TetGeom.cpp

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////////////////////////////////////////////////////////////////////////////////
//
//  File: TetGeom.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).
//
//  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: Tetrahedral geometry information.
//
////////////////////////////////////////////////////////////////////////////////
 
#include <SpatialDomains/TetGeom.h>
 
#include <SpatialDomains/Geometry1D.h>
#include <SpatialDomains/SegGeom.h>
#include <SpatialDomains/XmapFactory.hpp>
#include <StdRegions/StdTetExp.h>
 
namespace Nektar::SpatialDomains
{
const unsigned int TetGeom::VertexEdgeConnectivity[4][3] = {
    {0, 2, 3}, {0, 1, 4}, {1, 2, 5}, {3, 4, 5}};
const unsigned int TetGeom::VertexFaceConnectivity[4][3] = {
    {0, 1, 3}, {0, 1, 2}, {0, 2, 3}, {1, 2, 3}};
const unsigned int TetGeom::EdgeFaceConnectivity[6][2] = {
    {0, 1}, {0, 2}, {0, 3}, {1, 3}, {1, 2}, {2, 3}};
const unsigned int TetGeom::EdgeNormalToFaceVert[4][3] = {
    {3, 4, 5}, {1, 2, 5}, {0, 2, 3}, {0, 1, 4}};
 
XmapFactory<StdRegions::StdTetExp, 3> &GetStdTetFactory()
{
    static XmapFactory<StdRegions::StdTetExp, 3> factory;
    return factory;
}
 
TetGeom::TetGeom()
{
    m_shapeType = LibUtilities::eTetrahedron;
}
 
TetGeom::TetGeom(int id, std::array<TriGeom *, kNfaces> faces)
    : Geometry3D(faces[0]->GetEdge(0)->GetVertex(0)->GetCoordim())
{
    m_shapeType = LibUtilities::eTetrahedron;
    m_globalID  = id;
    m_faces     = faces;
 
    SetUpLocalEdges();
    SetUpLocalVertices();
    SetUpEdgeOrientation();
    SetUpFaceOrientation();
}
 
int TetGeom::v_GetDir(const int faceidx, const int facedir) const
{
    if (faceidx == 0)
    {
        return facedir;
    }
    else if (faceidx == 1)
    {
        return 2 * facedir;
    }
    else
    {
        return 1 + facedir;
    }
}
 
int TetGeom::v_GetVertexEdgeMap(const int i, const int j) const
{
    return VertexEdgeConnectivity[i][j];
}
 
int TetGeom::v_GetVertexFaceMap(const int i, const int j) const
{
    return VertexFaceConnectivity[i][j];
}
 
int TetGeom::v_GetEdgeFaceMap(const int i, const int j) const
{
    return EdgeFaceConnectivity[i][j];
}
 
int TetGeom::v_GetEdgeNormalToFaceVert(const int i, const int j) const
{
    return EdgeNormalToFaceVert[i][j];
}
 
void TetGeom::SetUpLocalEdges()
{
 
    // find edge 0
    int i, j;
    unsigned int check;
 
    // First set up the 3 bottom edges
 
    if (m_faces[0]->GetEid(0) != m_faces[1]->GetEid(0))
    {
        std::ostringstream errstrm;
        errstrm << "Local edge 0 (eid=" << m_faces[0]->GetEid(0);
        errstrm << ") on face " << m_faces[0]->GetGlobalID();
        errstrm << " must be the same as local edge 0 (eid="
                << m_faces[1]->GetEid(0);
        errstrm << ") on face " << m_faces[1]->GetGlobalID();
        NEKERROR(ErrorUtil::efatal, errstrm.str());
    }
 
    int faceConnected;
    for (faceConnected = 1; faceConnected < 4; faceConnected++)
    {
        check = 0;
        for (i = 0; i < 3; i++)
        {
            if ((m_faces[0])->GetEid(i) == (m_faces[faceConnected])->GetEid(0))
            {
                m_edges[faceConnected - 1] =
                    static_cast<SegGeom *>((m_faces[0])->GetEdge(i));
                check++;
            }
        }
 
        if (check < 1)
        {
            std::ostringstream errstrm;
            errstrm << "Face 0 does not share an edge with first edge of "
                       "adjacent face. Faces ";
            errstrm << (m_faces[0])->GetGlobalID() << ", "
                    << (m_faces[faceConnected])->GetGlobalID();
            NEKERROR(ErrorUtil::efatal, errstrm.str());
        }
        else if (check > 1)
        {
            std::ostringstream errstrm;
            errstrm << "Connected faces share more than one edge. Faces ";
            errstrm << (m_faces[0])->GetGlobalID() << ", "
                    << (m_faces[faceConnected])->GetGlobalID();
            NEKERROR(ErrorUtil::efatal, errstrm.str());
        }
    }
 
    // Then, set up the 3 vertical edges
    check = 0;
    for (i = 0; i < 3; i++) // Set up the vertical edge :face(1) and face(3)
    {
        for (j = 0; j < 3; j++)
        {
            if ((m_faces[1])->GetEid(i) == (m_faces[3])->GetEid(j))
            {
                m_edges[3] = static_cast<SegGeom *>((m_faces[1])->GetEdge(i));
                check++;
            }
        }
    }
    if (check < 1)
    {
        std::ostringstream errstrm;
        errstrm << "Connected faces do not share an edge. Faces ";
        errstrm << (m_faces[1])->GetGlobalID() << ", "
                << (m_faces[3])->GetGlobalID();
        NEKERROR(ErrorUtil::efatal, errstrm.str());
    }
    else if (check > 1)
    {
        std::ostringstream errstrm;
        errstrm << "Connected faces share more than one edge. Faces ";
        errstrm << (m_faces[1])->GetGlobalID() << ", "
                << (m_faces[3])->GetGlobalID();
        NEKERROR(ErrorUtil::efatal, errstrm.str());
    }
    // Set up vertical edges: face(1) through face(3)
    for (faceConnected = 1; faceConnected < 3; faceConnected++)
    {
        check = 0;
        for (i = 0; i < 3; i++)
        {
            for (j = 0; j < 3; j++)
            {
                if ((m_faces[faceConnected])->GetEid(i) ==
                    (m_faces[faceConnected + 1])->GetEid(j))
                {
                    m_edges[faceConnected + 3] = static_cast<SegGeom *>(
                        (m_faces[faceConnected])->GetEdge(i));
                    check++;
                }
            }
        }
 
        if (check < 1)
        {
            std::ostringstream errstrm;
            errstrm << "Connected faces do not share an edge. Faces ";
            errstrm << (m_faces[faceConnected])->GetGlobalID() << ", "
                    << (m_faces[faceConnected + 1])->GetGlobalID();
            NEKERROR(ErrorUtil::efatal, errstrm.str());
        }
        else if (check > 1)
        {
            std::ostringstream errstrm;
            errstrm << "Connected faces share more than one edge. Faces ";
            errstrm << (m_faces[faceConnected])->GetGlobalID() << ", "
                    << (m_faces[faceConnected + 1])->GetGlobalID();
            NEKERROR(ErrorUtil::efatal, errstrm.str());
        }
    }
}
 
void TetGeom::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[0] = m_edges[0]->GetVertex(1);
        m_verts[1] = 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[0] = m_edges[0]->GetVertex(0);
        m_verts[1] = m_edges[0]->GetVertex(1);
    }
    else
    {
        std::ostringstream errstrm;
        errstrm << "Connected edges do not share a vertex. Edges ";
        errstrm << m_edges[0]->GetGlobalID() << ", "
                << m_edges[1]->GetGlobalID();
        NEKERROR(ErrorUtil::efatal, errstrm.str());
    }
 
    // set up the other bottom vertices (i.e. vertex 2)
    for (int i = 1; i < 2; i++)
    {
        if (m_edges[i]->GetVid(0) == m_verts[i]->GetGlobalID())
        {
            m_verts[2] = m_edges[i]->GetVertex(1);
        }
        else if (m_edges[i]->GetVid(1) == m_verts[i]->GetGlobalID())
        {
            m_verts[2] = m_edges[i]->GetVertex(0);
        }
        else
        {
            std::ostringstream errstrm;
            errstrm << "Connected edges do not share a vertex. Edges ";
            errstrm << m_edges[i]->GetGlobalID() << ", "
                    << m_edges[i - 1]->GetGlobalID();
            NEKERROR(ErrorUtil::efatal, errstrm.str());
        }
    }
 
    // set up top vertex
    if (m_edges[3]->GetVid(0) == m_verts[0]->GetGlobalID())
    {
        m_verts[3] = m_edges[3]->GetVertex(1);
    }
    else
    {
        m_verts[3] = m_edges[3]->GetVertex(0);
    }
 
    // Check the other edges match up.
    int check = 0;
    for (int i = 4; i < 6; ++i)
    {
        if ((m_edges[i]->GetVid(0) == m_verts[i - 3]->GetGlobalID() &&
             m_edges[i]->GetVid(1) == m_verts[3]->GetGlobalID()) ||
            (m_edges[i]->GetVid(1) == m_verts[i - 3]->GetGlobalID() &&
             m_edges[i]->GetVid(0) == m_verts[3]->GetGlobalID()))
        {
            check++;
        }
    }
    if (check != 2)
    {
        std::ostringstream errstrm;
        errstrm << "Connected edges do not share a vertex. Edges ";
        errstrm << m_edges[3]->GetGlobalID() << ", "
                << m_edges[2]->GetGlobalID();
        NEKERROR(ErrorUtil::efatal, errstrm.str());
    }
}
 
void TetGeom::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}, {0, 2},
                                                {0, 3}, {1, 3}, {2, 3}};
 
    int i;
    for (i = 0; i < kNedges; i++)
    {
        if (m_edges[i]->GetVid(0) == m_verts[edgeVerts[i][0]]->GetGlobalID())
        {
            m_eorient[i] = StdRegions::eForwards;
        }
        else if (m_edges[i]->GetVid(0) ==
                 m_verts[edgeVerts[i][1]]->GetGlobalID())
        {
            m_eorient[i] = StdRegions::eBackwards;
        }
        else
        {
            NEKERROR(ErrorUtil::efatal,
                     "Could not find matching vertex for the edge");
        }
    }
}
 
void TetGeom::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][TriGeom::kNverts] = {
        {0, 1, 2}, {0, 1, 3}, {1, 2, 3}, {0, 2, 3}};
 
    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 (baseVertex == m_verts[faceVerts[f][0]]->GetGlobalID())
        {
            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][1]]->GetGlobalID())
        {
            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]]->GetGlobalID())
        {
            for (i = 0; i < m_coordim; i++)
            {
                elementAaxis[i] = (*m_verts[faceVerts[f][1]])[i] -
                                  (*m_verts[faceVerts[f][2]])[i];
                elementBaxis[i] = (*m_verts[faceVerts[f][2]])[i] -
                                  (*m_verts[faceVerts[f][0]])[i];
            }
        }
        else
        {
            NEKERROR(ErrorUtil::efatal,
                     "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++)
        {
            faceAaxis[i] =
                (*m_faces[f]->GetVertex(1))[i] - (*m_faces[f]->GetVertex(0))[i];
            faceBaxis[i] =
                (*m_faces[f]->GetVertex(2))[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];
        }
 
        NekDouble norm =
            fabs(dotproduct1) / elementAaxis_length / faceAaxis_length;
        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(norm - 1.0) < 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];
            }
 
            norm = fabs(dotproduct2) / elementBaxis_length / faceBaxis_length;
 
            // check that both these axis are indeed parallel
            if (fabs(norm - 1.0) >= NekConstants::kNekZeroTol)
            {
                NEKERROR(ErrorUtil::ewarning,
                         "These vectors should be parallel");
            }
 
            // 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];
            }
 
            norm = fabs(dotproduct1) / elementAaxis_length / faceBaxis_length;
 
            // check that both these axis are indeed parallel
            if (fabs(norm - 1.0) >= NekConstants::kNekZeroTol)
            {
                NEKERROR(ErrorUtil::ewarning,
                         "These vectors should be parallel");
            }
 
            // 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];
            }
 
            norm = fabs(dotproduct2) / elementBaxis_length / faceAaxis_length;
 
            // check that both these axis are indeed parallel
            if (fabs(norm - 1.0) >= NekConstants::kNekZeroTol)
            {
                NEKERROR(ErrorUtil::ewarning,
                         "These vectors should be parallel");
            }
 
            if (dotproduct2 < 0.0)
            {
                orientation++;
            }
        }
 
        orientation = orientation + 5;
 
        ASSERTL0(orientation < StdRegions::eDir1FwdDir2_Dir2FwdDir1,
                 "Orientation of triangular face (id = " +
                     std::to_string(m_faces[f]->GetGlobalID()) +
                     ") is inconsistent with face " + std::to_string(f) +
                     " of tet element (id = " + std::to_string(m_globalID) +
                     ") since Dir2 is aligned with Dir1. Mesh setup "
                     "needs investigation");
 
        // Fill the m_forient array
        m_forient[f] = (StdRegions::Orientation)orientation;
    }
}
 
void TetGeom::v_Reset(CurveMap &curvedEdges, CurveMap &curvedFaces)
{
    Geometry::v_Reset(curvedEdges, curvedFaces);
 
    for (int i = 0; i < 4; ++i)
    {
        m_faces[i]->Reset(curvedEdges, curvedFaces);
    }
}
 
void TetGeom::v_Setup()
{
    if (!m_setupState)
    {
        for (int i = 0; i < 4; ++i)
        {
            m_faces[i]->Setup();
        }
        SetUpXmap();
        SetUpCoeffs(m_xmap->GetNcoeffs());
 
        // check to see if expansions are linear
        m_straightEdge = 1;
        if (m_xmap->GetBasisNumModes(0) != 2 ||
            m_xmap->GetBasisNumModes(1) != 2 ||
            m_xmap->GetBasisNumModes(2) != 2)
        {
            m_straightEdge = 0;
        }
 
        m_setupState = true;
    }
}
 
/**
 * Generate the geometry factors for this element.
 */
GeomType TetGeom::v_CalcGeomType()
{
    if (!m_setupState)
    {
        TetGeom::v_Setup();
    }
    v_FillGeom();
 
    GeomType Gtype = eRegular;
 
    // check to see if expansions are linear
    if (m_xmap->GetBasisNumModes(0) != 2 || m_xmap->GetBasisNumModes(1) != 2 ||
        m_xmap->GetBasisNumModes(2) != 2)
    {
        Gtype = eDeformed;
    }
 
    if (Gtype == eRegular)
    {
        m_isoParameter = Array<OneD, Array<OneD, NekDouble>>(3);
        for (int i = 0; i < 3; ++i)
        {
            m_isoParameter[i]    = Array<OneD, NekDouble>(4, 0.);
            NekDouble A          = (*m_verts[0])(i);
            NekDouble B          = (*m_verts[1])(i);
            NekDouble C          = (*m_verts[2])(i);
            NekDouble D          = (*m_verts[3])(i);
            m_isoParameter[i][0] = 0.5 * (-A + B + C + D);
 
            m_isoParameter[i][1] = 0.5 * (-A + B); // xi1
            m_isoParameter[i][2] = 0.5 * (-A + C); // xi2
            m_isoParameter[i][3] = 0.5 * (-A + D); // xi3
        }
    }
 
    if (Gtype == eRegular)
    {
        v_CalculateInverseIsoParam();
    }
 
    return Gtype;
}
 
GeomFactorsUniquePtr TetGeom::v_GenGeomFactors(
    LibUtilities::PointsKeyVector &keyTgt)
{
    GeomType Gtype = CalcGeomType();
 
    return ObjPoolManager<GeomFactors>::AllocateUniquePtr(
        Gtype, m_coordim, m_xmap, m_coeffs, keyTgt);
}
 
/**
 * @brief Set up the #m_xmap object by determining the order of each
 * direction from derived faces.
 */
void TetGeom::SetUpXmap()
{
    std::vector<int> tmp;
    tmp.push_back(m_faces[0]->GetXmap()->GetTraceNcoeffs(0));
    int order0 = *std::max_element(tmp.begin(), tmp.end());
 
    tmp.clear();
    tmp.push_back(order0);
    tmp.push_back(m_faces[0]->GetXmap()->GetTraceNcoeffs(1));
    tmp.push_back(m_faces[0]->GetXmap()->GetTraceNcoeffs(2));
    int order1 = *std::max_element(tmp.begin(), tmp.end());
 
    tmp.clear();
    tmp.push_back(order0);
    tmp.push_back(order1);
    tmp.push_back(m_faces[1]->GetXmap()->GetTraceNcoeffs(1));
    tmp.push_back(m_faces[1]->GetXmap()->GetTraceNcoeffs(2));
    tmp.push_back(m_faces[3]->GetXmap()->GetTraceNcoeffs(1));
    int order2 = *std::max_element(tmp.begin(), tmp.end());
 
    std::array<LibUtilities::BasisKey, 3> basis = {
        LibUtilities::BasisKey(
            LibUtilities::eModified_A, order0,
            LibUtilities::PointsKey(order0 + 1,
                                    LibUtilities::eGaussLobattoLegendre)),
        LibUtilities::BasisKey(
            LibUtilities::eModified_B, order1,
            LibUtilities::PointsKey(order1,
                                    LibUtilities::eGaussRadauMAlpha1Beta0)),
        LibUtilities::BasisKey(
            LibUtilities::eModified_C, order2,
            LibUtilities::PointsKey(order2,
                                    LibUtilities::eGaussRadauMAlpha2Beta0))};
 
    m_xmap = GetStdTetFactory().CreateInstance(basis);
}
 
/**
 * @brief Put all quadrature information into face/edge structure and
 * backward transform.
 *
 * Note verts, edges, and faces are listed according to anticlockwise
 * convention but points in _coeffs have to be in array format from left
 * to right.
 */
void TetGeom::v_FillGeom()
{
    if (m_state == ePtsFilled)
    {
        return;
    }
 
    int i, j, k;
 
    for (i = 0; i < kNfaces; i++)
    {
        m_faces[i]->FillGeom();
 
        int nFaceCoeffs = m_faces[i]->GetXmap()->GetNcoeffs();
 
        Array<OneD, unsigned int> mapArray(nFaceCoeffs);
        Array<OneD, int> signArray(nFaceCoeffs);
 
        if (m_forient[i] < 9)
        {
            m_xmap->GetTraceToElementMap(
                i, mapArray, signArray, m_forient[i],
                m_faces[i]->GetXmap()->GetTraceNcoeffs(0),
                m_faces[i]->GetXmap()->GetTraceNcoeffs(1));
        }
        else
        {
            m_xmap->GetTraceToElementMap(
                i, mapArray, signArray, m_forient[i],
                m_faces[i]->GetXmap()->GetTraceNcoeffs(1),
                m_faces[i]->GetXmap()->GetTraceNcoeffs(0));
        }
 
        for (j = 0; j < m_coordim; j++)
        {
            const Array<OneD, const NekDouble> &coeffs =
                m_faces[i]->GetCoeffs(j);
 
            for (k = 0; k < nFaceCoeffs; k++)
            {
                NekDouble v              = signArray[k] * coeffs[k];
                m_coeffs[j][mapArray[k]] = v;
            }
        }
    }
 
    m_state = ePtsFilled;
}
 
} // namespace Nektar::SpatialDomains