  for(int i = 0; i < nVertex; i++)
+    *(*node)[i] = (*node)[i]->compose(mapX, mapY);
+
+  for(int i = 0; i < nEdgeClosure; i++)
+    for(int j = 0; j < nEdge; j++)
+      *(*(*edge)[i])[j] = (*(*edge)[i])[j]->compose(mapX, mapY);
+
+  for(int i = 0; i < nCell; i++)
+    *(*cell)[i] = (*cell)[i]->compose(mapX, mapY);
+  
+
   // Free Temporary Sapce //
   delete[] legendre;
 }

FunctionSpace/QuadNodeBasis.h

@@ -10,9 +10,13 @@
    This class can instantiate a Node-Based Basis 
    (high or low order) for Quads.@n
    
-   It uses 
+   It uses a variation of
    <a href="http://www.hpfem.jku.at/publications/szthesis.pdf">Zaglmayr's</a>  
    Basis for @em high @em order Polynomial%s generation.@n
+ 
+   The following mapping has been applied to Zaglmayr's Basis for Quads:
+   @li @f$x = \frac{u + 1}{2}@f$
+   @li @f$y = \frac{v + 1}{2}@f$
 */
 
 class QuadNodeBasis: public BasisScalar{