// Gmsh - Copyright (C) 1997-2015 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.

#include "pointsGenerators.h"
#include "GmshDefines.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MTetrahedron.h"
#include "MHexahedron.h"
#include "MPrism.h"
#include "MPyramid.h"


// Points Generators

void gmshGeneratePoints(FuncSpaceData data, fullMatrix<double> &points)
{
  switch (data.elementType()) {
    case TYPE_PNT :
      points = gmshGeneratePointsLine(0);
      return;
    case TYPE_LIN :
      points = gmshGeneratePointsLine(data.spaceOrder());
      return;
    case TYPE_TRI :
      points = gmshGeneratePointsTriangle(data.spaceOrder(),
                                          data.spaceIsSerendipity());
      return;
    case TYPE_QUA :
      points = gmshGeneratePointsQuadrangle(data.spaceOrder(),
                                            data.spaceIsSerendipity());
      return;
    case TYPE_TET :
      points = gmshGeneratePointsTetrahedron(data.spaceOrder(),
                                             data.spaceIsSerendipity());
      return;
    case TYPE_PRI :
      points = gmshGeneratePointsPrism(data.spaceOrder(),
                                       data.spaceIsSerendipity());
      return;
    case TYPE_HEX :
      points = gmshGeneratePointsHexahedron(data.spaceOrder(),
                                            data.spaceIsSerendipity());
      return;
    case TYPE_PYR :
      points = gmshGeneratePointsPyramidGeneral(data.isPyramidalSpace(),
                                                data.nij(),
                                                data.nk(),
                                                data.spaceIsSerendipity());
      return;
    default :
      Msg::Error("Unknown element type %d (tag %d) for points generation",
          data.elementType(), data.elementTag());
      return;
  }
}

fullMatrix<double> gmshGeneratePointsLine(int order)
{
  fullMatrix<double> points = gmshGenerateMonomialsLine(order);
  if (order == 0) return points;

  points.scale(2./order);
  points.add(-1.);
  return points;
}

fullMatrix<double> gmshGeneratePointsTriangle(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsTriangle(order, serendip);
  if (order == 0) return points;

  points.scale(1./order);
  return points;
}

fullMatrix<double> gmshGeneratePointsQuadrangle(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsQuadrangle(order, serendip);

  if (order == 0) return points;

  points.scale(2./order);
  points.add(-1.);
  return points;
}

fullMatrix<double> gmshGeneratePointsTetrahedron(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsTetrahedron(order, serendip);

  if (order == 0) return points;

  points.scale(1./order);
  return points;
}

fullMatrix<double> gmshGeneratePointsHexahedron(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsHexahedron(order, serendip);

  if (order == 0) return points;

  points.scale(2./order);
  points.add(-1.);
  return points;
}

fullMatrix<double> gmshGeneratePointsPrism(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsPrism(order, serendip);

  if (order == 0) return points;

  fullMatrix<double> tmp;
  tmp.setAsProxy(points, 0, 2);
  tmp.scale(1./order);

  tmp.setAsProxy(points, 2, 1);
  tmp.scale(2./order);
  tmp.add(-1.);

  return points;
}

fullMatrix<double> gmshGeneratePointsPyramid(int order, bool serendip)
{
  fullMatrix<double> points = gmshGenerateMonomialsPyramid(order, serendip);

  if (order == 0) return points;

  for (int i = 0; i < points.size1(); ++i) {
    points(i, 2) = 1 - points(i, 2) / order;
    const double duv = -1. + points(i, 2);
    points(i, 0) = duv + points(i, 0) * 2. / order;
    points(i, 1) = duv + points(i, 1) * 2. / order;
  }
  return points;
}

fullMatrix<double> gmshGeneratePointsPyramidGeneral(bool pyr, int nij, int nk, bool forSerendipPoints)
{
  fullMatrix<double> points =
      gmshGenerateMonomialsPyramidGeneral(pyr, nij, nk, forSerendipPoints);

  if (points.size1() == 1) return points;

  const int div = pyr ? nk+nij : std::max(nij, nk);
  for (int i = 0; i < points.size1(); ++i) {
    points(i, 2) = (nk - points(i, 2)) / div;
    const double scale = 1. - points(i, 2);
    points(i, 0) = scale * (-1 + points(i, 0) * 2. / div);
    points(i, 1) = scale * (-1 + points(i, 1) * 2. / div);
  }
  return points;
}

// Monomials Generators

void gmshGenerateMonomials(FuncSpaceData data, fullMatrix<double> &monomials)
{
  switch (data.elementType()) {
    case TYPE_PNT :
      monomials = gmshGenerateMonomialsLine(0);
      return;
    case TYPE_LIN :
      monomials = gmshGenerateMonomialsLine(data.spaceOrder());
      return;
    case TYPE_TRI :
      monomials = gmshGenerateMonomialsTriangle(data.spaceOrder(),
                                                data.spaceIsSerendipity());
      return;
    case TYPE_QUA :
      monomials = gmshGenerateMonomialsQuadrangle(data.spaceOrder(),
                                                  data.spaceIsSerendipity());
      return;
    case TYPE_TET :
      monomials = gmshGenerateMonomialsTetrahedron(data.spaceOrder(),
                                                   data.spaceIsSerendipity());
      return;
    case TYPE_PRI :
      monomials = gmshGenerateMonomialsPrism(data.spaceOrder(),
                                             data.spaceIsSerendipity());
      return;
    case TYPE_HEX :
      monomials = gmshGenerateMonomialsHexahedron(data.spaceOrder(),
                                                  data.spaceIsSerendipity());
      return;
    case TYPE_PYR :
      monomials = gmshGenerateMonomialsPyramidGeneral(data.isPyramidalSpace(),
                                                      data.nij(),
                                                      data.nk(),
                                                      data.spaceIsSerendipity());
      return;
    default :
      Msg::Error("Unknown element type %d (tag %d) for monomials generation",
          data.elementType(), data.elementTag());
      return;
  }
}

fullMatrix<double> gmshGenerateMonomialsLine(int order, bool serendip)
{
  fullMatrix<double> monomials(order + 1, 1);
  monomials(0,0) = 0;
  if (order > 0) {
    monomials(1, 0) = order;
    for (int i = 2; i < order + 1; i++) monomials(i, 0) = i-1;
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsTriangle(int order, bool serendip)
{
  int nbMonomials = serendip ? 3 * order : (order + 1) * (order + 2) / 2;
  if (serendip && !order) nbMonomials = 1;
  fullMatrix<double> monomials(nbMonomials, 2);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;

    monomials(2, 0) = 0;
    monomials(2, 1) = order;

    if (order > 1) {
      int index = 3;
      for (int iedge = 0; iedge < 3; ++iedge) {
        int i0 = MTriangle::edges_tri(iedge, 0);
        int i1 = MTriangle::edges_tri(iedge, 1);

        int u_0 = (monomials(i1,0)-monomials(i0,0)) / order;
        int u_1 = (monomials(i1,1)-monomials(i0,1)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + u_0 * i;
          monomials(index, 1) = monomials(i0, 1) + u_1 * i;
        }
      }
      if (!serendip && order > 2) {
        fullMatrix<double> inner = gmshGenerateMonomialsTriangle(order-3);
        inner.add(1);
        monomials.copy(inner, 0, nbMonomials - index, 0, 2, index, 0);
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsQuadrangle(int order, bool forSerendipPoints)
{
  int nbMonomials = forSerendipPoints ? order*4 : (order+1)*(order+1);
  if (forSerendipPoints && !order) nbMonomials = 1;
  fullMatrix<double> monomials(nbMonomials, 2);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;

    monomials(2, 0) = order;
    monomials(2, 1) = order;

    monomials(3, 0) = 0;
    monomials(3, 1) = order;

    if (order > 1) {
      int index = 4;
      for (int iedge = 0; iedge < 4; ++iedge) {
        int i0 = MQuadrangle::edges_quad(iedge, 0);
        int i1 = MQuadrangle::edges_quad(iedge, 1);

        int u_0 = (monomials(i1,0)-monomials(i0,0)) / order;
        int u_1 = (monomials(i1,1)-monomials(i0,1)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + u_0 * i;
          monomials(index, 1) = monomials(i0, 1) + u_1 * i;
        }
      }

      if (!forSerendipPoints) {
        fullMatrix<double> inner = gmshGenerateMonomialsQuadrangle(order-2);
        inner.add(1);
        monomials.copy(inner, 0, nbMonomials - index, 0, 2, index, 0);
      }
    }
  }
  return monomials;
}

/*
00 10 20 30 40 ...
01 11 21 31 41 ...
02 12
03 13
04 14
...
*/

fullMatrix<double> gmshGenerateMonomialsQuadSerendipity(int order)
{
  int nbMonomials = order ? order*4 : 1;
  fullMatrix<double> monomials(nbMonomials, 2);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;

  if (order > 0) {
    monomials(1, 0) = 1;
    monomials(1, 1) = 0;

    monomials(2, 0) = 1;
    monomials(2, 1) = 1;

    monomials(3, 0) = 0;
    monomials(3, 1) = 1;

    if (order > 1) {
      int index = 3;
      for (int p = 2; p <= order; ++p) {
        monomials(++index, 0) = p;
        monomials(  index, 1) = 0;

        monomials(++index, 0) = p;
        monomials(  index, 1) = 1;

        monomials(++index, 0) = 1;
        monomials(  index, 1) = p;

        monomials(++index, 0) = 0;
        monomials(  index, 1) = p;
      }
    }
  }
  return monomials;
}

//KH : caveat : node coordinates are not yet coherent with node numbering associated
//              to numbering of principal vertices of face !!!!
fullMatrix<double> gmshGenerateMonomialsTetrahedron(int order, bool serendip)
{
  int nbMonomials = serendip ? 4 + (order - 1)*6 : (order + 1)*(order + 2)*(order + 3)/6;
  if (serendip && !order) nbMonomials = 1;
  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = 0;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;
    monomials(1, 2) = 0;

    monomials(2, 0) = 0;
    monomials(2, 1) = order;
    monomials(2, 2) = 0;

    monomials(3, 0) = 0;
    monomials(3, 1) = 0;
    monomials(3, 2) = order;

    // the template has been defined in table edges_tetra and faces_tetra (MElement.h)

    if (order > 1) {
      int index = 4;
      for (int iedge = 0; iedge < 6; ++iedge) {
        int i0 = MTetrahedron::edges_tetra(iedge, 0);
        int i1 = MTetrahedron::edges_tetra(iedge, 1);

        int u[3];
        u[0] = (monomials(i1,0)-monomials(i0,0)) / order;
        u[1] = (monomials(i1,1)-monomials(i0,1)) / order;
        u[2] = (monomials(i1,2)-monomials(i0,2)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + u[0] * i;
          monomials(index, 1) = monomials(i0, 1) + u[1] * i;
          monomials(index, 2) = monomials(i0, 2) + u[2] * i;
        }
      }

      if (!serendip && order > 2) {
        fullMatrix<double> dudv = gmshGenerateMonomialsTriangle(order - 3);
        dudv.add(1);

        for (int iface = 0; iface < 4; ++iface) {
          int i0 = MTetrahedron::faces_tetra(iface, 0);
          int i1 = MTetrahedron::faces_tetra(iface, 1);
          int i2 = MTetrahedron::faces_tetra(iface, 2);

          int u[3];
          u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
          u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
          u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
          int v[3];
          v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
          v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
          v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;

          for (int i = 0; i < dudv.size1(); ++i, ++index) {
            monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
            monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
            monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
          }
        }

        if (order > 3) {
          fullMatrix<double> inner = gmshGenerateMonomialsTetrahedron(order - 4);
          inner.add(1);
          monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
        }
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsPrism(int order, bool forSerendipPoints)
{
  int nbMonomials = forSerendipPoints ? 6 + (order-1)*9 :
                                        (order + 1)*(order + 1)*(order + 2)/2;
  if (forSerendipPoints && !order) nbMonomials = 1;
  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = 0;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;
    monomials(1, 2) = 0;

    monomials(2, 0) = 0;
    monomials(2, 1) = order;
    monomials(2, 2) = 0;

    monomials(3, 0) = 0;
    monomials(3, 1) = 0;
    monomials(3, 2) = order;

    monomials(4, 0) = order;
    monomials(4, 1) = 0;
    monomials(4, 2) = order;

    monomials(5, 0) = 0;
    monomials(5, 1) = order;
    monomials(5, 2) = order;

    if (order > 1) {
      int index = 6;
      for (int iedge = 0; iedge < 9; ++iedge) {
        int i0 = MPrism::edges_prism(iedge, 0);
        int i1 = MPrism::edges_prism(iedge, 1);

        int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
        int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
        int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + i * u_1;
          monomials(index, 1) = monomials(i0, 1) + i * u_2;
          monomials(index, 2) = monomials(i0, 2) + i * u_3;
        }
      }

      if (!forSerendipPoints) {
        fullMatrix<double> dudvQ = gmshGenerateMonomialsQuadrangle(order - 2);
        dudvQ.add(1);

        fullMatrix<double> dudvT;
        if (order > 2) {
          dudvT = gmshGenerateMonomialsTriangle(order - 3);
          dudvT.add(1);
        }

        for (int iface = 0; iface < 5; ++iface) {
          int i0, i1, i2;
          i0 = MPrism::faces_prism(iface, 0);
          i1 = MPrism::faces_prism(iface, 1);
          fullMatrix<double> dudv;
          if (MPrism::faces_prism(iface, 3) != -1) {
            i2 = MPrism::faces_prism(iface, 3);
            dudv.setAsProxy(dudvQ);
          }
          else if (order > 2) {
            i2 = MPrism::faces_prism(iface, 2);
            dudv.setAsProxy(dudvT);
          }
          else continue;

          int u[3];
          u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
          u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
          u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
          int v[3];
          v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
          v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
          v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;

          for (int i = 0; i < dudv.size1(); ++i, ++index) {
            monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
            monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
            monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
          }
        }

        if (order > 2) {
          fullMatrix<double> triMonomials  = gmshGenerateMonomialsTriangle(order - 3);
          fullMatrix<double> lineMonomials = gmshGenerateMonomialsLine(order - 2);

          for (int i = 0; i < triMonomials.size1(); ++i) {
            for (int j = 0; j < lineMonomials.size1(); ++j, ++index) {
              monomials(index, 0) = 1 + triMonomials(i, 0);
              monomials(index, 1) = 1 + triMonomials(i, 1);
              monomials(index, 2) = 1 + lineMonomials(j, 0);
            }
          }
        }
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsPrismSerendipity(int order)
{
  int nbMonomials = order ? 6 + (order-1) * 9 : 1;
  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = 0;

  if (order > 0) {
    monomials(1, 0) = 1;
    monomials(1, 1) = 0;
    monomials(1, 2) = 0;

    monomials(2, 0) = 0;
    monomials(2, 1) = 1;
    monomials(2, 2) = 0;

    monomials(3, 0) = 0;
    monomials(3, 1) = 0;
    monomials(3, 2) = 1;

    monomials(4, 0) = 1;
    monomials(4, 1) = 0;
    monomials(4, 2) = 1;

    monomials(5, 0) = 0;
    monomials(5, 1) = 1;
    monomials(5, 2) = 1;

    if (order > 1) {
      const int ind[7][3] = {
        {2, 0, 0},
        {2, 0, 1},

        {0, 2, 0},
        {0, 2, 1},

        {0, 0, 2},
        {1, 0, 2},
        {0, 1, 2}
      };
      int val[3] = {0, 1, -1};
      int index = 5;
      for (int p = 2; p <= order; ++p) {
        val[2] = p;
        for (int i = 0; i < 7; ++i) {
          monomials(++index, 0) = val[ind[i][0]];
          monomials(  index, 1) = val[ind[i][1]];
          monomials(  index, 2) = val[ind[i][2]];
        }
      }

      int val0 = 1;
      int val1 = order - 1;
      for (int p = 2; p <= order; ++p) {
        monomials(++index, 0) = val0;
        monomials(  index, 1) = val1;
        monomials(  index, 2) = 0;

        monomials(++index, 0) = val0;
        monomials(  index, 1) = val1;
        monomials(  index, 2) = 1;

        ++val0;
        --val1;
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsHexahedron(int order, bool forSerendipPoints)
{
  int nbMonomials = forSerendipPoints ? 8 + (order-1)*12 :
                                        (order+1)*(order+1)*(order+1);
  if (forSerendipPoints && !order) nbMonomials = 1;
  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = 0;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;
    monomials(1, 2) = 0;

    monomials(2, 0) = order;
    monomials(2, 1) = order;
    monomials(2, 2) = 0;

    monomials(3, 0) = 0;
    monomials(3, 1) = order;
    monomials(3, 2) = 0;

    monomials(4, 0) = 0;
    monomials(4, 1) = 0;
    monomials(4, 2) = order;

    monomials(5, 0) = order;
    monomials(5, 1) = 0;
    monomials(5, 2) = order;

    monomials(6, 0) = order;
    monomials(6, 1) = order;
    monomials(6, 2) = order;

    monomials(7, 0) = 0;
    monomials(7, 1) = order;
    monomials(7, 2) = order;

    if (order > 1) {
      int index = 8;
      for (int iedge = 0; iedge < 12; ++iedge) {
        int i0 = MHexahedron::edges_hexa(iedge, 0);
        int i1 = MHexahedron::edges_hexa(iedge, 1);

        int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
        int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
        int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + i * u_1;
          monomials(index, 1) = monomials(i0, 1) + i * u_2;
          monomials(index, 2) = monomials(i0, 2) + i * u_3;
        }
      }

      if (!forSerendipPoints) {
        fullMatrix<double> dudv = gmshGenerateMonomialsQuadrangle(order - 2);
        dudv.add(1);

        for (int iface = 0; iface < 6; ++iface) {
          int i0 = MHexahedron::faces_hexa(iface, 0);
          int i1 = MHexahedron::faces_hexa(iface, 1);
          int i3 = MHexahedron::faces_hexa(iface, 3);

          int u[3];
          u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
          u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
          u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
          int v[3];
          v[0] = (monomials(i3, 0) - monomials(i0, 0)) / order;
          v[1] = (monomials(i3, 1) - monomials(i0, 1)) / order;
          v[2] = (monomials(i3, 2) - monomials(i0, 2)) / order;

          for (int i = 0; i < dudv.size1(); ++i, ++index) {
            monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
            monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
            monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
          }
        }

        fullMatrix<double> inner = gmshGenerateMonomialsHexahedron(order - 2);
        inner.add(1);
        monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsHexaSerendipity(int order)
{
  int nbMonomials = order ? 8 + (order-1) * 12 : 1;
  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = 0;

  if (order > 0) {
    monomials(1, 0) = 1;
    monomials(1, 1) = 0;
    monomials(1, 2) = 0;

    monomials(2, 0) = 1;
    monomials(2, 1) = 1;
    monomials(2, 2) = 0;

    monomials(3, 0) = 0;
    monomials(3, 1) = 1;
    monomials(3, 2) = 0;

    monomials(4, 0) = 0;
    monomials(4, 1) = 0;
    monomials(4, 2) = 1;

    monomials(5, 0) = 1;
    monomials(5, 1) = 0;
    monomials(5, 2) = 1;

    monomials(6, 0) = 1;
    monomials(6, 1) = 1;
    monomials(6, 2) = 1;

    monomials(7, 0) = 0;
    monomials(7, 1) = 1;
    monomials(7, 2) = 1;

    if (order > 1) {
      const int ind[12][3] = {
        {2, 0, 0},
        {2, 0, 1},
        {2, 1, 1},
        {2, 1, 0},

        {0, 2, 0},
        {0, 2, 1},
        {1, 2, 1},
        {1, 2, 0},

        {0, 0, 2},
        {0, 1, 2},
        {1, 1, 2},
        {1, 0, 2}
      };
      int val[3] = {0, 1, -1};
      int index = 7;
      for (int p = 2; p <= order; ++p) {
        val[2] = p;
        for (int i = 0; i < 12; ++i) {
          monomials(++index, 0) = val[ind[i][0]];
          monomials(  index, 1) = val[ind[i][1]];
          monomials(  index, 2) = val[ind[i][2]];
        }
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsPyramid(int order, bool forSerendipPoints)
{
  int nbMonomials = forSerendipPoints ? 5 + (order-1)*8 :
                                        (order+1)*((order+1)+1)*(2*(order+1)+1)/6;
  if (forSerendipPoints && !order) nbMonomials = 1;

  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = order;

  if (order > 0) {
    monomials(1, 0) = order;
    monomials(1, 1) = 0;
    monomials(1, 2) = order;

    monomials(2, 0) = order;
    monomials(2, 1) = order;
    monomials(2, 2) = order;

    monomials(3, 0) = 0;
    monomials(3, 1) = order;
    monomials(3, 2) = order;

    monomials(4, 0) = 0;
    monomials(4, 1) = 0;
    monomials(4, 2) = 0;

    if (order > 1) {
      int index = 5;
      for (int iedge = 0; iedge < 8; ++iedge) {
        int i0 = MPyramid::edges_pyramid(iedge, 0);
        int i1 = MPyramid::edges_pyramid(iedge, 1);

        int u_1 = (monomials(i1,0)-monomials(i0,0)) / order;
        int u_2 = (monomials(i1,1)-monomials(i0,1)) / order;
        int u_3 = (monomials(i1,2)-monomials(i0,2)) / order;

        for (int i = 1; i < order; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + i * u_1;
          monomials(index, 1) = monomials(i0, 1) + i * u_2;
          monomials(index, 2) = monomials(i0, 2) + i * u_3;
        }
      }

      if (!forSerendipPoints) {
        fullMatrix<double> dudvQ = gmshGenerateMonomialsQuadrangle(order - 2);
        dudvQ.add(1);

        fullMatrix<double> dudvT;
        if (order > 2) {
          dudvT = gmshGenerateMonomialsTriangle(order - 3);
          dudvT.add(1);
        }

        for (int iface = 0; iface < 5; ++iface) {
          int i0, i1, i2;
          i0 = MPyramid::faces_pyramid(iface, 0);
          i1 = MPyramid::faces_pyramid(iface, 1);
          fullMatrix<double> dudv;
          if (MPyramid::faces_pyramid(iface, 3) != -1) {
            i2 = MPyramid::faces_pyramid(iface, 3);
            dudv.setAsProxy(dudvQ);
          }
          else if (order > 2) {
            i2 = MPyramid::faces_pyramid(iface, 2);
            dudv.setAsProxy(dudvT);
          }
          else continue;

          int u[3];
          u[0] = (monomials(i1, 0) - monomials(i0, 0)) / order;
          u[1] = (monomials(i1, 1) - monomials(i0, 1)) / order;
          u[2] = (monomials(i1, 2) - monomials(i0, 2)) / order;
          int v[3];
          v[0] = (monomials(i2, 0) - monomials(i0, 0)) / order;
          v[1] = (monomials(i2, 1) - monomials(i0, 1)) / order;
          v[2] = (monomials(i2, 2) - monomials(i0, 2)) / order;

          for (int i = 0; i < dudv.size1(); ++i, ++index) {
            monomials(index, 0) = monomials(i0, 0) + u[0] * dudv(i, 0) + v[0] * dudv(i, 1);
            monomials(index, 1) = monomials(i0, 1) + u[1] * dudv(i, 0) + v[1] * dudv(i, 1);
            monomials(index, 2) = monomials(i0, 2) + u[2] * dudv(i, 0) + v[2] * dudv(i, 1);
          }
        }

        if (order > 2) {
          fullMatrix<double> inner = gmshGenerateMonomialsPyramid(order - 3);
          fullMatrix<double> prox;
          prox.setAsProxy(inner, 0, 2);
          prox.add(1);
          prox.setAsProxy(inner, 2, 1);
          prox.add(2);
          monomials.copy(inner, 0, nbMonomials - index, 0, 3, index, 0);
        }
      }
    }
  }
  return monomials;
}

fullMatrix<double> gmshGenerateMonomialsPyramidGeneral(
    bool pyr, int nij, int nk, bool forSerendipPoints)
{
  if (nij < 0 || nk < 0) {
    Msg::Fatal("Wrong arguments for pyramid's monomials generation ! (%d & %d)", nij, nk);
  }
  if (!pyr && nk > 0 && nij == 0) {
    Msg::Error("Wrong argument association for pyramid's monomials generation ! Setting nij to 1");
    nij = 1;
  }

  // If monomials for pyramidal space, generate them in gmsh convention.
  if (forSerendipPoints || (pyr && nij == 0))
    return gmshGenerateMonomialsPyramid(nk, forSerendipPoints);

  // Otherwise, just put corners at first places,
  // order of others having no importance.

  int nbMonomials;
  if (pyr) {
    nbMonomials = 0;
    for (int k = 0; k <= nk; ++k) {
      nbMonomials += (k+nij+1) * (k+nij+1);
    }
  }
  else nbMonomials = (nij+1) * (nij+1) * (nk+1);

  fullMatrix<double> monomials(nbMonomials, 3);

  monomials(0, 0) = 0;
  monomials(0, 1) = 0;
  monomials(0, 2) = nk;

  if (nk == 0 && nij == 0) return monomials;

  // Here, nij > 0
  int nijBase = pyr ? nk+nij : nij;

  // Corners
  monomials(1, 0) = nijBase;
  monomials(1, 1) = 0;
  monomials(1, 2) = nk;

  monomials(2, 0) = nijBase;
  monomials(2, 1) = nijBase;
  monomials(2, 2) = nk;

  monomials(3, 0) = 0;
  monomials(3, 1) = nijBase;
  monomials(3, 2) = nk;

  int index = 4;

  if (nk > 0) {
    monomials(4, 0) = 0;
    monomials(4, 1) = 0;
    monomials(4, 2) = 0;

    monomials(5, 0) = nij;
    monomials(5, 1) = 0;
    monomials(5, 2) = 0;

    monomials(6, 0) = nij;
    monomials(6, 1) = nij;
    monomials(6, 2) = 0;

    monomials(7, 0) = 0;
    monomials(7, 1) = nij;
    monomials(7, 2) = 0;

    index = 8;
  }

  // Base
  if (nijBase > 1) {
    for (int iedge = 0; iedge < 4; ++iedge) {
      int i0 = iedge;
      int i1 = (iedge+1) % 4;

      int u0 = (monomials(i1,0)-monomials(i0,0)) / nijBase;
      int u1 = (monomials(i1,1)-monomials(i0,1)) / nijBase;

      for (int i = 1; i < nijBase; ++i, ++index) {
        monomials(index, 0) = monomials(i0, 0) + i * u0;
        monomials(index, 1) = monomials(i0, 1) + i * u1;
        monomials(index, 2) = nk;
      }
    }

    for (int i = 1; i < nijBase; ++i) {
      for (int j = 1; j < nijBase; ++j, ++index) {
        monomials(index, 0) = i;
        monomials(index, 1) = j;
        monomials(index, 2) = nk;
      }
    }
  }

  // Above base
  if (nk > 0) {
    // Top
    if (nij > 1) {
      for (int iedge = 0; iedge < 4; ++iedge) {
        int i0 = 4 + iedge;
        int i1 = 4 + (iedge+1)%4;

        int u0 = (monomials(i1,0)-monomials(i0,0)) / nijBase;
        int u1 = (monomials(i1,1)-monomials(i0,1)) / nijBase;

        for (int i = 1; i < nijBase; ++i, ++index) {
          monomials(index, 0) = monomials(i0, 0) + i * u0;
          monomials(index, 1) = monomials(i0, 1) + i * u1;
          monomials(index, 2) = 0;
        }
      }

      for (int i = 1; i < nijBase; ++i) {
        for (int j = 1; j < nijBase; ++j, ++index) {
          monomials(index, 0) = i;
          monomials(index, 1) = j;
          monomials(index, 2) = 0;
        }
      }
    }

    // Between bottom & top
    for (int k = nk-1; k > 0; --k) {
      int currentnij = pyr ? k+nij : nij;
      for (int i = 0; i <= currentnij; ++i) {
        for (int j = 0; j <= currentnij; ++j, ++index) {
          monomials(index, 0) = i;
          monomials(index, 1) = j;
          monomials(index, 2) = k;
        }
      }
    }
  }

  return monomials;
}

