PyrGeom.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File: PyrGeom.cpp
//
//  For more information, please see: http://www.nektar.info/
//
//  The MIT License
//
//  Copyright (c) 2006 Division of Applied Mathematics, Brown University (USA),
//  Department of Aeronautics, Imperial College London (UK), and Scientific
//  Computing and Imaging Institute, University of Utah (USA).
//
//  License for the specific language governing rights and limitations under
//  Permission is hereby granted, free of charge, to any person obtaining a
//  copy of this software and associated documentation files (the "Software"),
//  to deal in the Software without restriction, including without limitation
//  the rights to use, copy, modify, merge, publish, distribute, sublicense,
//  and/or sell copies of the Software, and to permit persons to whom the
//  Software is furnished to do so, subject to the following conditions:
//
//  The above copyright notice and this permission notice shall be included
//  in all copies or substantial portions of the Software.
//
//  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
//  OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
//  FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
//  THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
//  LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
//  FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
//  DEALINGS IN THE SOFTWARE.
//
//  Description: Pyramidic geometry information.
//
////////////////////////////////////////////////////////////////////////////////

#include <SpatialDomains/PyrGeom.h>

#include <SpatialDomains/Geometry1D.h>
#include <SpatialDomains/Geometry2D.h>
#include <StdRegions/StdPyrExp.h>
#include <SpatialDomains/SegGeom.h>
#include <SpatialDomains/TriGeom.h>
#include <SpatialDomains/MeshComponents.h>


namespace Nektar
{
    namespace SpatialDomains
    {
        PyrGeom::PyrGeom()
        {
            m_shapeType = LibUtilities::ePyramid;
        }

        PyrGeom::PyrGeom(const Geometry2DSharedPtr faces[]) :
            Geometry3D(faces[0]->GetEdge(0)->GetVertex(0)->GetCoordim())
        {
            m_shapeType = LibUtilities::ePyramid;

            /// Copy the face shared pointers
            m_faces.insert(m_faces.begin(), faces, faces+PyrGeom::kNfaces);

            /// Set up orientation vectors with correct amount of elements.
            m_eorient.resize(kNedges);
            m_forient.resize(kNfaces);

            SetUpLocalEdges();
            SetUpLocalVertices();
            SetUpEdgeOrientation();
            SetUpFaceOrientation();

            /// Determine necessary order for standard region.
            vector<int> tmp;
            
            int order0, points0, order1, points1;
            
            if (m_forient[0] < 9)
            {
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(0));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(2));
                order0 = *max_element(tmp.begin(), tmp.end());

                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(0));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(2));
                points0 = *max_element(tmp.begin(), tmp.end());
            }
            else
            {
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(1));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(3));
                order0 = *max_element(tmp.begin(), tmp.end());

                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(1));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(3));
                points0 = *max_element(tmp.begin(), tmp.end());
            }
            
            if (m_forient[0] < 9)
            {
                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(1));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(3));
                tmp.push_back(faces[2]->GetXmap()->GetEdgeNcoeffs(2));
                order1 = *max_element(tmp.begin(), tmp.end());
                
                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(1));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(3));
                tmp.push_back(faces[2]->GetXmap()->GetEdgeNumPoints(2));
                points1 = *max_element(tmp.begin(), tmp.end());
            }
            else
            {
                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(0));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNcoeffs(2));
                tmp.push_back(faces[2]->GetXmap()->GetEdgeNcoeffs(2));
                order1 = *max_element(tmp.begin(), tmp.end());
                
                tmp.clear();
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(0));
                tmp.push_back(faces[0]->GetXmap()->GetEdgeNumPoints(2));
                tmp.push_back(faces[2]->GetXmap()->GetEdgeNumPoints(2));
                points1 = *max_element(tmp.begin(), tmp.end());
            }
            
            tmp.clear();
            tmp.push_back(order0);
            tmp.push_back(order1);
            tmp.push_back(faces[1]->GetXmap()->GetEdgeNcoeffs(1));
            tmp.push_back(faces[1]->GetXmap()->GetEdgeNcoeffs(2));
            tmp.push_back(faces[3]->GetXmap()->GetEdgeNcoeffs(1));
            tmp.push_back(faces[3]->GetXmap()->GetEdgeNcoeffs(2));
            int order2 = *max_element(tmp.begin(), tmp.end());
            
            tmp.clear();
            tmp.push_back(points0);
            tmp.push_back(points1);
            tmp.push_back(faces[1]->GetXmap()->GetEdgeNumPoints(1));
            tmp.push_back(faces[1]->GetXmap()->GetEdgeNumPoints(2));
            tmp.push_back(faces[3]->GetXmap()->GetEdgeNumPoints(1));
            tmp.push_back(faces[3]->GetXmap()->GetEdgeNumPoints(2));
            tmp.push_back(faces[1]->GetEdge(1)->GetBasis(0)->GetNumPoints());
            tmp.push_back(faces[1]->GetEdge(2)->GetBasis(0)->GetNumPoints());
            tmp.push_back(faces[3]->GetEdge(1)->GetBasis(0)->GetNumPoints());
            tmp.push_back(faces[3]->GetEdge(2)->GetBasis(0)->GetNumPoints());
            int points2 = *max_element(tmp.begin(), tmp.end());
            
            const LibUtilities::BasisKey A1(
                LibUtilities::eModified_A, order0,
                LibUtilities::PointsKey(
                    points0, LibUtilities::eGaussLobattoLegendre));
            const LibUtilities::BasisKey A2(
                LibUtilities::eModified_A, order1,
                LibUtilities::PointsKey(
                    points1, LibUtilities::eGaussLobattoLegendre));
            const LibUtilities::BasisKey C(
                LibUtilities::eModified_C, order2,
                LibUtilities::PointsKey(
                    points2, LibUtilities::eGaussRadauMAlpha2Beta0));

            m_xmap = MemoryManager<StdRegions::StdPyrExp>::AllocateSharedPtr(
                A1, A2, C);
            SetUpCoeffs(m_xmap->GetNcoeffs());
        }

        PyrGeom::~PyrGeom()
        {
            
        }

        void PyrGeom::v_GenGeomFactors()
        {
            if (m_geomFactorsState != ePtsFilled)
            {
                int i;
                GeomType Gtype = eRegular;

                v_FillGeom();

                // check to see if expansions are linear
                for(i = 0; i < m_coordim; ++i)
                {
                    if (m_xmap->GetBasisNumModes(0) != 2 ||
                        m_xmap->GetBasisNumModes(1) != 2 ||
                        m_xmap->GetBasisNumModes(2) != 2 )
                    {
                        Gtype = eDeformed;
                    }
                }

                // check to see if all quadrilateral faces are parallelograms
                if(Gtype == eRegular)
                {
                    // Ensure each face is a parallelogram? Check this.
                    for (i = 0; i < m_coordim; i++)
                    {
                        if( fabs( (*m_verts[0])(i) -
                                  (*m_verts[1])(i) +
                                  (*m_verts[2])(i) -
                                  (*m_verts[3])(i) )
                            > NekConstants::kNekZeroTol )
                        {
                            Gtype = eDeformed;
                            break;
                        }
                    }
                }

                m_geomFactors = MemoryManager<GeomFactors>::AllocateSharedPtr(
                    Gtype, m_coordim, m_xmap, m_coeffs);
                m_geomFactorsState = ePtsFilled;
            }
        }

        NekDouble PyrGeom::v_GetLocCoords(
            const Array<OneD, const NekDouble> &coords,
                  Array<OneD,       NekDouble> &Lcoords)
        {
            NekDouble resid = 0.0;

            v_FillGeom();

            // calculate local coordinate for coord
            if(GetMetricInfo()->GetGtype() == eRegular)
            {   // Based on Spen's book, page 99

                // Point inside tetrahedron
                PointGeom r(m_coordim, 0, coords[0], coords[1], coords[2]);

                // Edges
                PointGeom er0, e10, e30, e40;
                er0.Sub(r,*m_verts[0]);
                e10.Sub(*m_verts[1],*m_verts[0]);
                e30.Sub(*m_verts[3],*m_verts[0]);
                e40.Sub(*m_verts[4],*m_verts[0]);


                // Cross products (Normal times area)
                PointGeom cp1030, cp3040, cp4010;
                cp1030.Mult(e10,e30);
                cp3040.Mult(e30,e40);
                cp4010.Mult(e40,e10);


                // Barycentric coordinates (relative volume)
                NekDouble V = e40.dot(cp1030); // Pyramid Volume = {(e40)dot(e10)x(e30)}/4
                NekDouble scaleFactor = 2.0/3.0;
                NekDouble v1 = er0.dot(cp3040) / V; // volume1 = {(er0)dot(e30)x(e40)}/6
                NekDouble v2 = er0.dot(cp4010) / V; // volume2 = {(er0)dot(e40)x(e10)}/6
                NekDouble beta  = v1 * scaleFactor;
                NekDouble gamma = v2 * scaleFactor;
                NekDouble delta = er0.dot(cp1030) / V; // volume3 = {(er0)dot(e10)x(e30)}/4


                // Make Pyramid bigger
                Lcoords[0] = 2.0*beta  - 1.0;
                Lcoords[1] = 2.0*gamma - 1.0;
                Lcoords[2] = 2.0*delta - 1.0;
            }
            else
            {
                NEKERROR(ErrorUtil::efatal,
                         "inverse mapping must be set up to use this call");
            }
            return resid;
        }

        int PyrGeom::v_GetNumVerts() const
        {
            return 5;
        }
        
        int PyrGeom::v_GetNumEdges() const
        {
            return 8;
        }

        int PyrGeom::v_GetDir(const int faceidx, const int facedir) const
        {
            if (faceidx == 0)
            {
                return facedir;
            }
            else if (faceidx == 1 || faceidx == 3)
            {
                return 2 * facedir;
            }
            else
            {
                return 1 + facedir;
            }
        }

        void PyrGeom::SetUpLocalEdges()
        {
            // find edge 0
            int i,j;
            unsigned int check;

            SegGeomSharedPtr edge;

            // First set up the 4 bottom edges
            int f;
            for (f = 1; f < 5; f++)
            {
                int nEdges = m_faces[f]->GetNumEdges();
                check = 0;
                for (i = 0; i < 4; i++)
                {
                    for (j = 0; j < nEdges; j++)
                    {
                        if (m_faces[0]->GetEid(i) == m_faces[f]->GetEid(j))
                        {
                            edge = boost::dynamic_pointer_cast<SegGeom>((m_faces[0])->GetEdge(i));
                            m_edges.push_back(edge);
                            check++;
                        }
                    }
                }

                if (check < 1)
                {
                    std::ostringstream errstrm;
                    errstrm << "Connected faces do not share an edge. Faces ";
                    errstrm << (m_faces[0])->GetFid() << ", " << (m_faces[f])->GetFid();
                    ASSERTL0(false, errstrm.str());
                }
                else if (check > 1)
                {
                    std::ostringstream errstrm;
                    errstrm << "Connected faces share more than one edge. Faces ";
                    errstrm << (m_faces[0])->GetFid() << ", " << (m_faces[f])->GetFid();
                    ASSERTL0(false, errstrm.str());
                }
            }

            // Then, set up the 4 vertical edges
            check = 0;
            for(i = 0; i < 3; i++) //Set up the vertical edge :face(1) and face(4)
            {
                for(j = 0; j < 3; j++)
                {
                    if( (m_faces[1])->GetEid(i) == (m_faces[4])->GetEid(j) )
                    {
                        edge = boost::dynamic_pointer_cast<SegGeom>((m_faces[1])->GetEdge(i));
                        m_edges.push_back(edge);
                        check++;
                    }
                }
            }
            if( check < 1 )
            {
                std::ostringstream errstrm;
                errstrm << "Connected faces do not share an edge. Faces ";
                errstrm << (m_faces[1])->GetFid() << ", " << (m_faces[4])->GetFid();
                ASSERTL0(false, errstrm.str());
            }
            else if( check > 1)
            {
                std::ostringstream errstrm;
                errstrm << "Connected faces share more than one edge. Faces ";
                errstrm << (m_faces[1])->GetFid() << ", " << (m_faces[4])->GetFid();
                ASSERTL0(false, errstrm.str());
            }

            // Set up vertical edges: face(1) through face(4)
            for (f = 1; f < 4; f++)
            {
                check = 0;
                for(i = 0; i < m_faces[f]->GetNumEdges(); i++)
                {
                    for(j = 0; j < m_faces[f+1]->GetNumEdges(); j++)
                    {
                        if( (m_faces[f])->GetEid(i) == (m_faces[f+1])->GetEid(j))
                        {
                            edge = boost::dynamic_pointer_cast<SegGeom>((m_faces[f])->GetEdge(i));
                            m_edges.push_back(edge);
                            check++;
                        }
                    }
                }

                if( check < 1 )
                {
                    std::ostringstream errstrm;
                    errstrm << "Connected faces do not share an edge. Faces ";
                    errstrm << (m_faces[f])->GetFid() << ", " << (m_faces[f+1])->GetFid();
                    ASSERTL0(false, errstrm.str());
                }
                else if( check > 1)
                {
                    std::ostringstream errstrm;
                    errstrm << "Connected faces share more than one edge. Faces ";
                    errstrm << (m_faces[f])->GetFid() << ", " << (m_faces[f+1])->GetFid();
                    ASSERTL0(false, errstrm.str());
                }
            }
        }

        void PyrGeom::SetUpLocalVertices()
        {
            // Set up the first 2 vertices (i.e. vertex 0,1)
            if (m_edges[0]->GetVid(0) == m_edges[1]->GetVid(0) ||
                m_edges[0]->GetVid(0) == m_edges[1]->GetVid(1))
            {
                m_verts.push_back(m_edges[0]->GetVertex(1));
                m_verts.push_back(m_edges[0]->GetVertex(0));
            }
            else if (m_edges[0]->GetVid(1) == m_edges[1]->GetVid(0) ||
                     m_edges[0]->GetVid(1) == m_edges[1]->GetVid(1))
            {
                m_verts.push_back(m_edges[0]->GetVertex(0));
                m_verts.push_back(m_edges[0]->GetVertex(1));
            }
            else
            {
                std::ostringstream errstrm;
                errstrm << "Connected edges do not share a vertex. Edges ";
                errstrm << m_edges[0]->GetEid() << ", " << m_edges[1]->GetEid();
                ASSERTL0(false, errstrm.str());
            }

            // set up the other bottom vertices (i.e. vertex 2,3)
            for(int i = 1; i < 3; i++)
            {
                if (m_edges[i]->GetVid(0) == m_verts[i]->GetVid())
                {
                    m_verts.push_back(m_edges[i]->GetVertex(1));
                }
                else if (m_edges[i]->GetVid(1) == m_verts[i]->GetVid())
                {
                    m_verts.push_back(m_edges[i]->GetVertex(0));
                }
                else
                {
                    std::ostringstream errstrm;
                    errstrm << "Connected edges do not share a vertex. Edges ";
                    errstrm << m_edges[i]->GetEid() << ", " << m_edges[i-1]->GetEid();
                    ASSERTL0(false, errstrm.str());
                }
            }

            // set up top vertex
            if (m_edges[4]->GetVid(0) == m_verts[0]->GetVid())
            {
                m_verts.push_back(m_edges[4]->GetVertex(1));
            }
            else
            {
                m_verts.push_back(m_edges[4]->GetVertex(0));
            }

            int check = 0;
            for (int i = 5; i < 8; ++i)
            {
                if( (m_edges[i]->GetVid(0) == m_verts[i-4]->GetVid()
                    && m_edges[i]->GetVid(1) == m_verts[4]->GetVid())
                    ||(m_edges[i]->GetVid(1) == m_verts[i-4]->GetVid()
                    && m_edges[i]->GetVid(0) == m_verts[4]->GetVid()))
                {
                    check++;
                }
            }
            if (check != 3) {
                std::ostringstream errstrm;
                errstrm << "Connected edges do not share a vertex. Edges ";
                errstrm << m_edges[3]->GetEid() << ", " << m_edges[2]->GetEid();
                ASSERTL0(false, errstrm.str());
            }
        }
        
        void PyrGeom::SetUpEdgeOrientation()
        {
            // This 2D array holds the local id's of all the vertices for every
            // edge. For every edge, they are ordered to what we define as being
            // Forwards.
            const unsigned int edgeVerts[kNedges][2] =
                { {0,1}, {1,2}, {3,2}, {0,3}, {0,4}, {1,4}, {2,4}, {3,4} };

            int i;
            for (i = 0; i < kNedges; i++)
            {
                if (m_edges[i]->GetVid(0) == m_verts[edgeVerts[i][0]]->GetVid())
                {
                    m_eorient[i] = StdRegions::eForwards;
                }
                else if (m_edges[i]->GetVid(0) == m_verts[edgeVerts[i][1]]->GetVid())
                {
                    m_eorient[i] = StdRegions::eBackwards;
                }
                else
                {
                    ASSERTL0(false,"Could not find matching vertex for the edge");
                }
            }
        }

        void PyrGeom::SetUpFaceOrientation()
        {
            int f,i;

            // These arrays represent the vector of the A and B coordinate of
            // the local elemental coordinate system where A corresponds with
            // the coordinate direction xi_i with the lowest index i (for that
            // particular face) Coordinate 'B' then corresponds to the other
            // local coordinate (i.e. with the highest index)
            Array<OneD,NekDouble> elementAaxis(m_coordim);
            Array<OneD,NekDouble> elementBaxis(m_coordim);

            // These arrays correspond to the local coordinate
            // system of the face itself (i.e. the Geometry2D)
            // faceAaxis correspond to the xi_0 axis
            // faceBaxis correspond to the xi_1 axis
            Array<OneD,NekDouble> faceAaxis(m_coordim);
            Array<OneD,NekDouble> faceBaxis(m_coordim);

            // This is the base vertex of the face (i.e. the Geometry2D) This
            // corresponds to thevertex with local ID 0 of the Geometry2D
            unsigned int baseVertex;

            // The lenght of the vectors above
            NekDouble elementAaxis_length;
            NekDouble elementBaxis_length;
            NekDouble faceAaxis_length;
            NekDouble faceBaxis_length;

            // This 2D array holds the local id's of all the vertices for every
            // face. For every face, they are ordered in such a way that the
            // implementation below allows a unified approach for all faces.
            const unsigned int faceVerts[kNfaces][4] = {
                {0,1,2,3},
                {0,1,4,0}, // Last four elements are triangles which only
                {1,2,4,0}, // require three vertices.
                {3,2,4,0},
                {0,3,4,0}
            };

            NekDouble dotproduct1 = 0.0;
            NekDouble dotproduct2 = 0.0;

            unsigned int orientation;

            // Loop over all the faces to set up the orientation
            for(f = 0; f < kNqfaces + kNtfaces; f++)
            {
                // initialisation
                elementAaxis_length = 0.0;
                elementBaxis_length = 0.0;
                faceAaxis_length = 0.0;
                faceBaxis_length = 0.0;

                dotproduct1 = 0.0;
                dotproduct2 = 0.0;

                baseVertex = m_faces[f]->GetVid(0);

                // We are going to construct the vectors representing the A and
                // B axis of every face. These vectors will be constructed as a
                // vector-representation of the edges of the face. However, for
                // both coordinate directions, we can represent the vectors by
                // two different edges. That's why we need to make sure that we
                // pick the edge to which the baseVertex of the
                // Geometry2D-representation of the face belongs...

                // Compute the length of edges on a base-face
                if (f > 0)
                {
                    for(i = 0; i < m_coordim; i++)
                    {
                        elementAaxis[i] = (*m_verts[ faceVerts[f][1] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                        elementBaxis[i] = (*m_verts[ faceVerts[f][2] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                    }
                }
                else
                {
                    if( baseVertex == m_verts[ faceVerts[f][0] ]->GetVid() )
                    {
                        for(i = 0; i < m_coordim; i++)
                        {
                            elementAaxis[i] = (*m_verts[ faceVerts[f][1] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                            elementBaxis[i] = (*m_verts[ faceVerts[f][3] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                        }
                    }
                    else if( baseVertex == m_verts[ faceVerts[f][1] ]->GetVid() )
                    {
                        for(i = 0; i < m_coordim; i++)
                        {
                            elementAaxis[i] = (*m_verts[ faceVerts[f][1] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                            elementBaxis[i] = (*m_verts[ faceVerts[f][2] ])[i] - (*m_verts[ faceVerts[f][1] ])[i];
                        }
                    }
                    else if( baseVertex == m_verts[ faceVerts[f][2] ]->GetVid() )
                    {
                        for(i = 0; i < m_coordim; i++)
                        {
                            elementAaxis[i] = (*m_verts[ faceVerts[f][2] ])[i] - (*m_verts[ faceVerts[f][3] ])[i];
                            elementBaxis[i] = (*m_verts[ faceVerts[f][2] ])[i] - (*m_verts[ faceVerts[f][1] ])[i];
                        }
                    }
                    else if( baseVertex == m_verts[ faceVerts[f][3] ]->GetVid() )
                    {
                        for(i = 0; i < m_coordim; i++)
                        {
                            elementAaxis[i] = (*m_verts[ faceVerts[f][2] ])[i] - (*m_verts[ faceVerts[f][3] ])[i];
                            elementBaxis[i] = (*m_verts[ faceVerts[f][3] ])[i] - (*m_verts[ faceVerts[f][0] ])[i];
                        }
                    }
                    else
                    {
                        ASSERTL0(false, "Could not find matching vertex for the face");
                    }
                }

                // Now, construct the edge-vectors of the local coordinates of
                // the Geometry2D-representation of the face
                for(i = 0; i < m_coordim; i++)
                {
                    int v = m_faces[f]->GetNumVerts()-1;
                    faceAaxis[i] = (*m_faces[f]->GetVertex(1))[i] - (*m_faces[f]->GetVertex(0))[i];
                    faceBaxis[i] = (*m_faces[f]->GetVertex(v))[i] - (*m_faces[f]->GetVertex(0))[i];

                    elementAaxis_length += pow(elementAaxis[i],2);
                    elementBaxis_length += pow(elementBaxis[i],2);
                    faceAaxis_length += pow(faceAaxis[i],2);
                    faceBaxis_length += pow(faceBaxis[i],2);
                }

                elementAaxis_length = sqrt(elementAaxis_length);
                elementBaxis_length = sqrt(elementBaxis_length);
                faceAaxis_length = sqrt(faceAaxis_length);
                faceBaxis_length = sqrt(faceBaxis_length);

                // Calculate the inner product of both the A-axis
                // (i.e. Elemental A axis and face A axis)
                for(i = 0 ; i < m_coordim; i++)
                {
                    dotproduct1 += elementAaxis[i]*faceAaxis[i];
                }

                orientation = 0;
                // if the innerproduct is equal to the (absolute value of the ) products of the lengths
                // of both vectors, then, the coordinate systems will NOT be transposed
                if( fabs(elementAaxis_length*faceAaxis_length - fabs(dotproduct1)) < NekConstants::kNekZeroTol )
                {
                    // if the inner product is negative, both A-axis point
                    // in reverse direction
                    if(dotproduct1 < 0.0)
                    {
                        orientation += 2;
                    }

                    // calculate the inner product of both B-axis
                    for(i = 0 ; i < m_coordim; i++)
                    {
                        dotproduct2 += elementBaxis[i]*faceBaxis[i];
                    }

                    // if the inner product is negative, both B-axis point
                    // in reverse direction
                    if( dotproduct2 < 0.0 )
                    {
                        orientation++;
                    }
                }
                // The coordinate systems are transposed
                else
                {
                    orientation = 4;

                    // Calculate the inner product between the elemental A-axis
                    // and the B-axis of the face (which are now the corresponding axis)
                    dotproduct1 = 0.0;
                    for(i = 0 ; i < m_coordim; i++)
                    {
                        dotproduct1 += elementAaxis[i]*faceBaxis[i];
                    }

                    // check that both these axis are indeed parallel
                    if (fabs(elementAaxis_length*faceBaxis_length
                            - fabs(dotproduct1)) > NekConstants::kNekZeroTol)
                    {
                        cout << "Warning: Prism axes not parallel" << endl;
                    }

                    // if the result is negative, both axis point in reverse
                    // directions
                    if(dotproduct1 < 0.0)
                    {
                        orientation += 2;
                    }

                    // Do the same for the other two corresponding axis
                    dotproduct2 = 0.0;
                    for(i = 0 ; i < m_coordim; i++)
                    {
                        dotproduct2 += elementBaxis[i]*faceAaxis[i];
                    }

                    // check that both these axis are indeed parallel
                    if (fabs(elementBaxis_length*faceAaxis_length
                            - fabs(dotproduct2)) > NekConstants::kNekZeroTol)
                    {
                        cout << "Warning: Prism axes not parallel" << endl;
                    }

                    if( dotproduct2 < 0.0 )
                    {
                        orientation++;
                    }
                }
                
                orientation = orientation + 5;

                // Fill the m_forient array
                m_forient[f] = (StdRegions::Orientation) orientation;
            }
        }
    }; //end of namespace
}; //end of namespace