MElement.cpp

#if defined(HAVE_GMSH_EMBEDDED)
  return 0.;
#else
  double vol;
  return qmTet(this, QMTET_3, &vol);
#endif
}

double MTetrahedron::getVolume()
{
  double mat[3][3];
  getMat(mat);
  return det3x3(mat) / 6.;
}

void MTetrahedron::xyz2uvw(double xyz[3], double uvw[3])
{
  double mat[3][3], b[3], det;
  getMat(mat);
  b[0] = xyz[0] - getVertex(0)->x();
  b[1] = xyz[1] - getVertex(0)->y();
  b[2] = xyz[2] - getVertex(0)->z();
  sys3x3(mat, b, uvw, &det);
}

const gmshFunctionSpace* MTetrahedron::getFunctionSpace(int o) const
{
  int order = (o == -1) ? getPolynomialOrder() : o;

  int nv = getNumVolumeVertices();
  
  if ((nv == 0) && (o == -1)) {
    switch (order) {
    case 1: return &gmshFunctionSpaces::find(MSH_TET_4);
    case 2: return &gmshFunctionSpaces::find(MSH_TET_10);
    case 3: return &gmshFunctionSpaces::find(MSH_TET_20);
    case 4: return &gmshFunctionSpaces::find(MSH_TET_34);
    case 5: return &gmshFunctionSpaces::find(MSH_TET_52);
    default: Msg::Error("Order %d tetrahedron function space not implemented", order);
    }
  }
  else { 
    switch (order) {
    case 1: return &gmshFunctionSpaces::find(MSH_TET_4);
    case 2: return &gmshFunctionSpaces::find(MSH_TET_10);
    case 3: return &gmshFunctionSpaces::find(MSH_TET_20);
    case 4: return &gmshFunctionSpaces::find(MSH_TET_35);
    case 5: return &gmshFunctionSpaces::find(MSH_TET_56);
    default: Msg::Error("Order %d tetrahedron function space not implemented", order);
    }
  }
  return 0;
}

int MTetrahedron10::getNumEdgesRep(){ return 6 * CTX.mesh.num_sub_edges; }
int MTetrahedronN::getNumEdgesRep(){ return 6 * CTX.mesh.num_sub_edges; }

static void _myGetEdgeRep(MTetrahedron *tet, int num, double *x, double *y, double *z,
                          SVector3 *n, int numSubEdges)
{
  static double pp[4][3] = {{0,0,0},{1,0,0},{0,1,0},{0,0,1}};
  static int ed [6][2] = {{0,1},{0,2},{0,3},{1,2},{1,3},{2,3}};
  int iEdge = num / numSubEdges;
  int iSubEdge = num % numSubEdges;  

  int iVertex1 = ed [iEdge][0];
  int iVertex2 = ed [iEdge][1];
  double t1 = (double) iSubEdge / (double) numSubEdges;
  double u1 = pp[iVertex1][0] * (1.-t1) + pp[iVertex2][0] * t1;
  double v1 = pp[iVertex1][1] * (1.-t1) + pp[iVertex2][1] * t1;
  double w1 = pp[iVertex1][2] * (1.-t1) + pp[iVertex2][2] * t1;

  double t2 = (double) (iSubEdge+1) / (double) numSubEdges;
  double u2 = pp[iVertex1][0] * (1.-t2) + pp[iVertex2][0] * t2;
  double v2 = pp[iVertex1][1] * (1.-t2) + pp[iVertex2][1] * t2;
  double w2 = pp[iVertex1][2] * (1.-t2) + pp[iVertex2][2] * t2;

  SPoint3 pnt1, pnt2;
  tet->pnt(u1,v1,w1,pnt1);
  tet->pnt(u2,v2,w2,pnt2);
  x[0] = pnt1.x(); x[1] = pnt2.x(); 
  y[0] = pnt1.y(); y[1] = pnt2.y();
  z[0] = pnt1.z(); z[1] = pnt2.z();

  // not great, but better than nothing
  static const int f[6] = {0, 0, 0, 1, 2, 3};
  n[0] = n[1] = tet->getFace(f[iEdge]).normal();
}

void MTetrahedron10::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetEdgeRep(this, num, x, y, z, n, CTX.mesh.num_sub_edges);
}

void MTetrahedronN::getEdgeRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetEdgeRep(this, num, x, y, z, n, CTX.mesh.num_sub_edges);
}

int MTetrahedronN::getNumFacesRep(){ return 4 * SQU(CTX.mesh.num_sub_edges); }
int MTetrahedron10::getNumFacesRep(){ return 4 * SQU(CTX.mesh.num_sub_edges); }

static void _myGetFaceRep(MTetrahedron *tet, int num, double *x, double *y, double *z, 
                          SVector3 *n, int numSubEdges)
{
  static double pp[4][3] = {{0,0,0},{1,0,0},{0,1,0},{0,0,1}};
  static int fak [4][3] = {{0,1,2},{0,1,3},{0,2,3},{1,2,3}};
  int iFace    = num / (numSubEdges * numSubEdges);
  int iSubFace = num % (numSubEdges * numSubEdges);  
  
  int iVertex1 = fak[iFace][0];
  int iVertex2 = fak[iFace][1];
  int iVertex3 = fak[iFace][2];

  /*
    0
    0 1
    0 1 2
    0 1 2 3
    0 1 2 3 4
    0 1 2 3 4 5
  */

  // on the first layer, we have (numSubEdges-1) * 2 + 1 triangles
  // on the second layer, we have (numSubEdges-2) * 2 + 1 triangles
  // on the ith layer, we have (numSubEdges-1-i) * 2 + 1 triangles
  int ix = 0, iy = 0;
  int nbt = 0;
  for (int i = 0; i < numSubEdges; i++){
    int nbl = (numSubEdges - i - 1) * 2 + 1;
    nbt += nbl;
    if (nbt > iSubFace){
      iy = i;
      ix = nbl - (nbt - iSubFace);
      break;
    }
  }

  const double d = 1. / numSubEdges;

  SPoint3 pnt1, pnt2, pnt3;
  double J1[2][3], J2[2][3], J3[2][3];
  double u1,v1,u2,v2,u3,v3;
  if (ix % 2 == 0){
    u1 = ix / 2 * d; v1= iy*d;
    u2 = (ix / 2 + 1) * d ; v2 =  iy * d;
    u3 = ix / 2 * d ; v3 =  (iy+1) * d;
  }
  else{
    u1 = (ix / 2 + 1) * d; v1= iy * d;
    u2 = (ix / 2 + 1) * d; v2= (iy + 1) * d;
    u3 = ix / 2 * d ; v3 =  (iy + 1) * d;
  }

  double U1 = pp[iVertex1][0] * (1.-u1-v1) + pp[iVertex2][0] * u1 + pp[iVertex3][0] * v1;
  double U2 = pp[iVertex1][0] * (1.-u2-v2) + pp[iVertex2][0] * u2 + pp[iVertex3][0] * v2;
  double U3 = pp[iVertex1][0] * (1.-u3-v3) + pp[iVertex2][0] * u3 + pp[iVertex3][0] * v3;

  double V1 = pp[iVertex1][1] * (1.-u1-v1) + pp[iVertex2][1] * u1 + pp[iVertex3][1] * v1;
  double V2 = pp[iVertex1][1] * (1.-u2-v2) + pp[iVertex2][1] * u2 + pp[iVertex3][1] * v2;
  double V3 = pp[iVertex1][1] * (1.-u3-v3) + pp[iVertex2][1] * u3 + pp[iVertex3][1] * v3;

  double W1 = pp[iVertex1][2] * (1.-u1-v1) + pp[iVertex2][2] * u1 + pp[iVertex3][2] * v1;
  double W2 = pp[iVertex1][2] * (1.-u2-v2) + pp[iVertex2][2] * u2 + pp[iVertex3][2] * v2;
  double W3 = pp[iVertex1][2] * (1.-u3-v3) + pp[iVertex2][2] * u3 + pp[iVertex3][2] * v3;

  tet->pnt(U1,V1,W1,pnt1);
  tet->pnt(U2,V2,W2,pnt2);
  tet->pnt(U3,V3,W3,pnt3);

  x[0] = pnt1.x(); x[1] = pnt2.x(); x[2] = pnt3.x();
  y[0] = pnt1.y(); y[1] = pnt2.y(); y[2] = pnt3.y();
  z[0] = pnt1.z(); z[1] = pnt2.z(); z[2] = pnt3.z();

  SVector3 d1(x[1]-x[0],y[1]-y[0],z[1]-z[0]);
  SVector3 d2(x[2]-x[0],y[2]-y[0],z[2]-z[0]);
  n[0] = crossprod(d1, d2);
  n[0].normalize();
  n[1] = n[0];
  n[2] = n[0];
}

void MTetrahedronN::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetFaceRep(this, num, x, y, z, n, CTX.mesh.num_sub_edges);
}

void MTetrahedron10::getFaceRep(int num, double *x, double *y, double *z, SVector3 *n)
{
  _myGetFaceRep(this, num, x, y, z, n, CTX.mesh.num_sub_edges);
}

void MTetrahedron::getIntegrationPoints(int pOrder, int *npts, IntPt **pts) const
{
#if !defined(HAVE_GMSH_EMBEDDED)
  *npts = getNGQTetPts(pOrder);
  *pts = getGQTetPts(pOrder);
#endif
}

int MHexahedron::getVolumeSign()
{ 
  double mat[3][3];
  mat[0][0] = _v[1]->x() - _v[0]->x();
  mat[0][1] = _v[3]->x() - _v[0]->x();
  mat[0][2] = _v[4]->x() - _v[0]->x();
  mat[1][0] = _v[1]->y() - _v[0]->y();
  mat[1][1] = _v[3]->y() - _v[0]->y();
  mat[1][2] = _v[4]->y() - _v[0]->y();
  mat[2][0] = _v[1]->z() - _v[0]->z();
  mat[2][1] = _v[3]->z() - _v[0]->z();
  mat[2][2] = _v[4]->z() - _v[0]->z();
  return sign(det3x3(mat));
}

void MHexahedron::getIntegrationPoints(int pOrder, int *npts, IntPt **pts) const
{
#if !defined(HAVE_GMSH_EMBEDDED)
  *npts = getNGQHPts(pOrder);
  *pts = getGQHPts(pOrder);
#endif
}

int MPrism::getVolumeSign()
{ 
  double mat[3][3];
  mat[0][0] = _v[1]->x() - _v[0]->x();
  mat[0][1] = _v[2]->x() - _v[0]->x();
  mat[0][2] = _v[3]->x() - _v[0]->x();
  mat[1][0] = _v[1]->y() - _v[0]->y();
  mat[1][1] = _v[2]->y() - _v[0]->y();
  mat[1][2] = _v[3]->y() - _v[0]->y();
  mat[2][0] = _v[1]->z() - _v[0]->z();
  mat[2][1] = _v[2]->z() - _v[0]->z();
  mat[2][2] = _v[3]->z() - _v[0]->z();
  return sign(det3x3(mat));
}

int MPyramid::getVolumeSign()
{ 
  double mat[3][3];
  mat[0][0] = _v[1]->x() - _v[0]->x();
  mat[0][1] = _v[3]->x() - _v[0]->x();
  mat[0][2] = _v[4]->x() - _v[0]->x();
  mat[1][0] = _v[1]->y() - _v[0]->y();
  mat[1][1] = _v[3]->y() - _v[0]->y();
  mat[1][2] = _v[4]->y() - _v[0]->y();
  mat[2][0] = _v[1]->z() - _v[0]->z();
  mat[2][1] = _v[3]->z() - _v[0]->z();
  mat[2][2] = _v[4]->z() - _v[0]->z();
  return sign(det3x3(mat));
}