text: /*=========================================================================
  
    Program:   Visualization Toolkit
    Module:    vtkTriQuadraticHexahedron.cxx
  
    Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
    All rights reserved.
    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
  
       This software is distributed WITHOUT ANY WARRANTY; without even
       the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
       PURPOSE.  See the above copyright notice for more information.
  
  =========================================================================*/
  
  // Thanks to Soeren Gebbert who developed this class and
  // integrated it into VTK 5.0.
  
  #include "vtkTriQuadraticHexahedron.h"
  
  #include "vtkBiQuadraticQuad.h"
  #include "vtkDoubleArray.h"
  #include "vtkHexahedron.h"
  #include "vtkMath.h"
  #include "vtkObjectFactory.h"
  #include "vtkPoints.h"
  #include "vtkQuadraticEdge.h"
  
  vtkStandardNewMacro(vtkTriQuadraticHexahedron);
  
  //------------------------------------------------------------------------------
  // Construct the triquadhex with 27 nodes
  vtkTriQuadraticHexahedron::vtkTriQuadraticHexahedron()
  {
    this->Points->SetNumberOfPoints(27);
    this->PointIds->SetNumberOfIds(27);
    for (int i = 0; i < 27; i++)
    {
      this->Points->SetPoint(i, 0.0, 0.0, 0.0);
      this->PointIds->SetId(i, 0);
    }
  
    this->Edge = vtkQuadraticEdge::New();
    this->Face = vtkBiQuadraticQuad::New();
    this->Hex = vtkHexahedron::New();
  
    this->Scalars = vtkDoubleArray::New();
    this->Scalars->SetNumberOfTuples(8); // vertices of a linear hexahedron
  }
  
  //------------------------------------------------------------------------------
  vtkTriQuadraticHexahedron::~vtkTriQuadraticHexahedron()
  {
    this->Edge->Delete();
    this->Face->Delete();
    this->Hex->Delete();
  
    this->Scalars->Delete();
  }
  
  //------------------------------------------------------------------------------
  static int LinearHexs[8][8] = {
    { 0, 8, 24, 11, 16, 22, 26, 20 },
    { 8, 1, 9, 24, 22, 17, 21, 26 },
    { 11, 24, 10, 3, 20, 26, 23, 19 },
    { 24, 9, 2, 10, 26, 21, 18, 23 },
    { 16, 22, 26, 20, 4, 12, 25, 15 },
    { 22, 17, 21, 26, 12, 5, 13, 25 },
    { 20, 26, 23, 19, 15, 25, 14, 7 },
    { 26, 21, 18, 23, 25, 13, 6, 14 },
  };
  
  static constexpr vtkIdType HexFaces[6][9] = {
    { 0, 4, 7, 3, 16, 15, 19, 11, 20 },
    { 1, 2, 6, 5, 9, 18, 13, 17, 21 },
    { 0, 1, 5, 4, 8, 17, 12, 16, 22 },
    { 3, 7, 6, 2, 19, 14, 18, 10, 23 },
    { 0, 3, 2, 1, 11, 10, 9, 8, 24 },
    { 4, 5, 6, 7, 12, 13, 14, 15, 25 },
  };
  
  static constexpr vtkIdType HexEdges[12][3] = {
    { 0, 1, 8 },
    { 1, 2, 9 },
    { 3, 2, 10 },
    { 0, 3, 11 },
    { 4, 5, 12 },
    { 5, 6, 13 },
    { 7, 6, 14 },
    { 4, 7, 15 },
    { 0, 4, 16 },
    { 1, 5, 17 },
    { 3, 7, 19 },
    { 2, 6, 18 },
  };
  
  //------------------------------------------------------------------------------
  const vtkIdType* vtkTriQuadraticHexahedron::GetEdgeArray(vtkIdType edgeId)
  {
    return HexEdges[edgeId];
  }
  //------------------------------------------------------------------------------
  const vtkIdType* vtkTriQuadraticHexahedron::GetFaceArray(vtkIdType faceId)
  {
    return HexFaces[faceId];
  }
  
  //------------------------------------------------------------------------------
  vtkCell* vtkTriQuadraticHexahedron::GetEdge(int edgeId)
  {
    edgeId = (edgeId < 0 ? 0 : (edgeId > 11 ? 11 : edgeId));
  
    for (int i = 0; i < 3; i++)
    {
      this->Edge->PointIds->SetId(i, this->PointIds->GetId(HexEdges[edgeId][i]));
      this->Edge->Points->SetPoint(i, this->Points->GetPoint(HexEdges[edgeId][i]));
    }
  
    return this->Edge;
  }
  
  //------------------------------------------------------------------------------
  vtkCell* vtkTriQuadraticHexahedron::GetFace(int faceId)
  {
    faceId = (faceId < 0 ? 0 : (faceId > 5 ? 5 : faceId));
  
    for (int i = 0; i < 9; i++)
    {
      this->Face->PointIds->SetId(i, this->PointIds->GetId(HexFaces[faceId][i]));
      this->Face->Points->SetPoint(i, this->Points->GetPoint(HexFaces[faceId][i]));
    }
  
    return this->Face;
  }
  
  //------------------------------------------------------------------------------
  static const double VTK_DIVERGED = 1.e6;
  static const int VTK_HEX_MAX_ITERATION = 10;
  static const double VTK_HEX_CONVERGED = 1.e-03;
  
  int vtkTriQuadraticHexahedron::EvaluatePosition(const double* x, double* closestPoint, int& subId,
    double pcoords[3], double& dist2, double* weights)
  {
    int iteration, converged;
    double params[3];
    double fcol[3], rcol[3], scol[3], tcol[3];
    int i, j;
    double pt[3];
    double derivs[81];
    double hexweights[8];
  
    //  set initial position for Newton's method
    pcoords[0] = pcoords[1] = pcoords[2] = params[0] = params[1] = params[2] = 0.5;
    subId = 0;
  
    // Use a tri-linear hexahederon to get good starting values
    vtkHexahedron* hex = vtkHexahedron::New();
    for (i = 0; i < 8; i++)
      hex->GetPoints()->SetPoint(i, this->Points->GetPoint(i));
  
    hex->EvaluatePosition(x, closestPoint, subId, pcoords, dist2, hexweights);
    hex->Delete();
  
    params[0] = pcoords[0];
    params[1] = pcoords[1];
    params[2] = pcoords[2];
  
    //  enter iteration loop
    for (iteration = converged = 0; !converged && (iteration < VTK_HEX_MAX_ITERATION); iteration++)
    {
      //  calculate element interpolation functions and derivatives
      this->InterpolationFunctions(pcoords, weights);
      this->InterpolationDerivs(pcoords, derivs);
  
      //  calculate newton functions
      for (i = 0; i < 3; i++)
      {
        fcol[i] = rcol[i] = scol[i] = tcol[i] = 0.0;
      }
      for (i = 0; i < 27; i++)
      {
        this->Points->GetPoint(i, pt);
        for (j = 0; j < 3; j++)
        {
          fcol[j] += pt[j] * weights[i];
          rcol[j] += pt[j] * derivs[i];
          scol[j] += pt[j] * derivs[i + 27];
          tcol[j] += pt[j] * derivs[i + 54];
        }
      }
  
      for (i = 0; i < 3; i++)
      {
        fcol[i] -= x[i];
      }
  
      //  compute determinants and generate improvements
      double d = vtkMath::Determinant3x3(rcol, scol, tcol);
      if (fabs(d) < 1.e-20)
      {
        vtkDebugMacro(<< "Determinant incorrect, iteration " << iteration);
        return -1;
      }
  
      pcoords[0] = params[0] - 0.5 * vtkMath::Determinant3x3(fcol, scol, tcol) / d;
      pcoords[1] = params[1] - 0.5 * vtkMath::Determinant3x3(rcol, fcol, tcol) / d;
      pcoords[2] = params[2] - 0.5 * vtkMath::Determinant3x3(rcol, scol, fcol) / d;
  
      //  check for convergence
      if (((fabs(pcoords[0] - params[0])) < VTK_HEX_CONVERGED) &&
        ((fabs(pcoords[1] - params[1])) < VTK_HEX_CONVERGED) &&
        ((fabs(pcoords[2] - params[2])) < VTK_HEX_CONVERGED))
      {
        converged = 1;
      }
  
      // Test for bad divergence (S.Hirschberg 11.12.2001)
      else if ((fabs(pcoords[0]) > VTK_DIVERGED) || (fabs(pcoords[1]) > VTK_DIVERGED) ||
        (fabs(pcoords[2]) > VTK_DIVERGED))
      {
        return -1;
      }
  
      //  if not converged, repeat
      else
      {
        params[0] = pcoords[0];
        params[1] = pcoords[1];
        params[2] = pcoords[2];
      }
    }
  
    //  if not converged, set the parametric coordinates to arbitrary values
    //  outside of element
    if (!converged)
    {
      return -1;
    }
  
    this->InterpolationFunctions(pcoords, weights);
  
    if (pcoords[0] >= -0.001 && pcoords[0] <= 1.001 && pcoords[1] >= -0.001 && pcoords[1] <= 1.001 &&
      pcoords[2] >= -0.001 && pcoords[2] <= 1.001)
    {
      if (closestPoint)
      {
        closestPoint[0] = x[0];
        closestPoint[1] = x[1];
        closestPoint[2] = x[2];
        dist2 = 0.0; // inside hexahedron
      }
      return 1;
    }
    else
    {
      double pc[3], w[27];
      if (closestPoint)
      {
        for (i = 0; i < 3; i++) // only approximate, not really true for warped hexa
        {
          if (pcoords[i] < 0.0)
          {
            pc[i] = 0.0;
          }
          else if (pcoords[i] > 1.0)
          {
            pc[i] = 1.0;
          }
          else
          {
            pc[i] = pcoords[i];
          }
        }
        this->EvaluateLocation(subId, pc, closestPoint, static_cast<double*>(w));
        dist2 = vtkMath::Distance2BetweenPoints(closestPoint, x);
      }
      return 0;
    }
  }
  
  //------------------------------------------------------------------------------
  void vtkTriQuadraticHexahedron::EvaluateLocation(
    int& vtkNotUsed(subId), const double pcoords[3], double x[3], double* weights)
  {
    int i, j;
    double pt[3];
  
    this->InterpolationFunctions(pcoords, weights);
  
    x[0] = x[1] = x[2] = 0.0;
    for (i = 0; i < 27; i++)
    {
      this->Points->GetPoint(i, pt);
      for (j = 0; j < 3; j++)
      {
        x[j] += pt[j] * weights[i];
      }
    }
  }
  
  //------------------------------------------------------------------------------
  int vtkTriQuadraticHexahedron::CellBoundary(int subId, const double pcoords[3], vtkIdList* pts)
  {
    return this->Hex->CellBoundary(subId, pcoords, pts);
  }
  
  //------------------------------------------------------------------------------
  void vtkTriQuadraticHexahedron::Contour(double value, vtkDataArray* cellScalars,
    vtkIncrementalPointLocator* locator, vtkCellArray* verts, vtkCellArray* lines,
    vtkCellArray* polys, vtkPointData* inPd, vtkPointData* outPd, vtkCellData* inCd, vtkIdType cellId,
    vtkCellData* outCd)
  {
    // contour each linear hex separately
    for (int i = 0; i < 8; i++)
    {
      for (int j = 0; j < 8; j++)
      {
        this->Hex->Points->SetPoint(j, this->Points->GetPoint(LinearHexs[i][j]));
        this->Hex->PointIds->SetId(j, this->PointIds->GetId(LinearHexs[i][j]));
        this->Scalars->SetValue(j, cellScalars->GetTuple1(LinearHexs[i][j]));
      }
      this->Hex->Contour(
        value, this->Scalars, locator, verts, lines, polys, inPd, outPd, inCd, cellId, outCd);
    }
  }
  
  //------------------------------------------------------------------------------
  // Clip this triquadratic hex using scalar value provided. Like contouring,
  // except that it cuts the hex to produce tetrahedra.
  void vtkTriQuadraticHexahedron::Clip(double value, vtkDataArray* cellScalars,
    vtkIncrementalPointLocator* locator, vtkCellArray* tets, vtkPointData* inPd, vtkPointData* outPd,
    vtkCellData* inCd, vtkIdType cellId, vtkCellData* outCd, int insideOut)
  {
    // clip each linear hex separately
    for (int i = 0; i < 8; i++)
    {
      for (int j = 0; j < 8; j++)
      {
        this->Hex->Points->SetPoint(j, this->Points->GetPoint(LinearHexs[i][j]));
        this->Hex->PointIds->SetId(j, this->PointIds->GetId(LinearHexs[i][j]));
        this->Scalars->SetValue(j, cellScalars->GetTuple1(LinearHexs[i][j]));
      }
      this->Hex->Clip(
        value, this->Scalars, locator, tets, inPd, outPd, inCd, cellId, outCd, insideOut);
    }
  }
  
  //------------------------------------------------------------------------------
  // Line-hex intersection. Intersection has to occur within [0,1] parametric
  // coordinates and with specified tolerance.
  int vtkTriQuadraticHexahedron::IntersectWithLine(
    const double* p1, const double* p2, double tol, double& t, double* x, double* pcoords, int& subId)
  {
    int intersection = 0;
    double tTemp;
    double pc[3], xTemp[3];
    int faceNum;
  
    t = VTK_DOUBLE_MAX;
    for (faceNum = 0; faceNum < 6; faceNum++)
    {
      for (int i = 0; i < 9; i++)
      {
        this->Face->PointIds->SetId(i, this->PointIds->GetId(HexFaces[faceNum][i]));
        this->Face->Points->SetPoint(i, this->Points->GetPoint(HexFaces[faceNum][i]));
      }
  
      if (this->Face->IntersectWithLine(p1, p2, tol, tTemp, xTemp, pc, subId))
      {
        intersection = 1;
        if (tTemp < t)
        {
          t = tTemp;
          x[0] = xTemp[0];
          x[1] = xTemp[1];
          x[2] = xTemp[2];
          switch (faceNum)
          {
            case 0:
              pcoords[0] = 0.0;
              pcoords[1] = pc[1];
              pcoords[2] = pc[0];
              break;
  
            case 1:
              pcoords[0] = 1.0;
              pcoords[1] = pc[0];
              pcoords[2] = pc[1];
              break;
  
            case 2:
              pcoords[0] = pc[0];
              pcoords[1] = 0.0;
              pcoords[2] = pc[1];
              break;
  
            case 3:
              pcoords[0] = pc[1];
              pcoords[1] = 1.0;
              pcoords[2] = pc[0];
              break;
  
            case 4:
              pcoords[0] = pc[1];
              pcoords[1] = pc[0];
              pcoords[2] = 0.0;
              break;
  
            case 5:
              pcoords[0] = pc[0];
              pcoords[1] = pc[1];
              pcoords[2] = 1.0;
              break;
          }
        }
      }
    }
    return intersection;
  }
  
  //------------------------------------------------------------------------------
  int vtkTriQuadraticHexahedron::Triangulate(int vtkNotUsed(index), vtkIdList* ptIds, vtkPoints* pts)
  {
    pts->Reset();
    ptIds->Reset();
  
    ptIds->InsertId(0, this->PointIds->GetId(0));
    pts->InsertPoint(0, this->Points->GetPoint(0));
  
    ptIds->InsertId(1, this->PointIds->GetId(1));
    pts->InsertPoint(1, this->Points->GetPoint(1));
  
    return 1;
  }
  
  //------------------------------------------------------------------------------
  // Given parametric coordinates compute inverse Jacobian transformation
  // matrix. Returns 9 elements of 3x3 inverse Jacobian plus interpolation
  // function derivatives.
  void vtkTriQuadraticHexahedron::JacobianInverse(
    const double pcoords[3], double** inverse, double derivs[81])
  {
    int i, j;
    double *m[3], m0[3], m1[3], m2[3];
    double x[3];
  
    // compute interpolation function derivatives
    this->InterpolationDerivs(pcoords, derivs);
  
    // create Jacobian matrix
    m[0] = m0;
    m[1] = m1;
    m[2] = m2;
    for (i = 0; i < 3; i++) // initialize matrix
    {
      m0[i] = m1[i] = m2[i] = 0.0;
    }
  
    for (j = 0; j < 27; j++)
    {
      this->Points->GetPoint(j, x);
      for (i = 0; i < 3; i++)
      {
        m0[i] += x[i] * derivs[j];
        m1[i] += x[i] * derivs[27 + j];
        m2[i] += x[i] * derivs[54 + j];
      }
    }
  
    // now find the inverse
    if (vtkMath::InvertMatrix(m, inverse, 3) == 0)
    {
      vtkErrorMacro(<< "Jacobian inverse not found");
      return;
    }
  }
  
  //------------------------------------------------------------------------------
  void vtkTriQuadraticHexahedron::Derivatives(
    int vtkNotUsed(subId), const double pcoords[3], const double* values, int dim, double* derivs)
  {
    double *jI[3], j0[3], j1[3], j2[3];
    double functionDerivs[81], sum[3];
    int i, j, k;
  
    // compute inverse Jacobian and interpolation function derivatives
    jI[0] = j0;
    jI[1] = j1;
    jI[2] = j2;
    this->JacobianInverse(pcoords, jI, functionDerivs);
  
    // now compute derivates of values provided
    for (k = 0; k < dim; k++) // loop over values per vertex
    {
      sum[0] = sum[1] = sum[2] = 0.0;
      for (i = 0; i < 27; i++) // loop over interp. function derivatives
      {
        sum[0] += functionDerivs[i] * values[dim * i + k];
        sum[1] += functionDerivs[27 + i] * values[dim * i + k];
        sum[2] += functionDerivs[54 + i] * values[dim * i + k];
      }
      for (j = 0; j < 3; j++) // loop over derivative directions
      {
        derivs[3 * k + j] = sum[0] * jI[j][0] + sum[1] * jI[j][1] + sum[2] * jI[j][2];
      }
    }
  }
  
  //------------------------------------------------------------------------------
  // Compute interpolation functions for the 27 nodes.
  void vtkTriQuadraticHexahedron::InterpolationFunctions(const double pcoords[3], double weights[27])
  {
    // VTK needs parametric coordinates to be between (0,1). Isoparametric
    // shape functions are formulated between (-1,1). Here we do a
    // coordinate system conversion from (0,1) to (-1,1).
    double r = 2.0 * (pcoords[0] - 0.5);
    double s = 2.0 * (pcoords[1] - 0.5);
    double t = 2.0 * (pcoords[2] - 0.5);
  
    double g1r = -0.5 * r * (1 - r);
    double g1s = -0.5 * s * (1 - s);
    double g1t = -0.5 * t * (1 - t);
  
    double g2r = (1 + r) * (1 - r);
    double g2s = (1 + s) * (1 - s);
    double g2t = (1 + t) * (1 - t);
  
    double g3r = 0.5 * r * (1 + r);
    double g3s = 0.5 * s * (1 + s);
    double g3t = 0.5 * t * (1 + t);
  
    // The eight corner points
    weights[0] = g1r * g1s * g1t;
    weights[1] = g3r * g1s * g1t;
    weights[2] = g3r * g3s * g1t;
    weights[3] = g1r * g3s * g1t;
    weights[4] = g1r * g1s * g3t;
    weights[5] = g3r * g1s * g3t;
    weights[6] = g3r * g3s * g3t;
    weights[7] = g1r * g3s * g3t;
  
    // The mid-edge nodes
    weights[8] = g2r * g1s * g1t;
    weights[9] = g3r * g2s * g1t;
    weights[10] = g2r * g3s * g1t;
    weights[11] = g1r * g2s * g1t;
    weights[12] = g2r * g1s * g3t;
    weights[13] = g3r * g2s * g3t;
    weights[14] = g2r * g3s * g3t;
    weights[15] = g1r * g2s * g3t;
    weights[16] = g1r * g1s * g2t;
    weights[17] = g3r * g1s * g2t;
    weights[18] = g3r * g3s * g2t;
    weights[19] = g1r * g3s * g2t;
  
    // face center nodes
    weights[22] = g2r * g1s * g2t;
    weights[21] = g3r * g2s * g2t;
    weights[23] = g2r * g3s * g2t;
    weights[20] = g1r * g2s * g2t;
    weights[24] = g2r * g2s * g1t;
    weights[25] = g2r * g2s * g3t;
  
    // Cell center node
    weights[26] = g2r * g2s * g2t;
  }
  
  //------------------------------------------------------------------------------
  // Derivatives in parametric space.
  void vtkTriQuadraticHexahedron::InterpolationDerivs(const double pcoords[3], double derivs[81])
  {
    // VTK needs parametric coordinates to be between (0,1). Isoparametric
    // shape functions are formulated between (-1,1). Here we do a
    // coordinate system conversion from (0,1) to (-1,1).
    double r = 2.0 * (pcoords[0] - 0.5);
    double s = 2.0 * (pcoords[1] - 0.5);
    double t = 2.0 * (pcoords[2] - 0.5);
  
    double g1r = -0.5 * r * (1 - r);
    double g1s = -0.5 * s * (1 - s);
    double g1t = -0.5 * t * (1 - t);
  
    double g2r = (1 + r) * (1 - r);
    double g2s = (1 + s) * (1 - s);
    double g2t = (1 + t) * (1 - t);
  
    double g3r = 0.5 * r * (1 + r);
    double g3s = 0.5 * s * (1 + s);
    double g3t = 0.5 * t * (1 + t);
  
    double g1r_r = r - 0.5;
    double g1s_s = s - 0.5;
    double g1t_t = t - 0.5;
  
    double g2r_r = -2 * r;
    double g2s_s = -2 * s;
    double g2t_t = -2 * t;
  
    double g3r_r = r + 0.5;
    double g3s_s = s + 0.5;
    double g3t_t = t + 0.5;
  
    // r-derivatives
    derivs[0] = g1r_r * g1s * g1t;
    derivs[1] = g3r_r * g1s * g1t;
    derivs[2] = g3r_r * g3s * g1t;
    derivs[3] = g1r_r * g3s * g1t;
    derivs[4] = g1r_r * g1s * g3t;
    derivs[5] = g3r_r * g1s * g3t;
    derivs[6] = g3r_r * g3s * g3t;
    derivs[7] = g1r_r * g3s * g3t;
    derivs[8] = g2r_r * g1s * g1t;
    derivs[9] = g3r_r * g2s * g1t;
    derivs[10] = g2r_r * g3s * g1t;
    derivs[11] = g1r_r * g2s * g1t;
    derivs[12] = g2r_r * g1s * g3t;
    derivs[13] = g3r_r * g2s * g3t;
    derivs[14] = g2r_r * g3s * g3t;
    derivs[15] = g1r_r * g2s * g3t;
    derivs[16] = g1r_r * g1s * g2t;
    derivs[17] = g3r_r * g1s * g2t;
    derivs[18] = g3r_r * g3s * g2t;
    derivs[19] = g1r_r * g3s * g2t;
    derivs[20] = g1r_r * g2s * g2t;
    derivs[21] = g3r_r * g2s * g2t;
    derivs[22] = g2r_r * g1s * g2t;
    derivs[23] = g2r_r * g3s * g2t;
    derivs[24] = g2r_r * g2s * g1t;
    derivs[25] = g2r_r * g2s * g3t;
    derivs[26] = g2r_r * g2s * g2t;
  
    // s-derivatives
    derivs[27] = g1r * g1s_s * g1t;
    derivs[28] = g3r * g1s_s * g1t;
    derivs[29] = g3r * g3s_s * g1t;
    derivs[30] = g1r * g3s_s * g1t;
    derivs[31] = g1r * g1s_s * g3t;
    derivs[32] = g3r * g1s_s * g3t;
    derivs[33] = g3r * g3s_s * g3t;
    derivs[34] = g1r * g3s_s * g3t;
    derivs[35] = g2r * g1s_s * g1t;
    derivs[36] = g3r * g2s_s * g1t;
    derivs[37] = g2r * g3s_s * g1t;
    derivs[38] = g1r * g2s_s * g1t;
    derivs[39] = g2r * g1s_s * g3t;
    derivs[40] = g3r * g2s_s * g3t;
    derivs[41] = g2r * g3s_s * g3t;
    derivs[42] = g1r * g2s_s * g3t;
    derivs[43] = g1r * g1s_s * g2t;
    derivs[44] = g3r * g1s_s * g2t;
    derivs[45] = g3r * g3s_s * g2t;
    derivs[46] = g1r * g3s_s * g2t;
    derivs[47] = g1r * g2s_s * g2t;
    derivs[48] = g3r * g2s_s * g2t;
    derivs[49] = g2r * g1s_s * g2t;
    derivs[50] = g2r * g3s_s * g2t;
    derivs[51] = g2r * g2s_s * g1t;
    derivs[52] = g2r * g2s_s * g3t;
    derivs[53] = g2r * g2s_s * g2t;
  
    // t-derivatives
    derivs[54] = g1r * g1s * g1t_t;
    derivs[55] = g3r * g1s * g1t_t;
    derivs[56] = g3r * g3s * g1t_t;
    derivs[57] = g1r * g3s * g1t_t;
    derivs[58] = g1r * g1s * g3t_t;
    derivs[59] = g3r * g1s * g3t_t;
    derivs[60] = g3r * g3s * g3t_t;
    derivs[61] = g1r * g3s * g3t_t;
    derivs[62] = g2r * g1s * g1t_t;
    derivs[63] = g3r * g2s * g1t_t;
    derivs[64] = g2r * g3s * g1t_t;
    derivs[65] = g1r * g2s * g1t_t;
    derivs[66] = g2r * g1s * g3t_t;
    derivs[67] = g3r * g2s * g3t_t;
    derivs[68] = g2r * g3s * g3t_t;
    derivs[69] = g1r * g2s * g3t_t;
    derivs[70] = g1r * g1s * g2t_t;
    derivs[71] = g3r * g1s * g2t_t;
    derivs[72] = g3r * g3s * g2t_t;
    derivs[73] = g1r * g3s * g2t_t;
    derivs[74] = g1r * g2s * g2t_t;
    derivs[75] = g3r * g2s * g2t_t;
    derivs[76] = g2r * g1s * g2t_t;
    derivs[77] = g2r * g3s * g2t_t;
    derivs[78] = g2r * g2s * g1t_t;
    derivs[79] = g2r * g2s * g3t_t;
    derivs[80] = g2r * g2s * g2t_t;
  
    // we compute derivatives in in [-1; 1] but we need them in [ 0; 1]
    for (int i = 0; i < 81; i++)
      derivs[i] *= 2;
  }
  
  //------------------------------------------------------------------------------
  static double vtkQHexCellPCoords[81] = {
    0.0, 0.0, 0.0, //
    1.0, 0.0, 0.0, //
    1.0, 1.0, 0.0, //
    0.0, 1.0, 0.0, //
    0.0, 0.0, 1.0, //
    1.0, 0.0, 1.0, //
    1.0, 1.0, 1.0, //
    0.0, 1.0, 1.0, //
    0.5, 0.0, 0.0, //
    1.0, 0.5, 0.0, //
    0.5, 1.0, 0.0, //
    0.0, 0.5, 0.0, //
    0.5, 0.0, 1.0, //
    1.0, 0.5, 1.0, //
    0.5, 1.0, 1.0, //
    0.0, 0.5, 1.0, //
    0.0, 0.0, 0.5, //
    1.0, 0.0, 0.5, //
    1.0, 1.0, 0.5, //
    0.0, 1.0, 0.5, //
    0.0, 0.5, 0.5, // 20
    1.0, 0.5, 0.5, // 21
    0.5, 0.0, 0.5, // 22
    0.5, 1.0, 0.5, // 23
    0.5, 0.5, 0.0, // 24
    0.5, 0.5, 1.0, // 25
    0.5, 0.5, 0.5  // 26
  };
  
  double* vtkTriQuadraticHexahedron::GetParametricCoords()
  {
    return vtkQHexCellPCoords;
  }
  
  //------------------------------------------------------------------------------
  void vtkTriQuadraticHexahedron::PrintSelf(ostream& os, vtkIndent indent)
  {
    this->Superclass::PrintSelf(os, indent);
  
    os << indent << "Edge:\n";
    this->Edge->PrintSelf(os, indent.GetNextIndent());
    os << indent << "Face:\n";
    this->Face->PrintSelf(os, indent.GetNextIndent());
    os << indent << "Hex:\n";
    this->Hex->PrintSelf(os, indent.GetNextIndent());
    os << indent << "Scalars:\n";
    this->Scalars->PrintSelf(os, indent.GetNextIndent());
  }
  