netgen/libsrc/meshing/improve2.cpp

#include <mystdlib.h>

#include "meshing.hpp"
#include <opti.hpp>


namespace netgen
{

  class Neighbour
  {
    int nr[3];
    int orient[3];

  public:
    Neighbour () { ; } 

    void SetNr (int side, int anr) { nr[side] = anr; }
    int GetNr (int side) { return nr[side]; }

    void SetOrientation (int side, int aorient) { orient[side] = aorient; }
    int GetOrientation (int side) { return orient[side]; }
  };




  class trionedge
  {
  public:
    SurfaceElementIndex tnr;
    int sidenr;

    trionedge () { tnr = 0; sidenr = 0; }
    trionedge (SurfaceElementIndex atnr, int asidenr)
    { tnr = atnr; sidenr = asidenr; }
  };



 
  void MeshOptimize2d :: EdgeSwapping (Mesh & mesh, int usemetric)
  {
    static Timer timer("EdgeSwapping (2D)"); RegionTimer reg(timer);
    if (!faceindex)
      {
	if (usemetric)
	  PrintMessage (3, "Edgeswapping, metric");
	else
	  PrintMessage (3, "Edgeswapping, topological");

	for (faceindex = 1; faceindex <= mesh.GetNFD(); faceindex++)
	  {
	    EdgeSwapping (mesh, usemetric);

	    if (multithread.terminate)
	      throw NgException ("Meshing stopped");
	  }

	faceindex = 0;
	mesh.CalcSurfacesOfNode();
	return;
      }


    static int timerstart = NgProfiler::CreateTimer ("EdgeSwapping 2D start");
    NgProfiler::StartTimer (timerstart);


    Array<SurfaceElementIndex> seia;
    mesh.GetSurfaceElementsOfFace (faceindex, seia);

    /*
    for (int i = 0; i < seia.Size(); i++)
      if (mesh[seia[i]].GetNP() != 3)
	{
	  GenericImprove (mesh);
	  return;
	}
    */
    for (SurfaceElementIndex sei : seia)
      if (mesh[sei].GetNP() != 3)
	{
	  GenericImprove (mesh);
	  return;
	}
      
    int surfnr = mesh.GetFaceDescriptor (faceindex).SurfNr();

    Array<Neighbour> neighbors(mesh.GetNSE());
    INDEX_2_HASHTABLE<trionedge> other(2*seia.Size() + 2);


    Array<bool> swapped(mesh.GetNSE());
    NgArray<int,PointIndex::BASE> pdef(mesh.GetNP());
    NgArray<double,PointIndex::BASE> pangle(mesh.GetNP());


    // int e;
    // double d;
    // Vec3d nv1, nv2;

    // double loch(-1);
    static const double minangle[] = { 0, 1.481, 2.565, 3.627, 4.683, 5.736, 7, 9 };


    for (int i = 0; i < seia.Size(); i++)
      {
	const Element2d & sel = mesh[seia[i]];
	for (int j = 0; j < 3; j++)
	  pangle[sel[j]] = 0.0;
      }
    // pangle = 0;

    for (int i = 0; i < seia.Size(); i++)
      {
	const Element2d & sel = mesh[seia[i]];
	for (int j = 0; j < 3; j++)
	  {
	    POINTTYPE typ = mesh[sel[j]].Type();
	    if (typ == FIXEDPOINT || typ == EDGEPOINT)
	      {
		pangle[sel[j]] +=
		  Angle (mesh[sel[(j+1)%3]] - mesh[sel[j]],
			 mesh[sel[(j+2)%3]] - mesh[sel[j]]);
	      }
	  }
      }

    // for (PointIndex pi = PointIndex::BASE; 
    // pi < mesh.GetNP()+PointIndex::BASE; pi++)
    
    // pdef = 0;
    for (int i = 0; i < seia.Size(); i++)
      {
	const Element2d & sel = mesh[seia[i]];
	for (int j = 0; j < 3; j++)
	  {
	    PointIndex pi = sel[j];
	    if (mesh[pi].Type() == INNERPOINT || mesh[pi].Type() == SURFACEPOINT)
	      pdef[pi] = -6;
	    else
	      for (int j = 0; j < 8; j++)
		if (pangle[pi] >= minangle[j])
		  pdef[pi] = -1-j;
	  }
      }

    /*
    for (int i = 0; i < seia.Size(); i++)
      {
	const Element2d & sel = mesh[seia[i]];
	for (int j = 0; j < 3; j++)
	  pdef[sel[j]]++;
      }
    */
    for (SurfaceElementIndex sei : seia)
      for (PointIndex pi : mesh[sei].PNums<3>())
        pdef[pi]++;
    
    // for (int i = 0; i < seia.Size(); i++)
    for (SurfaceElementIndex sei : seia)
      for (int j = 0; j < 3; j++)
        {
          neighbors[sei].SetNr (j, -1);
          neighbors[sei].SetOrientation (j, 0);
        }

    /*
      NgArray<Vec3d> normals(mesh.GetNP());
      for (i = 1; i <= mesh.GetNSE(); i++)
      {
      Element2d & hel = mesh.SurfaceElement(i);
      if (hel.GetIndex() == faceindex)
      for (k = 1; k <= 3; k++)
      {
      int pi = hel.PNum(k);
      SelectSurfaceOfPoint (mesh.Point(pi), hel.GeomInfoPi(k));
      int surfi = mesh.GetFaceDescriptor(faceindex).SurfNr();
      GetNormalVector (surfi, mesh.Point(pi), normals.Elem(pi));
      normals.Elem(pi) /= normals.Elem(pi).Length();
      }
      }
    */	    

    /*
    for (int i = 0; i < seia.Size(); i++)
      {
	const Element2d & sel = mesh[seia[i]];
    */

    for (SurfaceElementIndex sei : seia)
      {
	const Element2d & sel = mesh[sei];
        
	for (int j = 0; j < 3; j++)
	  {
	    PointIndex pi1 = sel.PNumMod(j+2);
	    PointIndex pi2 = sel.PNumMod(j+3);
	  
	    //	    double loch = mesh.GetH(mesh[pi1]);
	    
	    // INDEX_2 edge(pi1, pi2);
	    // edge.Sort();
	  
	    if (mesh.IsSegment (pi1, pi2))
	      continue;
	  
	    /*
	      if (segments.Used (edge))
	      continue;
	    */
	    INDEX_2 ii2 (pi1, pi2);
	    if (other.Used (ii2))
	      {
		// INDEX_2 i2s(ii2);
		// i2s.Sort();

                /*
		int i2 = other.Get(ii2).tnr;
		int j2 = other.Get(ii2).sidenr;
		*/
                auto othertrig = other.Get(ii2);
		SurfaceElementIndex i2 = othertrig.tnr;
		int j2 = othertrig.sidenr;
                
		neighbors[sei].SetNr (j, i2);
		neighbors[sei].SetOrientation (j, j2);
		neighbors[i2].SetNr (j2, sei);
		neighbors[i2].SetOrientation (j2, j);
	      }
	    else
	      {
		other.Set (INDEX_2 (pi2, pi1), trionedge (sei, j));
	      }
	  }
      }

    for (SurfaceElementIndex sei : seia)
      swapped[sei] = false;
    
    NgProfiler::StopTimer (timerstart);
  


    int t = 4;
    bool done = false;
    while (!done && t >= 2)
      {
	for (int i = 0; i < seia.Size(); i++)
	  {
	    SurfaceElementIndex t1 = seia[i];

	    if (mesh[t1].IsDeleted())
	      continue;

	    if (mesh[t1].GetIndex() != faceindex)
	      continue;

	    if (multithread.terminate)
	      throw NgException ("Meshing stopped");

	    for (int o1 = 0; o1 < 3; o1++)
	      {
		bool should;

		SurfaceElementIndex t2 = neighbors[t1].GetNr (o1);
		int o2 = neighbors[t1].GetOrientation (o1);

		if (t2 == -1) continue;
		if (swapped[t1] || swapped[t2]) continue;
	      

		PointIndex pi1 = mesh[t1].PNumMod(o1+1+1);
		PointIndex pi2 = mesh[t1].PNumMod(o1+1+2);
		PointIndex pi3 = mesh[t1].PNumMod(o1+1);
		PointIndex pi4 = mesh[t2].PNumMod(o2+1);
	      
		PointGeomInfo gi1 = mesh[t1].GeomInfoPiMod(o1+1+1);
		PointGeomInfo gi2 = mesh[t1].GeomInfoPiMod(o1+1+2);
		PointGeomInfo gi3 = mesh[t1].GeomInfoPiMod(o1+1);
		PointGeomInfo gi4 = mesh[t2].GeomInfoPiMod(o2+1);
	    
		bool allowswap = true;

		Vec<3> auxvec1 = mesh[pi3]-mesh[pi4];
		Vec<3> auxvec2 = mesh[pi1]-mesh[pi4];

		allowswap = allowswap && fabs(1.-(auxvec1*auxvec2)/(auxvec1.Length()*auxvec2.Length())) > 1e-4;

		if(!allowswap)
		  continue;

		// normal of new
		Vec<3> nv1 = Cross (auxvec1, auxvec2);

		auxvec1 = mesh.Point(pi4)-mesh.Point(pi3);
		auxvec2 = mesh.Point(pi2)-mesh.Point(pi3);
		allowswap = allowswap && fabs(1.-(auxvec1*auxvec2)/(auxvec1.Length()*auxvec2.Length())) > 1e-4;


		if(!allowswap)
		  continue;

		Vec<3> nv2 = Cross (auxvec1, auxvec2);

	      
		// normals of original
		Vec<3> nv3 = Cross (mesh[pi1]-mesh[pi4], mesh[pi2]-mesh[pi4]);
		Vec<3> nv4 = Cross (mesh[pi2]-mesh[pi3], mesh[pi1]-mesh[pi3]);
	      
		nv3 *= -1;
		nv4 *= -1;
		nv3.Normalize();
		nv4.Normalize();

		nv1.Normalize();
		nv2.Normalize();
	    
		Vec<3> nvp3, nvp4;
		SelectSurfaceOfPoint (mesh.Point(pi3), gi3);
		GetNormalVector (surfnr, mesh.Point(pi3), gi3, nvp3);

		nvp3.Normalize();

		SelectSurfaceOfPoint (mesh.Point(pi4), gi4);
		GetNormalVector (surfnr, mesh.Point(pi4), gi4, nvp4);
	    
		nvp4.Normalize();
	      
	      
	      
		double critval = cos (M_PI / 6);  // 30 degree
		allowswap = allowswap &&
		  (nv1 * nvp3 > critval) && 
		  (nv1 * nvp4 > critval) && 
		  (nv2 * nvp3 > critval) && 
		  (nv2 * nvp4 > critval) &&
		  (nvp3 * nv3 > critval) && 
		  (nvp4 * nv4 > critval);
	      

		double horder = Dist (mesh[pi1], mesh[pi2]);

		if ( // nv1 * nv2 >= 0 &&
		    nv1.Length() > 1e-3 * horder * horder &&
		    nv2.Length() > 1e-3 * horder * horder &&
		    allowswap )
		  {
		    if (!usemetric)
		      {
			int e = pdef[pi1] + pdef[pi2] - pdef[pi3] - pdef[pi4];
			double d = 
			  Dist2 (mesh[pi1], mesh[pi2]) - 
			  Dist2 (mesh[pi3], mesh[pi4]);
		      
			should = e >= t && (e > 2 || d > 0);
		      }
		    else
		      {
			double loch = mesh.GetH(mesh[pi1]);
			should = 
			  CalcTriangleBadness (mesh[pi4], mesh[pi3], mesh[pi1], metricweight, loch) +
			  CalcTriangleBadness (mesh[pi3], mesh[pi4], mesh[pi2], metricweight, loch) <
			  CalcTriangleBadness (mesh[pi1], mesh[pi2], mesh[pi3], metricweight, loch) +
			  CalcTriangleBadness (mesh[pi2], mesh[pi1], mesh[pi4], metricweight, loch);
		      }
		  
		    if (allowswap)
		      {
			Element2d sw1 (pi4, pi3, pi1);
			Element2d sw2 (pi3, pi4, pi2);

			int legal1 = 
			  mesh.LegalTrig (mesh[t1]) + 
			  mesh.LegalTrig (mesh[t2]);
			int legal2 = 
			  mesh.LegalTrig (sw1) + mesh.LegalTrig (sw2);

			if (legal1 < legal2) should = true;
			if (legal2 < legal1) should = false;
		      }
		  
		    if (should)
		      {
			// do swapping !
		      
			done = true;

                        /*
                        mesh[t1] = { pi1, pi4, pi3 };
                        mesh[t2] = { pi2, pi3, pi4 };
                        
			mesh[t1].GeomInfoPi(1) = gi1;
			mesh[t1].GeomInfoPi(2) = gi4;
			mesh[t1].GeomInfoPi(3) = gi3;
		      
			mesh[t2].GeomInfoPi(1) = gi2;
			mesh[t2].GeomInfoPi(2) = gi3;
			mesh[t2].GeomInfoPi(3) = gi4;
                        */
                        mesh[t1] = { { pi1, gi1 }, { pi4, gi4 }, { pi3, gi3 } };
                        mesh[t2] = { { pi2, gi2 }, { pi3, gi3 }, { pi4, gi4 } };
                        
			pdef[pi1]--;
			pdef[pi2]--;
			pdef[pi3]++;
			pdef[pi4]++;
		      
			swapped[t1] = true;
			swapped[t2] = true;
		      }
		  }
	      }
	  }
	t--;
      }

    mesh.SetNextTimeStamp();
  }







 
  void MeshOptimize2d :: CombineImprove (Mesh & mesh)
  {
    if (!faceindex)
      {
	PrintMessage (3, "Combine improve");

	for (faceindex = 1; faceindex <= mesh.GetNFD(); faceindex++)
	  {
	    CombineImprove (mesh);

	    if (multithread.terminate)
	      throw NgException ("Meshing stopped");
	  }
	faceindex = 0;
	return;
      }


    static int timer = NgProfiler::CreateTimer ("Combineimprove 2D");
    NgProfiler::RegionTimer reg (timer);

    static int timerstart = NgProfiler::CreateTimer ("Combineimprove 2D start");
    NgProfiler::StartTimer  (timerstart);


    static int timerstart1 = NgProfiler::CreateTimer ("Combineimprove 2D start1");
    NgProfiler::StartTimer  (timerstart1);

    
    Array<SurfaceElementIndex> seia;
    mesh.GetSurfaceElementsOfFace (faceindex, seia);


    for (SurfaceElementIndex sei : seia)
      if (mesh[sei].GetNP() != 3)
	return;


    int surfnr = 0;
    if (faceindex)
      surfnr = mesh.GetFaceDescriptor (faceindex).SurfNr();


    Vec<3> nv;

    int np = mesh.GetNP();

    TABLE<SurfaceElementIndex,PointIndex::BASE> elementsonnode(np); 
    Array<SurfaceElementIndex> hasonepi, hasbothpi;

    for (SurfaceElementIndex sei : seia)
      for (PointIndex pi : mesh[sei].PNums<3>())
        elementsonnode.Add (pi, sei);

    Array<bool,PointIndex> fixed(np);
    fixed = false;

    NgProfiler::StopTimer  (timerstart1);

    /*
    for (SegmentIndex si = 0; si < mesh.GetNSeg(); si++)
      {
	INDEX_2 i2(mesh[si][0], mesh[si][1]);
	fixed[i2.I1()] = true;
	fixed[i2.I2()] = true;
      }
    */

    for (SurfaceElementIndex sei : seia)
      {
	Element2d & sel = mesh[sei];
	for (int j = 0; j < sel.GetNP(); j++)
	  {
	    PointIndex pi1 = sel.PNumMod(j+2);
	    PointIndex pi2 = sel.PNumMod(j+3);
	    if (mesh.IsSegment (pi1, pi2))
	      {	
		fixed[pi1] = true;
		fixed[pi2] = true;
	      }
	  }
      }


    /*
    for(int i = 0; i < mesh.LockedPoints().Size(); i++)
      fixed[mesh.LockedPoints()[i]] = true;
    */
    for (PointIndex pi : mesh.LockedPoints())
      fixed[pi] = true;


    Array<Vec<3>,PointIndex> normals(np);

    // for (PointIndex pi = mesh.Points().Begin(); pi < mesh.Points().End(); pi++)
    for (PointIndex pi : mesh.Points().Range())
      {
	if (elementsonnode[pi].Size())
	  {
	    Element2d & hel = mesh[elementsonnode[pi][0]];
	    for (int k = 0; k < 3; k++)
	      if (hel[k] == pi)
		{
		  SelectSurfaceOfPoint (mesh[pi], hel.GeomInfoPi(k+1));
		  GetNormalVector (surfnr, mesh[pi], hel.GeomInfoPi(k+1), normals[pi]);
		  break;
		}
	  }
      }

    NgProfiler::StopTimer  (timerstart);

    for (int i = 0; i < seia.Size(); i++)
      {
	SurfaceElementIndex sei = seia[i];
	Element2d & elem = mesh[sei];

	for (int j = 0; j < 3; j++)
	  {
            if (elem.IsDeleted()) continue;
	    PointIndex pi1 = elem[j];
	    PointIndex pi2 = elem[(j+1) % 3];

            /*
	    if (pi1 < PointIndex::BASE || 
		pi2 < PointIndex::BASE)
	      continue;
            */
            if (!pi1.IsValid() || !pi2.IsValid())
	      continue;              
	    /*
	      INDEX_2 i2(pi1, pi2);
	      i2.Sort();
	      if (segmentht.Used(i2))
	      continue;
	    */

	    bool debugflag = 0;

	    if (debugflag)
	      {
		(*testout) << "Combineimprove, face = " << faceindex 
			   << "pi1 = " << pi1 << " pi2 = " << pi2 << endl;
	      }

	    /*
	    // save version:
	    if (fixed.Get(pi1) || fixed.Get(pi2)) 
	    continue;
	    if (pi2 < pi1) swap (pi1, pi2);
	    */

	    // more general 
	    if (fixed[pi2]) 
	      Swap (pi1, pi2);

	    if (fixed[pi2])  
	      continue;

	    double loch = mesh.GetH (mesh[pi1]);

	    // INDEX_2 si2 (pi1, pi2);
	    // si2.Sort();

	    /*	  
	      if (edgetested.Used (si2))
	      continue;
	      edgetested.Set (si2, 1);
	    */

	    hasonepi.SetSize(0);
	    hasbothpi.SetSize(0);

	    // for (int k = 0; k < elementsonnode[pi1].Size(); k++)
            for (SurfaceElementIndex sei2 : elementsonnode[pi1])
	      {
		const Element2d & el2 = mesh[sei2];

		if (el2.IsDeleted()) continue;

		if (el2[0] == pi2 || el2[1] == pi2 || el2[2] == pi2)
		  {
		    hasbothpi.Append (sei2);
		    nv = Cross (Vec3d (mesh[el2[0]], mesh[el2[1]]),
				Vec3d (mesh[el2[0]], mesh[el2[2]]));
		  }
		else
		  {
		    hasonepi.Append (sei2);
		  }
	      } 


	    Element2d & hel = mesh[hasbothpi[0]];
	    for (int k = 0; k < 3; k++)
	      if (hel[k] == pi1)
		{
		  SelectSurfaceOfPoint (mesh[pi1],
					hel.GeomInfoPi(k+1));
		  GetNormalVector (surfnr, mesh[pi1], hel.GeomInfoPi(k+1), nv);
		  break;
		}

	    //	  nv = normals.Get(pi1);


            for (SurfaceElementIndex sei2 :  elementsonnode[pi2])
	      {
		const Element2d & el2 = mesh[sei2];
		if (el2.IsDeleted()) continue;
                if (!el2.PNums<3>().Contains (pi1))
		  hasonepi.Append (sei2);                  
	      } 

	    double bad1 = 0;
	    int illegal1 = 0, illegal2 = 0;
            /*
            for (SurfaceElementIndex sei : hasonepi)
              {
                const Element2d & el = mesh[sei];
		bad1 += CalcTriangleBadness (mesh[el[0]], mesh[el[1]], mesh[el[2]],
					     nv, -1, loch);
		illegal1 += 1-mesh.LegalTrig(el);
	      }
            */
            for (const Element2d & el : mesh.SurfaceElements()[hasonepi])
              {
		bad1 += CalcTriangleBadness (mesh[el[0]], mesh[el[1]], mesh[el[2]],
					     nv, -1, loch);
		illegal1 += 1-mesh.LegalTrig(el);
	      }

	    for (int k = 0; k < hasbothpi.Size(); k++)
	      {
		const Element2d & el = mesh[hasbothpi[k]];
		bad1 += CalcTriangleBadness (mesh[el[0]], mesh[el[1]], mesh[el[2]],
					     nv, -1, loch);
		illegal1 += 1-mesh.LegalTrig(el);
	      }
	    bad1 /= (hasonepi.Size()+hasbothpi.Size());

	    MeshPoint p1 = mesh[pi1];
	    MeshPoint p2 = mesh[pi2];

	    MeshPoint pnew = p1;
	    mesh[pi1] = pnew;
	    mesh[pi2] = pnew;

	    double bad2 = 0;
	    for (int k = 0; k < hasonepi.Size(); k++)
	      {
		Element2d & el = mesh[hasonepi[k]];
		double err = 
		  CalcTriangleBadness (mesh[el[0]], mesh[el[1]], mesh[el[2]],
				       nv, -1, loch);
		bad2 += err;

		Vec<3> hnv = Cross (Vec3d (mesh[el[0]],
					   mesh[el[1]]),
				    Vec3d (mesh[el[0]],
					   mesh[el[2]]));
		if (hnv * nv < 0)
		  bad2 += 1e10;
              
		for (int l = 0; l < 3; l++)
		  if ( (normals[el[l]] * nv) < 0.5)
		    bad2 += 1e10;

		illegal2 += 1-mesh.LegalTrig(el);
	      }
	    bad2 /= hasonepi.Size();

	    mesh[pi1] = p1;
	    mesh[pi2] = p2;
       
	    if (debugflag)
	      {
		(*testout) << "bad1 = " << bad1 << ", bad2 = " << bad2 << endl;
	      }

	    bool should = (bad2 < bad1 && bad2 < 1e4);
	    if (bad2 < 1e4)
	      {
		if (illegal1 > illegal2) should = true;
		if (illegal2 > illegal1) should = false;
	      }
	  

	    if (should)
	      {
                /*
                (*testout) << "combine !" << endl;
                (*testout) << "bad1 = " << bad1 << ", bad2 = " << bad2 << endl;
                (*testout) << "illegal1 = " << illegal1 << ", illegal2 = " << illegal2 << endl;
                (*testout) << "loch = " << loch << endl;
                */

		mesh[pi1] = pnew;
		PointGeomInfo gi;
		// bool gi_set(false);
	      
                /*
		Element2d *el1p(NULL);
		int l = 0;
		while(mesh[elementsonnode[pi1][l]].IsDeleted() && l<elementsonnode[pi1].Size()) l++;
		if(l<elementsonnode[pi1].Size())
		  el1p = &mesh[elementsonnode[pi1][l]];
		else
		  cerr << "OOPS!" << endl;

		for (l = 0; l < el1p->GetNP(); l++)
		  if ((*el1p)[l] == pi1)
		    {
		      gi = el1p->GeomInfoPi (l+1);
		      // gi_set = true;
		    }
                */
                for (SurfaceElementIndex sei : elementsonnode[pi1])
                  {
                    const Element2d & el1p = mesh[sei];
                    if (el1p.IsDeleted()) continue;
                      
                    for (int l = 0; l < el1p.GetNP(); l++)
                      if (el1p[l] == pi1)
                        // gi = el1p.GeomInfoPi (l+1);
                        gi = el1p.GeomInfo()[l];
                    break;
                  }

                

		// (*testout) << "Connect point " << pi2 << " to " << pi1 << "\n";
		// for (int k = 0; k < elementsonnode[pi2].Size(); k++)
                for (SurfaceElementIndex sei2 : elementsonnode[pi2])
		  {
                    Element2d & el = mesh[sei2];
		    if (el.IsDeleted()) continue;
                    if (el.PNums().Contains(pi1)) continue;

		    elementsonnode.Add (pi1, sei2);
                    
		    for (auto l : Range(el.GetNP()))
		      {
			if (el[l] == pi2)
			  {
			    el[l] = pi1;
			    el.GeomInfo()[l] = gi;
			  }

			fixed[el[l]] = true;
		      }
		  }

                for (auto sei : hasbothpi)
                  mesh[sei].Delete();
	      }
	  }
      }

    //  mesh.Compress();
    mesh.SetNextTimeStamp();
  }


  void MeshOptimize2d :: CheckMeshApproximation (Mesh & mesh)
  {
    // Check angles between elements and normals at corners
    /*
  
    int i, j;
    int ne = mesh.GetNSE();
    int surfnr;
  
    Vec3d n, ng;
    NgArray<Vec3d> ngs(3);

    (*mycout) << "Check Surface Approximation" << endl;
    (*testout) << "Check Surface Approximation" << endl;

    for (i = 1; i <= ne; i++)
    {
    const Element2d & el = mesh.SurfaceElement(i);
    surfnr = mesh.GetFaceDescriptor (el.GetIndex()).SurfNr();
    Vec3d n = Cross (mesh.Point (el.PNum(1)) - mesh.Point (el.PNum(2)),
    mesh.Point (el.PNum(1)) - mesh.Point (el.PNum(3)));
    n /= n.Length();

    for (j = 1; j <= el.GetNP(); j++)
    {
    SelectSurfaceOfPoint (mesh.Point(el.PNum(j)), el.GeomInfoPi(j));
    GetNormalVector (surfnr, mesh.Point(el.PNum(j)), ng);
    ng /= ng.Length();
    ngs.Elem(j) = ng;

    double angle =  (180.0 / M_PI) * Angle (n, ng);
    if (angle > 60)
    {
    (*testout) << "el " << i << " node " << el.PNum(j)
    << "has angle = " << angle << endl;
    }
    }	

    for (j = 1; j <= 3; j++)
    {
    double angle =  (180.0 / M_PI) * Angle (ngs.Get(j), ngs.Get(j%3+1));
    if (angle > 60)
    {
    (*testout) << "el " << i << " node-node " 
    << ngs.Get(j) << " - " << ngs.Get(j%3+1)
    << " has angle = " << angle << endl;
    }
    }
    }
    */
  }
}