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41 results

drawGlyph.cpp

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  • MElement.cpp 63.79 KiB
    // Gmsh - Copyright (C) 1997-2016 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@onelab.info>.
    
    #include <stdlib.h>
    #include <math.h>
    #include <limits>
    #include "GmshConfig.h"
    #include "GmshMessage.h"
    #include "GModel.h"
    #include "MElement.h"
    #include "MPoint.h"
    #include "MLine.h"
    #include "MTriangle.h"
    #include "MQuadrangle.h"
    #include "MTetrahedron.h"
    #include "MHexahedron.h"
    #include "MPrism.h"
    #include "MPyramid.h"
    #include "MTrihedron.h"
    #include "MElementCut.h"
    #include "MSubElement.h"
    #include "GEntity.h"
    #include "StringUtils.h"
    #include "Numeric.h"
    #include "CondNumBasis.h"
    #include "Context.h"
    #include "qualityMeasuresJacobian.h"
    
    #define SQU(a)      ((a)*(a))
    
    double MElement::_isInsideTolerance = 1.e-6;
    
    MElement::MElement(int num, int part) : _visible(1)
    {
    #if defined(_OPENMP)
      #pragma omp critical
    #endif
      {
        // we should make GModel a mandatory argument to the constructor
        GModel *m = GModel::current();
        if(num){
          _num = num;
          m->setMaxElementNumber(std::max(m->getMaxElementNumber(), _num));
        }
        else{
          m->setMaxElementNumber(m->getMaxElementNumber() + 1);
          _num = m->getMaxElementNumber();
        }
        _partition = (short)part;
      }
    }
    
    void MElement::setTolerance(const double tol)
    {
      _isInsideTolerance = tol;
    }
    
    double MElement::getTolerance()
    {
      return _isInsideTolerance;
    }
    
    void MElement::_getEdgeRep(MVertex *v0, MVertex *v1,
                               double *x, double *y, double *z, SVector3 *n,
                               int faceIndex)
    {
      x[0] = v0->x(); y[0] = v0->y(); z[0] = v0->z();
      x[1] = v1->x(); y[1] = v1->y(); z[1] = v1->z();
      if(faceIndex >= 0){
        n[0] = n[1] = getFace(faceIndex).normal();
      }
      else{
        MEdge e(v0, v1);
        n[0] = n[1] = e.normal();
      }
    }
    
    void MElement::_getFaceRep(MVertex *v0, MVertex *v1, MVertex *v2,
                               double *x, double *y, double *z, SVector3 *n)
    {
      x[0] = v0->x(); x[1] = v1->x(); x[2] = v2->x();
      y[0] = v0->y(); y[1] = v1->y(); y[2] = v2->y();
      z[0] = v0->z(); z[1] = v1->z(); z[2] = v2->z();
      SVector3 t1(x[1] - x[0], y[1] - y[0], z[1] - z[0]);
      SVector3 t2(x[2] - x[0], y[2] - y[0], z[2] - z[0]);
      SVector3 normal = crossprod(t1, t2);
      normal.normalize();
      for(int i = 0; i < 3; i++) n[i] = normal;
    }
    
    char MElement::getVisibility() const
    {
      if(CTX::instance()->hideUnselected && _visible < 2) return false;
      return _visible;
    }
    
    double MElement::minEdge()
    {
      double m = 1.e25;
      for(int i = 0; i < getNumEdges(); i++){
        MEdge e = getEdge(i);
        m = std::min(m, e.getVertex(0)->distance(e.getVertex(1)));
      }
      return m;
    }
    
    double MElement::maxEdge()
    {
      double m = 0.;
      for(int i = 0; i < getNumEdges(); i++){
        MEdge e = getEdge(i);
        m = std::max(m, e.getVertex(0)->distance(e.getVertex(1)));
      }
      return m;
    }
    
    double MElement::rhoShapeMeasure()
    {
      double min = minEdge();
      double max = maxEdge();
      if(max)
        return min / max;
      else
        return 0.;
    }
    
    double MElement::maxDistToStraight() const
    {
      const nodalBasis *lagBasis = getFunctionSpace();
      const fullMatrix<double> &uvw = lagBasis->points;
      const int &nV = uvw.size1();
      const int &dim = uvw.size2();
      const nodalBasis *lagBasis1 = getFunctionSpace(1);
      const int &nV1 = lagBasis1->points.size1();
      std::vector<SPoint3> xyz1(nV1);
      for (int iV = 0; iV < nV1; ++iV) xyz1[iV] = getVertex(iV)->point();
      double maxdx = 0.;
      for (int iV = nV1; iV < nV; ++iV) {
        double f[256];
        lagBasis1->f(uvw(iV, 0), (dim > 1) ? uvw(iV, 1) : 0., (dim > 2) ? uvw(iV, 2) : 0., f);
        SPoint3 xyzS(0.,0.,0.);
        for (int iSF = 0; iSF < nV1; ++iSF) xyzS += xyz1[iSF]*f[iSF];
        SVector3 vec(xyzS,getVertex(iV)->point());
        double dx = vec.norm();
        if (dx > maxdx) maxdx = dx;
      }
      return maxdx;
    }
    
    double MElement::minIsotropyMeasure(bool knownValid, bool reversedOK)
    {
    #if defined(HAVE_MESH)
      return jacobianBasedQuality::minIsotropyMeasure(this, knownValid, reversedOK);
    #else
      return 0.;
    #endif
    }
    
    double MElement::minScaledJacobian(bool knownValid, bool reversedOK)
    {
    #if defined(HAVE_MESH)
      return jacobianBasedQuality::minScaledJacobian(this, knownValid, reversedOK);
    #else
      return 0.;
    #endif
    }
    
    double MElement::specialQuality()
    {
    #if defined(HAVE_MESH)
      double minJ, maxJ;
      jacobianBasedQuality::minMaxJacobianDeterminant(this, minJ, maxJ);
      if (minJ <= 0.) return minJ;
    //  if (minJ < 0 && maxJ >= 0) return minJ/maxJ; // accept -inf as an answer
    //  if (minJ < 0 && maxJ < 0) return -std::numeric_limits<double>::infinity();
      return jacobianBasedQuality::minIsotropyMeasure(this, true);
    #else
      return 0;
    #endif
    }
    
    double MElement::specialQuality2()
    {
    #if defined(HAVE_MESH)
      double minJ, maxJ;
      jacobianBasedQuality::minMaxJacobianDeterminant(this, minJ, maxJ);
      if (minJ <= 0.) return minJ;
    //  if (minJ < 0 && maxJ >= 0) return minJ/maxJ; // accept -inf as an answer
    //  if (minJ < 0 && maxJ < 0) return -std::numeric_limits<double>::infinity();
      return jacobianBasedQuality::minScaledJacobian(this, true);
    #else
      return 0;
    #endif
    }
    
    void MElement::scaledJacRange(double &jmin, double &jmax, GEntity *ge) const
    {
      jmin = jmax = 1.0;
    #if defined(HAVE_MESH)
      const JacobianBasis *jac = getJacobianFuncSpace();
      const int numJacNodes = jac->getNumJacNodes();
      fullMatrix<double> nodesXYZ(jac->getNumMapNodes(),3);
      getNodesCoord(nodesXYZ);
      fullVector<double> SJi(numJacNodes), Bi(numJacNodes);
      jac->getScaledJacobian(nodesXYZ,SJi);
      if (ge && (ge->dim() == 2) && ge->haveParametrization()) {
        // If parametrized surface entity provided...
        SVector3 geoNorm(0.,0.,0.);
        // ... correct Jacobian sign with geometrical normal
        for (int i=0; i<jac->getNumPrimMapNodes(); i++) {
          const MVertex *vert = getVertex(i);
          if (vert->onWhat() == ge) {
            double u, v;
            vert->getParameter(0,u);
            vert->getParameter(1,v);
            geoNorm += ((GFace*)ge)->normal(SPoint2(u,v));
          }
        }
        if (geoNorm.normSq() == 0.) {
          // If no vertex on surface or average is zero, take normal at barycenter
          SPoint2 param = ((GFace*)ge)->parFromPoint(barycenter(true),false);
          geoNorm = ((GFace*)ge)->normal(param);
        }
        fullMatrix<double> elNorm(1,3);
        jac->getPrimNormal2D(nodesXYZ,elNorm);
        const double scal = geoNorm(0) * elNorm(0,0) + geoNorm(1) * elNorm(0,1) +
          geoNorm(2) * elNorm(0,2);
        if (scal < 0.) SJi.scale(-1.);
      }
      jac->lag2Bez(SJi,Bi);
      jmin = *std::min_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
      jmax = *std::max_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
    #endif
    }
    
    void MElement::idealJacRange(double &jmin, double &jmax, GEntity *ge)
    {
      jmin = jmax = 1.0;
    #if defined(HAVE_MESH)
      const JacobianBasis *jac = getJacobianFuncSpace();
      const int numJacNodes = jac->getNumJacNodes();
      fullMatrix<double> nodesXYZ(jac->getNumMapNodes(),3);
      getNodesCoord(nodesXYZ);
      fullVector<double> iJi(numJacNodes), Bi(numJacNodes);
      jac->getSignedIdealJacobian(nodesXYZ,iJi);
      const int nEd = getNumEdges(), dim = getDim();
      double sumEdLength = 0.;
      for(int iEd = 0; iEd < nEd; iEd++)
        sumEdLength += getEdge(iEd).length();
      const double invMeanEdLength = double(nEd)/sumEdLength;
      if (sumEdLength == 0.) {
        jmin = 0.; jmax = 0.;
        return;
      }
      double scale = (dim == 1.) ? invMeanEdLength :
                     (dim == 2.) ? invMeanEdLength*invMeanEdLength :
                     invMeanEdLength*invMeanEdLength*invMeanEdLength;
      if (ge && (ge->dim() == 2) && ge->haveParametrization()) {
        // If parametrized surface entity provided...
        SVector3 geoNorm(0.,0.,0.);
        // ... correct Jacobian sign with geometrical normal
        for (int i=0; i<jac->getNumPrimMapNodes(); i++) {
          const MVertex *vert = getVertex(i);
          if (vert->onWhat() == ge) {
            double u, v;
            vert->getParameter(0,u);
            vert->getParameter(1,v);
            geoNorm += ((GFace*)ge)->normal(SPoint2(u,v));
          }
        }
        if (geoNorm.normSq() == 0.) {
          // If no vertex on surface or average is zero, take normal at barycenter
          SPoint2 param = ((GFace*)ge)->parFromPoint(barycenter(true),false);
          geoNorm = ((GFace*)ge)->normal(param);
        }
        fullMatrix<double> elNorm(1,3);
        jac->getPrimNormal2D(nodesXYZ, elNorm, true);
        const double dp = geoNorm(0) * elNorm(0,0) + geoNorm(1) * elNorm(0,1) +
          geoNorm(2) * elNorm(0,2);
        if (dp < 0.) scale = -scale;
      }
      iJi.scale(scale);
      jac->lag2Bez(iJi,Bi);
      jmin = *std::min_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
      jmax = *std::max_element(Bi.getDataPtr(),Bi.getDataPtr()+Bi.size());
    #endif
    }
    
    void MElement::signedInvCondNumRange(double &iCNMin, double &iCNMax, GEntity *ge)
    {
      iCNMin = iCNMax = 1.0;
    #if defined(HAVE_MESH)
      const CondNumBasis *cnb = BasisFactory::getCondNumBasis(getTypeForMSH());
      const int numCNNodes = cnb->getNumCondNumNodes();
      fullMatrix<double> nodesXYZ(cnb->getNumMapNodes(), 3), normals;
      getNodesCoord(nodesXYZ);
      if (getDim() == 2.) {
        SVector3 nVec = getFace(0).normal();
        normals.resize(1, 3);
        normals(0, 0) = nVec[0]; normals(0, 1) = nVec[1]; normals(0, 2) = nVec[2];
      }
      if (ge && (ge->dim() == 2) && ge->haveParametrization()) {
        // If parametrized surface entity provided...
        SVector3 geoNorm(0., 0., 0.);
        // ... correct Jacobian sign with geometrical normal
        for (int i=0; i<getNumPrimaryVertices(); i++) {
          const MVertex *vert = getVertex(i);
          if (vert->onWhat() == ge) {
            double u, v;
            vert->getParameter(0, u);
            vert->getParameter(1, v);
            geoNorm += ((GFace*)ge)->normal(SPoint2(u, v));
          }
        }
        if (geoNorm.normSq() == 0.) {
          // If no vertex on surface or average is zero, take normal at barycenter
          SPoint2 param = ((GFace*)ge)->parFromPoint(barycenter(true), false);
          geoNorm = ((GFace*)ge)->normal(param);
        }
        const double dp = geoNorm(0) * normals(0, 0) + geoNorm(1) * normals(0, 1)
                        + geoNorm(2) * normals(0, 2);
        if (dp < 0.) {
           normals(0, 0) = -normals(0, 0);
           normals(0, 1) = -normals(0, 1);
           normals(0, 2) = -normals(0, 2);
        }
      }
      fullVector<double> invCondNum(numCNNodes);
      cnb->getSignedInvCondNum(nodesXYZ, normals, invCondNum);
      iCNMin = *std::min_element(invCondNum.getDataPtr(), invCondNum.getDataPtr()+numCNNodes);
      iCNMax = *std::max_element(invCondNum.getDataPtr(), invCondNum.getDataPtr()+numCNNodes);
    #endif
    }
    
    void MElement::getNode(int num, double &u, double &v, double &w) const
    {
      // only for MElements that don't have a lookup table for this
      // (currently only 1st order elements have)
      double uvw[3];
      const MVertex* ver = getVertex(num);
      double xyz[3] = {ver->x(), ver->y(), ver->z()};
      xyz2uvw(xyz, uvw);
      u = uvw[0];
      v = uvw[1];
      w = uvw[2];
    }
    
    void MElement::getShapeFunctions(double u, double v, double w, double s[], int o) const
    {
      const nodalBasis* fs = getFunctionSpace(o);
      if(fs) fs->f(u, v, w, s);
      else Msg::Error("Function space not implemented for this type of element");
    }
    
    void MElement::getGradShapeFunctions(double u, double v, double w, double s[][3],int o) const
    {
      const nodalBasis* fs = getFunctionSpace(o);
      if(fs) fs->df(u, v, w, s);
      else Msg::Error("Function space not implemented for this type of element");
    }
    
    void MElement::getHessShapeFunctions(double u, double v, double w, double s[][3][3],
                                         int o) const
    {
      const nodalBasis* fs = getFunctionSpace(o);
      if(fs) fs->ddf(u, v, w, s);
      else Msg::Error("Function space not implemented for this type of element");
    }
    
    void MElement::getThirdDerivativeShapeFunctions(double u, double v, double w,
                                                    double s[][3][3][3], int o) const
    {
      const nodalBasis* fs = getFunctionSpace(o);
      if(fs) fs->dddf(u, v, w, s);
      else Msg::Error("Function space not implemented for this type of element");
    }
    
    SPoint3 MElement::barycenter_infty () const
    {
      double xmin =  getVertex(0)->x();
      double xmax = xmin;
      double ymin =  getVertex(0)->y();
      double ymax = ymin;
      double zmin =  getVertex(0)->z();
      double zmax = zmin;
      int n = getNumVertices();
      for(int i = 0; i < n; i++) {
        const MVertex *v = getVertex(i);
        xmin = std::min(xmin,v->x());
        xmax = std::max(xmax,v->x());
        ymin = std::min(ymin,v->y());
        ymax = std::max(ymax,v->y());
        zmin = std::min(zmin,v->z());
        zmax = std::max(zmax,v->z());
      }
      return SPoint3(0.5*(xmin+xmax),0.5*(ymin+ymax),0.5*(zmin+zmax));
    }
    
    SPoint3 MElement::barycenter(bool primary) const
    {
      SPoint3 p(0., 0., 0.);
      int n = primary ? getNumPrimaryVertices() : getNumVertices();
      for(int i = 0; i < n; i++) {
        const MVertex *v = getVertex(i);
        p[0] += v->x();
        p[1] += v->y();
        p[2] += v->z();
      }
      p[0] /= (double)n;
      p[1] /= (double)n;
      p[2] /= (double)n;
      return p;
    }
    
    SPoint3 MElement::barycenterUVW() const
    {
      SPoint3 p(0., 0., 0.);
      int n = getNumVertices();
      for(int i = 0; i < n; i++) {
        double x, y, z;
        getNode(i, x, y, z);
        p[0] += x;
        p[1] += y;
        p[2] += z;
      }
      p[0] /= (double)n;
      p[1] /= (double)n;
      p[2] /= (double)n;
      return p;
    }
    
    double MElement::getVolume()
    {
      int npts;
      IntPt *pts;
      getIntegrationPoints(getDim() * (getPolynomialOrder() - 1), &npts, &pts);
      double vol = 0.;
      for (int i = 0; i < npts; i++){
        vol += getJacobianDeterminant(pts[i].pt[0], pts[i].pt[1], pts[i].pt[2])
          * pts[i].weight;
      }
      return vol;
    }
    
    int MElement::getVolumeSign()
    {
      double v = getVolume();
      if(v < 0.) return -1;
      else if(v > 0.) return 1;
      else return 0;
    }
    
    bool MElement::setVolumePositive()
    {
      if(getDim() < 3) return true;
      int s = getVolumeSign();
      if(s < 0) reverse();
      if(!s) return false;
      return true;
    }
    
    int MElement::getValidity()
    {
    #if defined(HAVE_MESH)
      double jmin, jmax;
      jacobianBasedQuality::minMaxJacobianDeterminant(this, jmin, jmax);
      if (jmin > .0) return 1; // valid
      if (jmax >= .0) return 0; // invalid
      // Here, jmax < 0 (and jmin < 0). The element validity is quite indeterminate.
      // It can be valid but with a wrong numbering of the nodes,
      // or it can be invalid, i.e. with nodes that are incorrectly located.
      return -1;
    #else
      return 0;
    #endif
    }
    
    std::string MElement::getInfoString()
    {
      char tmp[256];
      sprintf(tmp, "Element %d", getNum());
      return std::string(tmp);
    }
    
    const nodalBasis* MElement::getFunctionSpace(int order, bool serendip) const
    {
      if (order == -1) return BasisFactory::getNodalBasis(getTypeForMSH());
      int tag = ElementType::getTag(getType(), order, serendip);
      return tag ? BasisFactory::getNodalBasis(tag) : NULL;
    }
    
    const JacobianBasis* MElement::getJacobianFuncSpace(int order) const
    {
      if (order == -1) return BasisFactory::getJacobianBasis(getTypeForMSH());
      return BasisFactory::getJacobianBasis(FuncSpaceData(this, order));
    }
    
    static double _computeDeterminantAndRegularize(const MElement *ele, double jac[3][3])
    {
      double dJ = 0;
    
      switch (ele->getDim()) {
    
      case 0:
        {
          dJ = 1.0;
          jac[0][0] = jac[1][1] = jac[2][2] = 1.0;
          jac[0][1] = jac[1][0] = jac[2][0] = 0.0;
          jac[0][2] = jac[1][2] = jac[2][1] = 0.0;
          break;
        }
      case 1:
        {
          dJ = sqrt(SQU(jac[0][0]) + SQU(jac[0][1]) + SQU(jac[0][2]));
    
          // regularize matrix
          double a[3], b[3], c[3];
          a[0] = jac[0][0];
          a[1] = jac[0][1];
          a[2] = jac[0][2];
          if((fabs(a[0]) >= fabs(a[1]) && fabs(a[0]) >= fabs(a[2])) ||
             (fabs(a[1]) >= fabs(a[0]) && fabs(a[1]) >= fabs(a[2]))) {
            b[0] = a[1]; b[1] = -a[0]; b[2] = 0.;
          }
          else {
            b[0] = 0.; b[1] = a[2]; b[2] = -a[1];
          }
          norme(b);
          prodve(a, b, c);
          norme(c);
          jac[1][0] = b[0]; jac[1][1] = b[1]; jac[1][2] = b[2];
          jac[2][0] = c[0]; jac[2][1] = c[1]; jac[2][2] = c[2];
          break;
        }
      case 2:
        {
          dJ = sqrt(SQU(jac[0][0] * jac[1][1] - jac[0][1] * jac[1][0]) +
                    SQU(jac[0][2] * jac[1][0] - jac[0][0] * jac[1][2]) +
                    SQU(jac[0][1] * jac[1][2] - jac[0][2] * jac[1][1]));
    
          // regularize matrix
          double a[3], b[3], c[3];
          a[0] = jac[0][0];
          a[1] = jac[0][1];
          a[2] = jac[0][2];
          b[0] = jac[1][0];
          b[1] = jac[1][1];
          b[2] = jac[1][2];
          prodve(a, b, c);
          norme(c);
          jac[2][0] = c[0]; jac[2][1] = c[1]; jac[2][2] = c[2];
          break;
        }
      case 3:
        {
          dJ = (jac[0][0] * jac[1][1] * jac[2][2] + jac[0][2] * jac[1][0] * jac[2][1] +
    	    jac[0][1] * jac[1][2] * jac[2][0] - jac[0][2] * jac[1][1] * jac[2][0] -
    	    jac[0][0] * jac[1][2] * jac[2][1] - jac[0][1] * jac[1][0] * jac[2][2]);
          break;
        }
      }
      return dJ;
    }
    
    double MElement::getJacobian(double u, double v, double w, double jac[3][3]) const
    {
      jac[0][0] = jac[0][1] = jac[0][2] = 0.;
      jac[1][0] = jac[1][1] = jac[1][2] = 0.;
      jac[2][0] = jac[2][1] = jac[2][2] = 0.;
    
      double gsf[1256][3];
      getGradShapeFunctions(u, v, w, gsf);
      for (int i = 0; i < getNumShapeFunctions(); i++) {
        const MVertex *ver = getShapeFunctionNode(i);
        double* gg = gsf[i];
        for (int j = 0; j < getDim(); j++) {
          jac[j][0] += ver->x() * gg[j];
          jac[j][1] += ver->y() * gg[j];
          jac[j][2] += ver->z() * gg[j];
        }
      }
    
      return _computeDeterminantAndRegularize(this, jac);
    }
    
    double MElement::getJacobian(const fullMatrix<double> &gsf, double jac[3][3]) const
    {
      jac[0][0] = jac[0][1] = jac[0][2] = 0.;
      jac[1][0] = jac[1][1] = jac[1][2] = 0.;
      jac[2][0] = jac[2][1] = jac[2][2] = 0.;
    
      for (int i = 0; i < getNumShapeFunctions(); i++) {
        const MVertex *v = getShapeFunctionNode(i);
        for (int j = 0; j < gsf.size2(); j++) {
          jac[j][0] += v->x() * gsf(i, j);
          jac[j][1] += v->y() * gsf(i, j);
          jac[j][2] += v->z() * gsf(i, j);
        }
      }
      return _computeDeterminantAndRegularize(this, jac);
    }
    
    double MElement::getJacobian(const std::vector<SVector3> &gsf, double jac[3][3])
    const {
      jac[0][0] = jac[0][1] = jac[0][2] = 0.;
      jac[1][0] = jac[1][1] = jac[1][2] = 0.;
      jac[2][0] = jac[2][1] = jac[2][2] = 0.;
    
      for (int i = 0; i < getNumShapeFunctions(); i++) {
        const MVertex *v = getShapeFunctionNode(i);
        for (int j = 0; j < 3; j++) {
          double mult = gsf[i][j];
          jac[j][0] += v->x() * mult;
          jac[j][1] += v->y() * mult;
          jac[j][2] += v->z() * mult;
        }
      }
      return _computeDeterminantAndRegularize(this, jac);
    }
    
    double MElement::getPrimaryJacobian(double u, double v, double w, double jac[3][3]) const
    {
      jac[0][0] = jac[0][1] = jac[0][2] = 0.;
      jac[1][0] = jac[1][1] = jac[1][2] = 0.;
      jac[2][0] = jac[2][1] = jac[2][2] = 0.;
    
      double gsf[1256][3];
      getGradShapeFunctions(u, v, w, gsf, 1);
      for(int i = 0; i < getNumPrimaryShapeFunctions(); i++) {
        const MVertex *v = getShapeFunctionNode(i);
        double* gg = gsf[i];
        for (int j = 0; j < 3; j++) {
          jac[j][0] += v->x() * gg[j];
          jac[j][1] += v->y() * gg[j];
          jac[j][2] += v->z() * gg[j];
        }
      }
    
      return _computeDeterminantAndRegularize(this, jac);
    }
    
    void MElement::getSignedJacobian(fullVector<double> &jacobian, int o) const
    {
      const int numNodes = getNumVertices();
      fullMatrix<double> nodesXYZ(numNodes,3);
      getNodesCoord(nodesXYZ);
      getJacobianFuncSpace(o)->getSignedJacobian(nodesXYZ,jacobian);
    }
    
    void MElement::getNodesCoord(fullMatrix<double> &nodesXYZ) const
    {
      const int numNodes = getNumVertices();
      for (int i = 0; i < numNodes; i++) {
        const MVertex *v = getShapeFunctionNode(i);
        nodesXYZ(i,0) = v->x();
        nodesXYZ(i,1) = v->y();
        nodesXYZ(i,2) = v->z();
      }
    }
    
    double MElement::getEigenvaluesMetric(double u, double v, double w, double values[3]) const
    {
      double jac[3][3];
      getJacobian(u, v, w, jac);
      GradientBasis::mapFromIdealElement(getType(), jac);
    
      switch (getDim()) {
      case 1:
        values[0] = 0;
        values[1] = -1;
        values[2] = -1;
        for (int d = 0; d < 3; ++d)
          values[0] += jac[d][0] * jac[d][0];
        return 1;
    
      case 2:
      {
        fullMatrix<double> metric(2, 2);
        for (int i = 0; i < 2; ++i) {
          for (int j = 0; j < 2; ++j) {
            for (int d = 0; d < 3; ++d)
              metric(i, j) += jac[d][i] * jac[d][j];
          }
        }
        fullVector<double> valReal(values, 2), valImag(2);
        fullMatrix<double> vecLeft(2, 2), vecRight(2, 2);
        metric.eig(valReal, valImag, vecLeft, vecRight, true);
        values[2] = -1;
        return std::sqrt(valReal(0) / valReal(1));
      }
    
      case 3:
      {
        fullMatrix<double> metric(3, 3);
        for (int i = 0; i < 3; ++i) {
          for (int j = 0; j < 3; ++j) {
            for (int d = 0; d < 3; ++d)
              metric(i, j) += jac[d][i] * jac[d][j];
          }
        }
    
        fullVector<double> valReal(values, 3), valImag(3);
        fullMatrix<double> vecLeft(3, 3), vecRight(3, 3);
        metric.eig(valReal, valImag, vecLeft, vecRight, true);
    
        return std::sqrt(valReal(0) / valReal(2));
      }
    
      default:
        Msg::Error("wrong dimension for getEigenvaluesMetric function");
        return -1;
      }
    }
    
    void MElement::pnt(double u, double v, double w, SPoint3 &p) const
    {
      double x = 0., y = 0., z = 0.;
      double sf[1256];
      getShapeFunctions(u, v, w, sf);
      for (int j = 0; j < getNumShapeFunctions(); j++) {
        const MVertex *v = getShapeFunctionNode(j);
        x += sf[j] * v->x();
        y += sf[j] * v->y();
        z += sf[j] * v->z();
      }
      p = SPoint3(x, y, z);
    }
    
    void MElement::pnt(const std::vector<double> &sf, SPoint3 &p) const
    {
      double x = 0., y = 0., z = 0.;
      for (int j = 0; j < getNumShapeFunctions(); j++) {
        const MVertex *v = getShapeFunctionNode(j);
        x += sf[j] * v->x();
        y += sf[j] * v->y();
        z += sf[j] * v->z();
      }
      p = SPoint3(x, y, z);
    }
    
    void MElement::primaryPnt(double u, double v, double w, SPoint3 &p)
    {
      double x = 0., y = 0., z = 0.;
      double sf[1256];
      getShapeFunctions(u, v, w, sf, 1);
      for (int j = 0; j < getNumPrimaryShapeFunctions(); j++) {
        const MVertex *v = getShapeFunctionNode(j);
        x += sf[j] * v->x();
        y += sf[j] * v->y();
        z += sf[j] * v->z();
      }
      p = SPoint3(x,y,z);
    }
    
    void MElement::xyz2uvw(double xyz[3], double uvw[3]) const
    {
      // general Newton routine for the nonlinear case (more efficient
      // routines are implemented for simplices, where the basis functions
      // are linear)
      uvw[0] = uvw[1] = uvw[2] = 0.;
    
      // For high order elements, start from the nearer point
      if (getPolynomialOrder() > 2) {
        int numNearer = 0;
        const MVertex *v = getShapeFunctionNode(0);
        double distNearer = (v->x()-xyz[0])*(v->x()-xyz[0]) +
                            (v->y()-xyz[1])*(v->y()-xyz[1]) +
                            (v->z()-xyz[2])*(v->z()-xyz[2]);
        for (int i = 1; i < getNumShapeFunctions(); i++) {
          const MVertex *v = getShapeFunctionNode(i);
          double dist = (v->x()-xyz[0])*(v->x()-xyz[0]) +
                        (v->y()-xyz[1])*(v->y()-xyz[1]) +
                        (v->z()-xyz[2])*(v->z()-xyz[2]);
          if (dist < distNearer) {
            numNearer = i;
            distNearer = dist;
          }
        }
        const nodalBasis *nb = getFunctionSpace();
        fullMatrix<double> refpnts = nb->getReferenceNodes();
        uvw[0] = refpnts(numNearer, 0);
        uvw[1] = refpnts(numNearer, 1);
        uvw[2] = refpnts(numNearer, 2);
      }
    
      int iter = 1, maxiter = 20;
      double error = 1., tol = 1.e-6;
    
      while (error > tol && iter < maxiter){
        double jac[3][3];
        if(!getJacobian(uvw[0], uvw[1], uvw[2], jac)) break;
        double xn = 0., yn = 0., zn = 0.;
        double sf[1256];
        getShapeFunctions(uvw[0], uvw[1], uvw[2], sf);
        for (int i = 0; i < getNumShapeFunctions(); i++) {
          const MVertex *v = getShapeFunctionNode(i);
          xn += v->x() * sf[i];
          yn += v->y() * sf[i];
          zn += v->z() * sf[i];
        }
        double inv[3][3];
        inv3x3(jac, inv);
        double un = uvw[0] + inv[0][0] * (xyz[0] - xn) +
          inv[1][0] * (xyz[1] - yn) + inv[2][0] * (xyz[2] - zn);
        double vn = uvw[1] + inv[0][1] * (xyz[0] - xn) +
          inv[1][1] * (xyz[1] - yn) + inv[2][1] * (xyz[2] - zn);
        double wn = uvw[2] + inv[0][2] * (xyz[0] - xn) +
          inv[1][2] * (xyz[1] - yn) + inv[2][2] * (xyz[2] - zn);
        error = sqrt(SQU(un - uvw[0]) + SQU(vn - uvw[1]) + SQU(wn - uvw[2]));
        uvw[0] = un;
        uvw[1] = vn;
        uvw[2] = wn;
        iter++ ;
      }
    }
    
    void MElement::movePointFromParentSpaceToElementSpace(double &u, double &v, double &w) const
    {
      if(!getParent()) return;
      SPoint3 p;
      getParent()->pnt(u, v, w, p);
      double xyz[3] = {p.x(), p.y(), p.z()};
      double uvwE[3];
      xyz2uvw(xyz, uvwE);
      u = uvwE[0]; v = uvwE[1]; w = uvwE[2];
    }
    
    void MElement::movePointFromElementSpaceToParentSpace(double &u, double &v, double &w) const
    {
      if(!getParent()) return;
      SPoint3 p;
      pnt(u, v, w, p);
      double xyz[3] = {p.x(), p.y(), p.z()};
      double uvwP[3];
      getParent()->xyz2uvw(xyz, uvwP);
      u = uvwP[0]; v = uvwP[1]; w = uvwP[2];
    }
    
    double MElement::interpolate(double val[], double u, double v, double w, int stride,
                                 int order)
    {
      double sum = 0;
      int j = 0;
      double sf[1256];
      getShapeFunctions(u, v, w, sf, order);
      for(int i = 0; i < getNumShapeFunctions(); i++){
        sum += val[j] * sf[i];
        j += stride;
      }
      return sum;
    }
    
    void MElement::interpolateGrad(double val[], double u, double v, double w, double f[],
                                   int stride, double invjac[3][3], int order)
    {
      double dfdu[3] = {0., 0., 0.};
      int j = 0;
      double gsf[1256][3];
      getGradShapeFunctions(u, v, w, gsf, order);
      for(int i = 0; i < getNumShapeFunctions(); i++){
        dfdu[0] += val[j] * gsf[i][0];
        dfdu[1] += val[j] * gsf[i][1];
        dfdu[2] += val[j] * gsf[i][2];
        j += stride;
      }
      if(invjac){
        matvec(invjac, dfdu, f);
      }
      else{
        double jac[3][3], inv[3][3];
        getJacobian(u, v, w, jac);
        inv3x3(jac, inv);
        matvec(inv, dfdu, f);
      }
    }
    
    void MElement::interpolateCurl(double val[], double u, double v, double w, double f[],
                                   int stride, int order)
    {
      double fx[3], fy[3], fz[3], jac[3][3], inv[3][3];
      getJacobian(u, v, w, jac);
      inv3x3(jac, inv);
      interpolateGrad(&val[0], u, v, w, fx, stride, inv, order);
      interpolateGrad(&val[1], u, v, w, fy, stride, inv, order);
      interpolateGrad(&val[2], u, v, w, fz, stride, inv, order);
      f[0] = fz[1] - fy[2];
      f[1] = -(fz[0] - fx[2]);
      f[2] = fy[0] - fx[1];
    }
    
    double MElement::interpolateDiv(double val[], double u, double v, double w,
                                    int stride, int order)
    {
      double fx[3], fy[3], fz[3], jac[3][3], inv[3][3];
      getJacobian(u, v, w, jac);
      inv3x3(jac, inv);
      interpolateGrad(&val[0], u, v, w, fx, stride, inv, order);
      interpolateGrad(&val[1], u, v, w, fy, stride, inv, order);
      interpolateGrad(&val[2], u, v, w, fz, stride, inv, order);
      return fx[0] + fy[1] + fz[2];
    }
    
    double MElement::integrate(double val[], int pOrder, int stride, int order)
    {
      int npts; IntPt *gp;
      getIntegrationPoints(pOrder, &npts, &gp);
      double sum = 0;
      for (int i = 0; i < npts; i++){
        double u = gp[i].pt[0];
        double v = gp[i].pt[1];
        double w = gp[i].pt[2];
        double weight = gp[i].weight;
        double detuvw = getJacobianDeterminant(u, v, w);
        sum += interpolate(val, u, v, w, stride, order)*weight*detuvw;
      }
      return sum;
    }
    
    double MElement::integrateCirc(double val[], int edge, int pOrder, int order)
    {
      if(edge > getNumEdges() - 1){
        Msg::Error("No edge %d for this element", edge);
        return 0;
      }
    
      std::vector<MVertex*> v;
      getEdgeVertices(edge, v);
      MElementFactory f;
      int type = ElementType::getTag(TYPE_LIN, getPolynomialOrder());
      MElement* ee = f.create(type, v);
    
      double intv[3];
      for(int i = 0; i < 3; i++){
        intv[i] = ee->integrate(&val[i], pOrder, 3, order);
      }
      delete ee;
    
      double t[3] = {v[1]->x() - v[0]->x(), v[1]->y() - v[0]->y(), v[1]->z() - v[0]->z()};
      norme(t);
      double result;
      prosca(t, intv, &result);
      return result;
    }
    
    double MElement::integrateFlux(double val[], int face, int pOrder, int order)
    {
      if(face > getNumFaces() - 1){
        Msg::Error("No face %d for this element", face);
        return 0;
      }
      std::vector<MVertex*> v;
      getFaceVertices(face, v);
      MElementFactory f;
      int type = 0;
      switch(getType()) {
        case TYPE_TRI :
        case TYPE_TET :
        case TYPE_QUA :
        case TYPE_HEX :
          type = ElementType::getTag(getType(), getPolynomialOrder());
          break;
        case TYPE_PYR :
          if(face < 4) type = ElementType::getTag(TYPE_TRI, getPolynomialOrder());
          else type = ElementType::getTag(TYPE_QUA, getPolynomialOrder());
          break;
        case TYPE_PRI :
          if(face < 2) type = ElementType::getTag(TYPE_TRI, getPolynomialOrder());
          else type = ElementType::getTag(TYPE_QUA, getPolynomialOrder());
          break;
        default: type = 0; break;
      }
      MElement* fe = f.create(type, v);
    
      double intv[3];
      for(int i = 0; i < 3; i++){
        intv[i] = fe->integrate(&val[i], pOrder, 3, order);
      }
      delete fe;
    
      double n[3];
      normal3points(v[0]->x(), v[0]->y(), v[0]->z(),
                    v[1]->x(), v[1]->y(), v[1]->z(),
                    v[2]->x(), v[2]->y(), v[2]->z(), n);
      double result;
      prosca(n, intv, &result);
      return result;
    }
    
    void MElement::writeMSH(FILE *fp, bool binary, int entity,
                            std::vector<short> *ghosts)
    {
      int num = getNum();
      int type = getTypeForMSH();
      if(!type) return;
    
      std::vector<int> verts;
      getVerticesIdForMSH(verts);
    
      // FIXME: once we create elements using their own interpretion of data, we
      // should move this also into each element base class
      std::vector<int> data;
      data.insert(data.end(), verts.begin(), verts.end());
      if(getParent())
        data.push_back(getParent()->getNum());
      if(getPartition()){
        if(ghosts){
          data.push_back(1 + ghosts->size());
          data.push_back(getPartition());
          data.insert(data.end(), ghosts->begin(), ghosts->end());
        }
        else{
          data.push_back(1);
          data.push_back(getPartition());
        }
      }
      int numData = data.size();
    
      if(!binary){
        fprintf(fp, "%d %d %d %d", num, type, entity, numData);
        for(int i = 0; i < numData; i++)
          fprintf(fp, " %d", data[i]);
        fprintf(fp, "\n");
      }
      else{
        fwrite(&num, sizeof(int), 1, fp);
        fwrite(&type, sizeof(int), 1, fp);
        fwrite(&entity, sizeof(int), 1, fp);
        fwrite(&numData, sizeof(int), 1, fp);
        fwrite(&data[0], sizeof(int), numData, fp);
      }
    }
    
    void MElement::writeMSH2(FILE *fp, double version, bool binary, int num,
                             int elementary, int physical, int parentNum,
                             int dom1Num, int dom2Num, std::vector<short> *ghosts)
    {
      int type = getTypeForMSH();
    
      if(!type) return;
    
      int n = getNumVerticesForMSH();
      int par = (parentNum) ? 1 : 0;
      int dom = (dom1Num) ? 2 : 0;
      bool poly = (type == MSH_POLYG_ || type == MSH_POLYH_ || type == MSH_POLYG_B);
    
      // if polygon loop over children (triangles and tets)
      if(CTX::instance()->mesh.saveTri){
        if(poly){
          for (int i = 0; i < getNumChildren() ; i++){
             MElement *t = getChild(i);
             t->writeMSH2(fp, version, binary, num++, elementary, physical, 0, 0, 0, ghosts);
          }
          return;
        }
        if(type == MSH_TRI_B){
          MTriangle *t = new MTriangle(getVertex(0), getVertex(1), getVertex(2));
          t->writeMSH2(fp, version, binary, num++, elementary, physical, 0, 0, 0, ghosts);
          delete t;
          return;
        }
        if(type == MSH_LIN_B || type == MSH_LIN_C){
          MLine *l = new MLine(getVertex(0), getVertex(1));
          l->writeMSH2(fp, version, binary, num++, elementary, physical, 0, 0, 0, ghosts);
          delete l;
          return;
        }
      }
    
      if(CTX::instance()->mesh.preserveNumberingMsh2) num = _num;
    
      if(!binary){
        fprintf(fp, "%d %d", num ? num : _num, type);
        if(version < 2.0)
          fprintf(fp, " %d %d %d", abs(physical), elementary, n);
        else if (version < 2.2)
          fprintf(fp, " %d %d %d", abs(physical), elementary, _partition);
        else if(!_partition && !par && !dom)
          fprintf(fp, " %d %d %d", 2 + par + dom, abs(physical), elementary);
        else if(!ghosts)
          fprintf(fp, " %d %d %d 1 %d", 4 + par + dom, abs(physical), elementary, _partition);
        else{
          int numGhosts = ghosts->size();
          fprintf(fp, " %d %d %d %d %d", 4 + numGhosts + par + dom, abs(physical),
                  elementary, 1 + numGhosts, _partition);
          for(unsigned int i = 0; i < ghosts->size(); i++)
            fprintf(fp, " %d", -(*ghosts)[i]);
        }
        if(version >= 2.0 && par)
          fprintf(fp, " %d", parentNum);
        if(version >= 2.0 && dom)
          fprintf(fp, " %d %d", dom1Num, dom2Num);
        if(version >= 2.0 && poly)
          fprintf(fp, " %d", n);
      }
      else{
        int numTags, numGhosts = 0;
        if(!_partition) numTags = 2;
        else if(!ghosts) numTags = 4;
        else{
          numGhosts = ghosts->size();
          numTags = 4 + numGhosts;
        }
        numTags += par;
        // we write elements in blobs of single elements; this will lead
        // to suboptimal reads, but it's much simpler when the number of
        // tags change from element to element (third-party codes can
        // still write MSH file optimized for reading speed, by grouping
        // elements with the same number of tags in blobs)
        int blob[60] = {type, 1, numTags, num ? num : _num, abs(physical), elementary,
                        1 + numGhosts, _partition};
        if(ghosts)
          for(int i = 0; i < numGhosts; i++) blob[8 + i] = -(*ghosts)[i];
        if(par) blob[8 + numGhosts] = parentNum;
        if(poly) Msg::Error("Unable to write polygons/polyhedra in binary files.");
        fwrite(blob, sizeof(int), 4 + numTags, fp);
      }
    
      if(physical < 0) reverse();
    
      std::vector<int> verts;
      getVerticesIdForMSH(verts);
    
      if(!binary){
        for(int i = 0; i < n; i++)
          fprintf(fp, " %d", verts[i]);
        fprintf(fp, "\n");
      }
      else{
        fwrite(&verts[0], sizeof(int), n, fp);
      }
    
      if(physical < 0) reverse();
    }
    
    void MElement::writePOS(FILE *fp, bool printElementary, bool printElementNumber,
                            bool printSICN, bool printGamma, bool printRho,
                            bool printDisto, double scalingFactor, int elementary)
    {
      const char *str = getStringForPOS();
      if(!str) return;
    
      int n = getNumVertices();
      fprintf(fp, "%s(", str);
      for(int i = 0; i < n; i++){
        if(i) fprintf(fp, ",");
        fprintf(fp, "%g,%g,%g", getVertex(i)->x() * scalingFactor,
                getVertex(i)->y() * scalingFactor, getVertex(i)->z() * scalingFactor);
      }
      fprintf(fp, "){");
      bool first = true;
      if(printElementary){
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%d", elementary);
        }
      }
      if(printElementNumber){
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%d", getNum());
        }
      }
      if(printSICN){
        double sICNMin = minSICNShapeMeasure();
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%g", sICNMin);
        }
      }
      if(printGamma){
        double gamma = gammaShapeMeasure();
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%g", gamma);
          //fprintf(fp, "%d", getVertex(i)->getNum());
        }
      }
      if(printRho){
        double rho = rhoShapeMeasure();
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%g", rho);
        }
      }
      if(printDisto){
        double disto = distoShapeMeasure();
        for(int i = 0; i < n; i++){
          if(first) first = false; else fprintf(fp, ",");
          fprintf(fp, "%g", disto);
        }
      }
      fprintf(fp, "};\n");
    }
    
    void MElement::writeSTL(FILE *fp, bool binary, double scalingFactor)
    {
      if(getType() != TYPE_TRI && getType() != TYPE_QUA) return;
      int qid[3] = {0, 2, 3};
      SVector3 n = getFace(0).normal();
      if(!binary){
        fprintf(fp, "facet normal %g %g %g\n", n[0], n[1], n[2]);
        fprintf(fp, "  outer loop\n");
        for(int j = 0; j < 3; j++)
          fprintf(fp, "    vertex %g %g %g\n",
                  getVertex(j)->x() * scalingFactor,
                  getVertex(j)->y() * scalingFactor,
                  getVertex(j)->z() * scalingFactor);
        fprintf(fp, "  endloop\n");
        fprintf(fp, "endfacet\n");
        if(getNumVertices() == 4){
          fprintf(fp, "facet normal %g %g %g\n", n[0], n[1], n[2]);
          fprintf(fp, "  outer loop\n");
          for(int j = 0; j < 3; j++)
            fprintf(fp, "    vertex %g %g %g\n",
                    getVertex(qid[j])->x() * scalingFactor,
                    getVertex(qid[j])->y() * scalingFactor,
                    getVertex(qid[j])->z() * scalingFactor);
          fprintf(fp, "  endloop\n");
          fprintf(fp, "endfacet\n");
        }
      }
      else{
        char data[50];
        float *coords = (float*)data;
        coords[0] = (float)n[0];
        coords[1] = (float)n[1];
        coords[2] = (float)n[2];
        for(int j = 0; j < 3; j++){
          coords[3 + 3 * j] = (float)(getVertex(j)->x() * scalingFactor);
          coords[3 + 3 * j + 1] = (float)(getVertex(j)->y() * scalingFactor);
          coords[3 + 3 * j + 2] = (float)(getVertex(j)->z() * scalingFactor);
        }
        data[48] = data[49] = 0;
        fwrite(data, sizeof(char), 50, fp);
        if(getNumVertices() == 4){
          for(int j = 0; j < 3; j++){
            coords[3 + 3 * j] = (float)(getVertex(qid[j])->x() * scalingFactor);
            coords[3 + 3 * j + 1] = (float)(getVertex(qid[j])->y() * scalingFactor);
            coords[3 + 3 * j + 2] = (float)(getVertex(qid[j])->z() * scalingFactor);
          }
          fwrite(data, sizeof(char), 50, fp);
        }
      }
    }
    
    void MElement::writePLY2(FILE *fp)
    {
      fprintf(fp, "3 ");
      for(int i = 0; i < getNumVertices(); i++)
        fprintf(fp, " %d", getVertex(i)->getIndex() - 1);
      fprintf(fp, "\n");
    }
    
    void MElement::writeVRML(FILE *fp)
    {
      for(int i = 0; i < getNumVertices(); i++)
        fprintf(fp, "%d,", getVertex(i)->getIndex() - 1);
      fprintf(fp, "-1,\n");
    }
    
    void MElement::writeTOCHNOG(FILE *fp, int num)
    {
      const char *str = getStringForTOCHNOG();
      if(!str) return;
    
      int n = getNumVertices();
      fprintf(fp, "element %d %s ", num, str);
      for(int i = 0; i < n; i++) {
        fprintf(fp, " %d", getVertexTOCHNOG(i)->getIndex());
      }
      fprintf(fp, "\n");
    }
    
    void MElement::writeVTK(FILE *fp, bool binary, bool bigEndian)
    {
      if(!getTypeForVTK()) return;
    
      int n = getNumVertices();
      if(binary){
        int verts[60];
        verts[0] = n;
        for(int i = 0; i < n; i++)
          verts[i + 1] = getVertexVTK(i)->getIndex() - 1;
        // VTK always expects big endian binary data
        if(!bigEndian) SwapBytes((char*)verts, sizeof(int), n + 1);
        fwrite(verts, sizeof(int), n + 1, fp);
      }
      else{
        fprintf(fp, "%d", n);
        for(int i = 0; i < n; i++)
          fprintf(fp, " %d", getVertexVTK(i)->getIndex() - 1);
        fprintf(fp, "\n");
      }
    }
    
    void MElement::writeUNV(FILE *fp, int num, int elementary, int physical)
    {
      int type = getTypeForUNV();
      if(!type) return;
    
      int n = getNumVertices();
      int physical_property = elementary;
      int material_property = abs(physical);
      int color = 7;
      fprintf(fp, "%10d%10d%10d%10d%10d%10d\n",
              num ? num : _num, type, physical_property, material_property, color, n);
      if(type == 21 || type == 24) // linear beam or parabolic beam
        fprintf(fp, "%10d%10d%10d\n", 0, 0, 0);
    
      if(physical < 0) reverse();
    
      for(int k = 0; k < n; k++) {
        fprintf(fp, "%10d", getVertexUNV(k)->getIndex());
        if(k % 8 == 7)
          fprintf(fp, "\n");
      }
      if(n - 1 % 8 != 7)
        fprintf(fp, "\n");
    
      if(physical < 0) reverse();
    }
    
    void MElement::writeMESH(FILE *fp, int elementTagType, int elementary,
                             int physical)
    {
      if(physical < 0) reverse();
    
      for(int i = 0; i < getNumVertices(); i++)
        if (getTypeForMSH() == MSH_TET_10 && i == 8)
          fprintf(fp, " %d", getVertex(9)->getIndex());
        else if (getTypeForMSH() == MSH_TET_10 && i == 9)
          fprintf(fp, " %d", getVertex(8)->getIndex());
        else
          fprintf(fp, " %d", getVertex(i)->getIndex());
      fprintf(fp, " %d\n", (elementTagType == 3) ? _partition :
              (elementTagType == 2) ? abs(physical) : elementary);
    
      if(physical < 0) reverse();
    }
    
    void MElement::writeIR3(FILE *fp, int elementTagType, int num, int elementary,
                            int physical)
    {
      if(physical < 0) reverse();
    
      int numVert = getNumVertices();
      fprintf(fp, "%d %d %d", num, (elementTagType == 3) ? _partition :
              (elementTagType == 2) ? abs(physical) : elementary, numVert);
      for(int i = 0; i < numVert; i++)
        fprintf(fp, " %d", getVertex(i)->getIndex());
      fprintf(fp, "\n");
    
      if(physical < 0) reverse();
    }
    
    void MElement::writeBDF(FILE *fp, int format, int elementTagType, int elementary,
                            int physical)
    {
      const char *str = getStringForBDF();
      if(!str) return;
    
      int n = getNumVertices();
      const char *cont[4] = {"E", "F", "G", "H"};
      int ncont = 0;
    
      if(physical < 0) reverse();
    
      int tag =  (elementTagType == 3) ? _partition : (elementTagType == 2) ?
        abs(physical) : elementary;
    
      if(format == 0){ // free field format
        fprintf(fp, "%s,%d,%d", str, _num, tag);
        for(int i = 0; i < n; i++){
          fprintf(fp, ",%d", getVertexBDF(i)->getIndex());
          if(i != n - 1 && !((i + 3) % 8)){
            fprintf(fp, ",+%s%d\n+%s%d", cont[ncont], _num, cont[ncont], _num);
            ncont++;
          }
        }
        if(n == 2) // CBAR
          fprintf(fp, ",0.,0.,0.");
        fprintf(fp, "\n");
      }
      else{ // small or large field format
        fprintf(fp, "%-8s%-8d%-8d", str, _num, tag);
        for(int i = 0; i < n; i++){
          fprintf(fp, "%-8d", getVertexBDF(i)->getIndex());
          if(i != n - 1 && !((i + 3) % 8)){
            fprintf(fp, "+%s%-6d\n+%s%-6d", cont[ncont], _num, cont[ncont], _num);
            ncont++;
          }
        }
        if(n == 2) // CBAR
          fprintf(fp, "%-8s%-8s%-8s", "0.", "0.", "0.");
        fprintf(fp, "\n");
      }
    
      if(physical < 0) reverse();
    }
    
    void MElement::writeDIFF(FILE *fp, int num, bool binary, int physical)
    {
      const char *str = getStringForDIFF();
      if(!str) return;
    
      if(physical < 0) reverse();
    
      int n = getNumVertices();
      if(binary){
        // TODO
      }
      else{
        fprintf(fp, "%d %s %d ", num, str, abs(physical));
        for(int i = 0; i < n; i++)
          fprintf(fp, " %d", getVertexDIFF(i)->getIndex());
        fprintf(fp, "\n");
      }
    
      if(physical < 0) reverse();
    }
    
    void MElement::writeINP(FILE *fp, int num)
    {
      fprintf(fp, "%d, ", num);
      int n = getNumVertices();
      for(int i = 0; i < n; i++){
        fprintf(fp, "%d", getVertexINP(i)->getIndex());
        if(i != n - 1){
          fprintf(fp, ", ");
          if(i && !((i+2) % 16)) fprintf(fp, "\n");
        }
      }
      fprintf(fp, "\n");
    }
    
    void MElement::writeSU2(FILE *fp, int num)
    {
      fprintf(fp, "%d ", getTypeForVTK());
      for(int i = 0; i < getNumVertices(); i++)
        fprintf(fp, "%d ", getVertexVTK(i)->getIndex() - 1);
      if(num >= 0) fprintf(fp, "%d\n", num);
      else fprintf(fp, "\n");
    }
    
    int MElement::getInfoMSH(const int typeMSH, const char **const name)
    {
      switch(typeMSH){
      case MSH_PNT     : if(name) *name = "Point";            return 1;
      case MSH_LIN_1   : if(name) *name = "Line 1";           return 1;
      case MSH_LIN_2   : if(name) *name = "Line 2";           return 2;
      case MSH_LIN_3   : if(name) *name = "Line 3";           return 2 + 1;
      case MSH_LIN_4   : if(name) *name = "Line 4";           return 2 + 2;
      case MSH_LIN_5   : if(name) *name = "Line 5";           return 2 + 3;
      case MSH_LIN_6   : if(name) *name = "Line 6";           return 2 + 4;
      case MSH_LIN_7   : if(name) *name = "Line 7";           return 2 + 5;
      case MSH_LIN_8   : if(name) *name = "Line 8";           return 2 + 6;
      case MSH_LIN_9   : if(name) *name = "Line 9";           return 2 + 7;
      case MSH_LIN_10  : if(name) *name = "Line 10";          return 2 + 8;
      case MSH_LIN_11  : if(name) *name = "Line 11";          return 2 + 9;
      case MSH_LIN_B   : if(name) *name = "Line Border";      return 2;
      case MSH_LIN_C   : if(name) *name = "Line Child";       return 2;
      case MSH_TRI_1   : if(name) *name = "Triangle 1";       return 1;
      case MSH_TRI_3   : if(name) *name = "Triangle 3";       return 3;
      case MSH_TRI_6   : if(name) *name = "Triangle 6";       return 3 + 3;
      case MSH_TRI_9   : if(name) *name = "Triangle 9";       return 3 + 6;
      case MSH_TRI_10  : if(name) *name = "Triangle 10";      return 3 + 6 + 1;
      case MSH_TRI_12  : if(name) *name = "Triangle 12";      return 3 + 9;
      case MSH_TRI_15  : if(name) *name = "Triangle 15";      return 3 + 9 + 3;
      case MSH_TRI_15I : if(name) *name = "Triangle 15I";     return 3 + 12;
      case MSH_TRI_21  : if(name) *name = "Triangle 21";      return 3 + 12 + 6;
      case MSH_TRI_28  : if(name) *name = "Triangle 28";      return 3 + 15 + 10;
      case MSH_TRI_36  : if(name) *name = "Triangle 36";      return 3 + 18 + 15;
      case MSH_TRI_45  : if(name) *name = "Triangle 45";      return 3 + 21 + 21;
      case MSH_TRI_55  : if(name) *name = "Triangle 55";      return 3 + 24 + 28;
      case MSH_TRI_66  : if(name) *name = "Triangle 66";      return 3 + 27 + 36;
      case MSH_TRI_18  : if(name) *name = "Triangle 18";      return 3 + 15;
      case MSH_TRI_21I : if(name) *name = "Triangle 21I";     return 3 + 18;
      case MSH_TRI_24  : if(name) *name = "Triangle 24";      return 3 + 21;
      case MSH_TRI_27  : if(name) *name = "Triangle 27";      return 3 + 24;
      case MSH_TRI_30  : if(name) *name = "Triangle 30";      return 3 + 27;
      case MSH_TRI_B   : if(name) *name = "Triangle Border";  return 3;
      case MSH_QUA_1   : if(name) *name = "Quadrilateral 1";  return 1;
      case MSH_QUA_4   : if(name) *name = "Quadrilateral 4";  return 4;
      case MSH_QUA_8   : if(name) *name = "Quadrilateral 8";  return 4 + 4;
      case MSH_QUA_9   : if(name) *name = "Quadrilateral 9";  return 9;
      case MSH_QUA_16  : if(name) *name = "Quadrilateral 16"; return 16;
      case MSH_QUA_25  : if(name) *name = "Quadrilateral 25"; return 25;
      case MSH_QUA_36  : if(name) *name = "Quadrilateral 36"; return 36;
      case MSH_QUA_49  : if(name) *name = "Quadrilateral 49"; return 49;
      case MSH_QUA_64  : if(name) *name = "Quadrilateral 64"; return 64;
      case MSH_QUA_81  : if(name) *name = "Quadrilateral 81"; return 81;
      case MSH_QUA_100 : if(name) *name = "Quadrilateral 100";return 100;
      case MSH_QUA_121 : if(name) *name = "Quadrilateral 121";return 121;
      case MSH_QUA_12  : if(name) *name = "Quadrilateral 12"; return 12;
      case MSH_QUA_16I : if(name) *name = "Quadrilateral 16I";return 16;
      case MSH_QUA_20  : if(name) *name = "Quadrilateral 20"; return 20;
      case MSH_QUA_24  : if(name) *name = "Quadrilateral 24"; return 24;
      case MSH_QUA_28  : if(name) *name = "Quadrilateral 28"; return 28;
      case MSH_QUA_32  : if(name) *name = "Quadrilateral 32"; return 32;
      case MSH_QUA_36I : if(name) *name = "Quadrilateral 36I";return 36;
      case MSH_QUA_40  : if(name) *name = "Quadrilateral 40"; return 40;
      case MSH_POLYG_  : if(name) *name = "Polygon";          return 0;
      case MSH_POLYG_B : if(name) *name = "Polygon Border";   return 0;
      case MSH_TET_1   : if(name) *name = "Tetrahedron 1";    return 1;
      case MSH_TET_4   : if(name) *name = "Tetrahedron 4";    return 4;
      case MSH_TET_10  : if(name) *name = "Tetrahedron 10";   return 4 + 6;
      case MSH_TET_20  : if(name) *name = "Tetrahedron 20";   return 4 + 12 + 4;
      case MSH_TET_35  : if(name) *name = "Tetrahedron 35";   return 4 + 18 + 12 + 1;
      case MSH_TET_56  : if(name) *name = "Tetrahedron 56";   return 4 + 24 + 24 + 4;
      case MSH_TET_84  : if(name) *name = "Tetrahedron 84";   return (7*8*9)/6;
      case MSH_TET_120 : if(name) *name = "Tetrahedron 120";  return (8*9*10)/6;
      case MSH_TET_165 : if(name) *name = "Tetrahedron 165";  return (9*10*11)/6;
      case MSH_TET_220 : if(name) *name = "Tetrahedron 220";  return (10*11*12)/6;
      case MSH_TET_286 : if(name) *name = "Tetrahedron 286";  return (11*12*13)/6;
      case MSH_TET_16  : if(name) *name = "Tetrahedron 16";   return 4 + 6*2;
      case MSH_TET_22  : if(name) *name = "Tetrahedron 22";   return 4 + 6*3;
      case MSH_TET_28  : if(name) *name = "Tetrahedron 28";   return 4 + 6*4;
      case MSH_TET_34  : if(name) *name = "Tetrahedron 34";   return 4 + 6*5;
      case MSH_TET_40  : if(name) *name = "Tetrahedron 40";   return 4 + 6*6;
      case MSH_TET_46  : if(name) *name = "Tetrahedron 46";   return 4 + 6*7;
      case MSH_TET_52  : if(name) *name = "Tetrahedron 52";   return 4 + 6*8;
      case MSH_TET_58  : if(name) *name = "Tetrahedron 58";   return 4 + 6*9;
      case MSH_HEX_1   : if(name) *name = "Hexahedron 1";     return 1;
      case MSH_HEX_8   : if(name) *name = "Hexahedron 8";     return 8;
      case MSH_HEX_20  : if(name) *name = "Hexahedron 20";    return 8 + 12;
      case MSH_HEX_27  : if(name) *name = "Hexahedron 27";    return 8 + 12 + 6 + 1;
      case MSH_HEX_64  : if(name) *name = "Hexahedron 64";    return 64;
      case MSH_HEX_125 : if(name) *name = "Hexahedron 125";   return 125;
      case MSH_HEX_216 : if(name) *name = "Hexahedron 216";   return 216;
      case MSH_HEX_343 : if(name) *name = "Hexahedron 343";   return 343;
      case MSH_HEX_512 : if(name) *name = "Hexahedron 512";   return 512;
      case MSH_HEX_729 : if(name) *name = "Hexahedron 729";   return 729;
      case MSH_HEX_1000: if(name) *name = "Hexahedron 1000";  return 1000;
      case MSH_HEX_32  : if(name) *name = "Hexahedron 32";    return 8 + 12*2;
      case MSH_HEX_44  : if(name) *name = "Hexahedron 44";    return 8 + 12*3;
      case MSH_HEX_56  : if(name) *name = "Hexahedron 56";    return 8 + 12*4;
      case MSH_HEX_68  : if(name) *name = "Hexahedron 68";    return 8 + 12*5;
      case MSH_HEX_80  : if(name) *name = "Hexahedron 80";    return 8 + 12*6;
      case MSH_HEX_92  : if(name) *name = "Hexahedron 92";    return 8 + 12*7;
      case MSH_HEX_104 : if(name) *name = "Hexahedron 104";   return 8 + 12*8;
      case MSH_PRI_1   : if(name) *name = "Prism 1";          return 1;
      case MSH_PRI_6   : if(name) *name = "Prism 6";          return 6;
      case MSH_PRI_15  : if(name) *name = "Prism 15";         return 6 + 9;
      case MSH_PRI_18  : if(name) *name = "Prism 18";         return 6 + 9 + 3;
      case MSH_PRI_40  : if(name) *name = "Prism 40";         return 6 + 18 + 12+2 + 2*1;
      case MSH_PRI_75  : if(name) *name = "Prism 75";         return 6 + 27 + 27+6 + 3*3;
      case MSH_PRI_126 : if(name) *name = "Prism 126";        return 6 + 36 + 48+12 + 4*6;
      case MSH_PRI_196 : if(name) *name = "Prism 196";        return 6 + 45 + 75+20 + 5*10;
      case MSH_PRI_288 : if(name) *name = "Prism 288";        return 6 + 54 + 108+30 + 6*15;
      case MSH_PRI_405 : if(name) *name = "Prism 405";        return 6 + 63 + 147+42 + 7*21;
      case MSH_PRI_550 : if(name) *name = "Prism 550";        return 6 + 72 + 192+56 + 8*28;
      case MSH_PRI_24  : if(name) *name = "Prism 24";         return 6 + 9*2;
      case MSH_PRI_33  : if(name) *name = "Prism 33";         return 6 + 9*3;
      case MSH_PRI_42  : if(name) *name = "Prism 42";         return 6 + 9*4;
      case MSH_PRI_51  : if(name) *name = "Prism 51";         return 6 + 9*5;
      case MSH_PRI_60  : if(name) *name = "Prism 60";         return 6 + 9*6;
      case MSH_PRI_69  : if(name) *name = "Prism 69";         return 6 + 9*7;
      case MSH_PRI_78  : if(name) *name = "Prism 78";         return 6 + 9*8;
      case MSH_PYR_1   : if(name) *name = "Pyramid 1";        return 1;
      case MSH_PYR_5   : if(name) *name = "Pyramid 5";        return 5;
      case MSH_PYR_13  : if(name) *name = "Pyramid 13";       return 5 + 8;
      case MSH_PYR_14  : if(name) *name = "Pyramid 14";       return 5 + 8 + 1;
      case MSH_PYR_30  : if(name) *name = "Pyramid 30";       return 5 + 8*2 + 4*1  + 1*4  + 1;
      case MSH_PYR_55  : if(name) *name = "Pyramid 55";       return 5 + 8*3 + 4*3  + 1*9  + 5;
      case MSH_PYR_91  : if(name) *name = "Pyramid 91";       return 5 + 8*4 + 4*6  + 1*16 + 14;
      case MSH_PYR_140 : if(name) *name = "Pyramid 140";      return 5 + 8*5 + 4*10 + 1*25 + 30;
      case MSH_PYR_204 : if(name) *name = "Pyramid 204";      return 5 + 8*6 + 4*15 + 1*36 + 55;
      case MSH_PYR_285 : if(name) *name = "Pyramid 285";      return 5 + 8*7 + 4*21 + 1*49 + 91;
      case MSH_PYR_385 : if(name) *name = "Pyramid 385";      return 5 + 8*8 + 4*28 + 1*64 + 140;
      case MSH_PYR_21  : if(name) *name = "Pyramid 21";       return 5 + 8*2;
      case MSH_PYR_29  : if(name) *name = "Pyramid 29";       return 5 + 8*3;
      case MSH_PYR_37  : if(name) *name = "Pyramid 37";       return 5 + 8*4;
      case MSH_PYR_45  : if(name) *name = "Pyramid 45";       return 5 + 8*5;
      case MSH_PYR_53  : if(name) *name = "Pyramid 53";       return 5 + 8*6;
      case MSH_PYR_61  : if(name) *name = "Pyramid 61";       return 5 + 8*7;
      case MSH_PYR_69  : if(name) *name = "Pyramid 69";       return 5 + 8*8;
      case MSH_TRIH_4 : if(name) *name = "Trihedron 4";       return 4;
      case MSH_POLYH_  : if(name) *name = "Polyhedron";       return 0;
      case MSH_PNT_SUB : if(name) *name = "Point Xfem";       return 1;
      case MSH_LIN_SUB : if(name) *name = "Line Xfem";        return 2;
      case MSH_TRI_SUB : if(name) *name = "Triangle Xfem";    return 3;
      case MSH_TET_SUB : if(name) *name = "Tetrahedron Xfem"; return 4;
      default:
        Msg::Error("Unknown type of element %d", typeMSH);
        if(name) *name = "Unknown";
        return 0;
      }
    }
    
    void MElement::getVerticesIdForMSH(std::vector<int> &verts)
    {
      int n = getNumVerticesForMSH();
      verts.resize(n);
      for(int i = 0; i < n; i++)
        verts[i] = getVertex(i)->getIndex();
    }
    
    MElement *MElement::copy(std::map<int, MVertex*> &vertexMap,
                             std::map<MElement*, MElement*> &newParents,
                             std::map<MElement*, MElement*> &newDomains)
    {
      if(newDomains.count(this))
        return newDomains.find(this)->second;
      std::vector<MVertex*> vmv;
      int eType = getTypeForMSH();
      MElement *eParent = getParent();
      if(getNumChildren() == 0) {
        for(int i = 0; i < getNumVertices(); i++) {
          MVertex *v = getVertex(i);
          int numV = v->getNum(); //Index();
          if(vertexMap.count(numV))
            vmv.push_back(vertexMap[numV]);
          else {
            MVertex *mv = new MVertex(v->x(), v->y(), v->z(), 0, numV);
            vmv.push_back(mv);
            vertexMap[numV] = mv;
          }
        }
      }
      else {
        for(int i = 0; i < getNumChildren(); i++) {
          for(int j = 0; j < getChild(i)->getNumVertices(); j++) {
            MVertex *v = getChild(i)->getVertex(j);
            int numV = v->getNum(); //Index();
            if(vertexMap.count(numV))
              vmv.push_back(vertexMap[numV]);
            else {
              MVertex *mv = new MVertex(v->x(), v->y(), v->z(), 0, numV);
              vmv.push_back(mv);
              vertexMap[numV] = mv;
            }
          }
        }
      }
    
      MElement *parent=0;
      if(eParent && !getDomain(0) && !getDomain(1)) {
        std::map<MElement*, MElement*>::iterator it = newParents.find(eParent);
        MElement *newParent;
        if(it == newParents.end()) {
          newParent = eParent->copy(vertexMap, newParents, newDomains);
          newParents[eParent] = newParent;
        }
        else
          newParent = it->second;
        parent = newParent;
      }
    
      MElementFactory f;
      MElement *newEl = f.create(eType, vmv, getNum(), _partition, ownsParent(), 0, parent);
    
      for(int i = 0; i < 2; i++) {
        MElement *dom = getDomain(i);
        if(!dom) continue;
        std::map<MElement*, MElement*>::iterator it = newDomains.find(dom);
        MElement *newDom;
        if(it == newDomains.end()) {
          newDom = dom->copy(vertexMap, newParents, newDomains);
          newDomains[dom] = newDom;
        }
        else
          newDom = newDomains.find(dom)->second;
        newEl->setDomain(newDom, i);
      }
      return newEl;
    }
    
    MElement *MElementFactory::create(int type, std::vector<MVertex*> &v,
                                      int num, int part, bool owner,
                                      int parent, MElement* parent_ptr,
                                      MElement *d1, MElement *d2)
    {
      switch (type) {
      case MSH_PNT:     return new MPoint(v, num, part);
      case MSH_LIN_2:   return new MLine(v, num, part);
      case MSH_LIN_3:   return new MLine3(v, num, part);
      case MSH_LIN_4:   return new MLineN(v, num, part);
      case MSH_LIN_5:   return new MLineN(v, num, part);
      case MSH_LIN_6:   return new MLineN(v, num, part);
      case MSH_LIN_7:   return new MLineN(v, num, part);
      case MSH_LIN_8:   return new MLineN(v, num, part);
      case MSH_LIN_9:   return new MLineN(v, num, part);
      case MSH_LIN_10:  return new MLineN(v, num, part);
      case MSH_LIN_11:  return new MLineN(v, num, part);
      case MSH_LIN_B:   return new MLineBorder(v, num, part, d1, d2);
      case MSH_LIN_C:   return new MLineChild(v, num, part, owner, parent_ptr);
      case MSH_TRI_3:   return new MTriangle(v, num, part);
      case MSH_TRI_6:   return new MTriangle6(v, num, part);
      case MSH_TRI_10:  return new MTriangleN(v, 3, num, part);
      case MSH_TRI_15:  return new MTriangleN(v, 4, num, part);
      case MSH_TRI_21:  return new MTriangleN(v, 5, num, part);
      case MSH_TRI_28:  return new MTriangleN(v, 6, num, part);
      case MSH_TRI_36:  return new MTriangleN(v, 7, num, part);
      case MSH_TRI_45:  return new MTriangleN(v, 8, num, part);
      case MSH_TRI_55:  return new MTriangleN(v, 9, num, part);
      case MSH_TRI_66:  return new MTriangleN(v,10, num, part);
      case MSH_TRI_9:   return new MTriangleN(v, 3, num, part);
      case MSH_TRI_12:  return new MTriangleN(v, 4, num, part);
      case MSH_TRI_15I: return new MTriangleN(v, 5, num, part);
      case MSH_TRI_18:  return new MTriangleN(v, 6, num, part);
      case MSH_TRI_21I: return new MTriangleN(v, 7, num, part);
      case MSH_TRI_24:  return new MTriangleN(v, 8, num, part);
      case MSH_TRI_27:  return new MTriangleN(v, 9, num, part);
      case MSH_TRI_30:  return new MTriangleN(v,10, num, part);
      case MSH_TRI_B:   return new MTriangleBorder(v, num, part, d1, d2);
      case MSH_QUA_4:   return new MQuadrangle(v, num, part);
      case MSH_QUA_9:   return new MQuadrangle9(v, num, part);
      case MSH_QUA_16:  return new MQuadrangleN(v, 3, num, part);
      case MSH_QUA_25:  return new MQuadrangleN(v, 4, num, part);
      case MSH_QUA_36:  return new MQuadrangleN(v, 5, num, part);
      case MSH_QUA_49:  return new MQuadrangleN(v, 6, num, part);
      case MSH_QUA_64:  return new MQuadrangleN(v, 7, num, part);
      case MSH_QUA_81:  return new MQuadrangleN(v, 8, num, part);
      case MSH_QUA_100: return new MQuadrangleN(v, 9, num, part);
      case MSH_QUA_121: return new MQuadrangleN(v, 10, num, part);
      case MSH_QUA_8:   return new MQuadrangle8(v, num, part);
      case MSH_QUA_12:  return new MQuadrangleN(v, 3, num, part);
      case MSH_QUA_16I: return new MQuadrangleN(v, 4, num, part);
      case MSH_QUA_20:  return new MQuadrangleN(v, 5, num, part);
      case MSH_QUA_24:  return new MQuadrangleN(v, 6, num, part);
      case MSH_QUA_28:  return new MQuadrangleN(v, 7, num, part);
      case MSH_QUA_32:  return new MQuadrangleN(v, 8, num, part);
      case MSH_QUA_36I: return new MQuadrangleN(v, 9, num, part);
      case MSH_QUA_40:  return new MQuadrangleN(v,10, num, part);
      case MSH_POLYG_:  return new MPolygon(v, num, part, owner, parent_ptr);
      case MSH_POLYG_B: return new MPolygonBorder(v, num, part, d1, d2);
      case MSH_TET_4:   return new MTetrahedron(v, num, part);
      case MSH_TET_10:  return new MTetrahedron10(v, num, part);
      case MSH_HEX_8:   return new MHexahedron(v, num, part);
      case MSH_HEX_20:  return new MHexahedron20(v, num, part);
      case MSH_HEX_27:  return new MHexahedron27(v, num, part);
      case MSH_PRI_6:   return new MPrism(v, num, part);
      case MSH_PRI_15:  return new MPrism15(v, num, part);
      case MSH_PRI_18:  return new MPrism18(v, num, part);
      case MSH_PRI_40:  return new MPrismN(v, 3, num, part);
      case MSH_PRI_75:  return new MPrismN(v, 4, num, part);
      case MSH_PRI_126: return new MPrismN(v, 5, num, part);
      case MSH_PRI_196: return new MPrismN(v, 6, num, part);
      case MSH_PRI_288: return new MPrismN(v, 7, num, part);
      case MSH_PRI_405: return new MPrismN(v, 8, num, part);
      case MSH_PRI_550: return new MPrismN(v, 9, num, part);
      case MSH_PRI_24:  return new MPrismN(v, 3, num, part);
      case MSH_PRI_33:  return new MPrismN(v, 4, num, part);
      case MSH_PRI_42:  return new MPrismN(v, 5, num, part);
      case MSH_PRI_51:  return new MPrismN(v, 6, num, part);
      case MSH_PRI_60:  return new MPrismN(v, 7, num, part);
      case MSH_PRI_69:  return new MPrismN(v, 8, num, part);
      case MSH_PRI_78:  return new MPrismN(v, 9, num, part);
      case MSH_PRI_1:   return new MPrismN(v, 0, num, part);
      case MSH_TET_20:  return new MTetrahedronN(v, 3, num, part);
      case MSH_TET_35:  return new MTetrahedronN(v, 4, num, part);
      case MSH_TET_56:  return new MTetrahedronN(v, 5, num, part);
      case MSH_TET_84:  return new MTetrahedronN(v, 6, num, part);
      case MSH_TET_120: return new MTetrahedronN(v, 7, num, part);
      case MSH_TET_165: return new MTetrahedronN(v, 8, num, part);
      case MSH_TET_220: return new MTetrahedronN(v, 9, num, part);
      case MSH_TET_286: return new MTetrahedronN(v, 10, num, part);
      case MSH_TET_16:  return new MTetrahedronN(v, 3, num, part);
      case MSH_TET_22:  return new MTetrahedronN(v, 4, num, part);
      case MSH_TET_28:  return new MTetrahedronN(v, 5, num, part);
      case MSH_TET_34:  return new MTetrahedronN(v, 6, num, part);
      case MSH_TET_40:  return new MTetrahedronN(v, 7, num, part);
      case MSH_TET_46:  return new MTetrahedronN(v, 8, num, part);
      case MSH_TET_52:  return new MTetrahedronN(v, 9, num, part);
      case MSH_TET_58:  return new MTetrahedronN(v, 10, num, part);
      case MSH_POLYH_:  return new MPolyhedron(v, num, part, owner, parent_ptr);
      case MSH_HEX_32:  return new MHexahedronN(v, 3, num, part);
      case MSH_HEX_64:  return new MHexahedronN(v, 3, num, part);
      case MSH_HEX_125: return new MHexahedronN(v, 4, num, part);
      case MSH_HEX_216: return new MHexahedronN(v, 5, num, part);
      case MSH_HEX_343: return new MHexahedronN(v, 6, num, part);
      case MSH_HEX_512: return new MHexahedronN(v, 7, num, part);
      case MSH_HEX_729: return new MHexahedronN(v, 8, num, part);
      case MSH_HEX_1000:return new MHexahedronN(v, 9, num, part);
      case MSH_PNT_SUB: return (parent_ptr) ? new MSubPoint(v, num, part, owner, parent_ptr)
                                            : new MSubPoint(v, num, part, owner, parent);
      case MSH_LIN_SUB: return (parent_ptr) ? new MSubLine(v, num, part, owner, parent_ptr)
                                            : new MSubLine(v, num, part, owner, parent);
      case MSH_TRI_SUB: return (parent_ptr) ? new MSubTriangle(v, num, part, owner, parent_ptr)
                                            : new MSubTriangle(v, num, part, owner, parent);
      case MSH_TET_SUB: return (parent_ptr) ? new MSubTetrahedron(v, num, part, owner, parent_ptr)
                                            : new MSubTetrahedron(v, num, part, owner, parent);
      case MSH_PYR_5:   return new MPyramid(v, num, part);
      case MSH_PYR_13:  return new MPyramidN(v, 2, num, part);
      case MSH_PYR_14:  return new MPyramidN(v, 2, num, part);
      case MSH_PYR_30:  return new MPyramidN(v, 3, num, part);
      case MSH_PYR_55:  return new MPyramidN(v, 4, num, part);
      case MSH_PYR_91:  return new MPyramidN(v, 5, num, part);
      case MSH_PYR_140: return new MPyramidN(v, 6, num, part);
      case MSH_PYR_204: return new MPyramidN(v, 7, num, part);
      case MSH_PYR_285: return new MPyramidN(v, 8, num, part);
      case MSH_PYR_385: return new MPyramidN(v, 9, num, part);
      case MSH_TRIH_4: return new MTrihedron(v, num, part);
      default:          return 0;
      }
    }
    
    MElement *MElementFactory::create(int num, int type, const std::vector<int> &data,
                                      GModel *model)
    {
      // This should be rewritten: each element should register itself in a static
      // factory owned e.g. directly by MElement, and interpret its data by
      // itself. This would remove the ugly switch in the routine above.
    
      int numVertices = MElement::getInfoMSH(type), startVertices = 0;
      if(data.size() && !numVertices){
        startVertices = 1;
        numVertices = data[0];
      }
    
      std::vector<MVertex*> vertices(numVertices);
      if((int) data.size() > startVertices + numVertices - 1){
        for(int i = 0; i < numVertices; i++){
          int numVertex = data[startVertices + i];
          MVertex *v = model->getMeshVertexByTag(numVertex);
          if(v){
            vertices[i] = v;
          }
          else{
            Msg::Error("Unknown vertex %d in element %d", numVertex, num);
            return 0;
          }
        }
      }
      else{
        Msg::Error("Missing data in element %d", num);
        return 0;
      }
    
      int part = 0;
      int startPartitions = startVertices + numVertices;
    
     int parent = 0;
      if((type == MSH_PNT_SUB || type == MSH_LIN_SUB ||
          type == MSH_TRI_SUB || type == MSH_TET_SUB)){
        parent = data[startPartitions];
        startPartitions += 1;
      }
    
      std::vector<short> ghosts;
      if((int) data.size() > startPartitions){
        int numPartitions = data[startPartitions];
        if(numPartitions > 0 && (int) data.size() > startPartitions + numPartitions - 1){
          part = data[startPartitions + 1];
          for(int i = 1; i < numPartitions; i++)
            ghosts.push_back(data[startPartitions + 1 + i]);
        }
      }
    
      MElement *element = create(type, vertices, num, part, false, parent);
    
      for(unsigned int j = 0; j < ghosts.size(); j++)
        model->getGhostCells().insert(std::pair<MElement*, short>(element, ghosts[j]));
      if(part) model->getMeshPartitions().insert(part);
    
      return element;
    }
    
    double MElement::skewness()
    {
      double minsk = 1.0;
      for (int i=0;i<getNumFaces();i++){
        MFace f = getFace(i);
        if (f.getNumVertices() == 3){
          //      MTriangle t (f.getVertex(0),f.getVertex(1),f.getVertex(2));
          //      minsk = std::min(minsk, t.etaShapeMeasure ());
        }
        else if (f.getNumVertices() == 4){
          MQuadrangle q (f.getVertex(0),f.getVertex(1),f.getVertex(2),f.getVertex(3));
          minsk = std::min(minsk, q.etaShapeMeasure ());
        }
      }
      return minsk;
    }