GModelIO_Fourier.cpp

#include "GModel.h"
#include "fourierFace.h"
#include "Message.h"
#include "Context.h"
#include "Views.h"

extern Context_T CTX;

#if defined(HAVE_FOURIER_MODEL)

#include "model.h"
#include "meshGFace.h"

static model *FM = 0;

void debugVertices(std::vector<MVertex*> &vertices, std::string file, 
		   bool parametric, int num=0)
{
  char name[256];
  sprintf(name, "%s_%d.pos", file.c_str(), num);
  FILE *fp = fopen(name, "w");
  fprintf(fp, "View \"debug\"{\n");
  for(unsigned int i = 0; i < vertices.size(); i++){
    double x, y, z;
    if(parametric){
      vertices[i]->getParameter(0, x); 
      vertices[i]->getParameter(1, y); 
      z = 0;
    }
    else{
      x = vertices[i]->x(); 
      y = vertices[i]->y(); 
      z = vertices[i]->z();
    }
    fprintf(fp, "SP(%g,%g,%g){%d};\n", x, y, z, i);
  }
  fprintf(fp, "};\n");    
  fclose(fp);
}

template<class T>
void debugElements(std::vector<T*> &elements, std::string file, 
		   bool parametric, int num=0)
{
  char name[256];
  sprintf(name, "%s_%d.pos", file.c_str(), num);
  FILE *fp = fopen(name, "w");
  fprintf(fp, "View \"debug\"{\n");
  for(unsigned int i = 0; i < elements.size(); i++){
    fprintf(fp, "%s(", elements[i]->getStringForPOS());
    for(int j = 0; j < elements[i]->getNumVertices(); j++){
      MVertex *v = elements[i]->getVertex(j);
      if(j) fprintf(fp, ",");
      double x, y, z;
      if(parametric){
	v->getParameter(0, x);
	v->getParameter(1, y);
	z = 0;
      }
      else{
	x = v->x(); y = v->y(); z = v->z();
      }
      fprintf(fp, "%g,%g,%g", x, y, z);
    }
    fprintf(fp, "){");
    for(int j = 0; j < elements[i]->getNumVertices(); j++){
      MVertex *v = elements[i]->getVertex(j);
      if(j) fprintf(fp, ",");
      if(v->getData()){
	double pou = *(double*)v->getData();
	fprintf(fp, "%g", pou);
      }
      else{
	fprintf(fp, "%d", v->onWhat()->tag());
      }
    }
    fprintf(fp, "};\n");
  }
  fprintf(fp, "};\n");
  fclose(fp);
}

class meshCartesian{
public:
  void operator() (GFace *gf)
  {  
    int M = (int)(30. / CTX.mesh.lc_factor), N = (int)(30. / CTX.mesh.lc_factor);

    //if(gf->tag() == 2){
    //M = 9;
    //N = 15;
    //}

    for(int i = 0; i < M; i++){
      for(int j = 0; j < N; j++){
	double u = i/(double)(M - 1);
	double v = j/(double)(N - 1);

	//if(gf->tag() == 2){
	  // hack for sttr report 2 (ship model, top right patch)
	  // XYZ_values_ship_Top(u,v=0) = 
	  // XYZ_values_ship_Med(u*matching_const1_+matching_const2_,v=1)
	  // where 0=<u=<1, 
	  //       matching_const1_=0.523540136032613,
	  //       matching_const2_=0.475747890863610. 
	//u = u * 0.5268 + 0.475;
	//}

	GPoint p = gf->point(u, v);
	double pou=1;
	//FM->GetPou(gf->tag(), u, v, pou);
	gf->mesh_vertices.push_back
	  (new MDataFaceVertex<double>(p.x(), p.y(), p.z(), gf, u, v, pou));
      }
    }
    for(int i = 0; i < M - 1; i++){
      for(int j = 0; j < N - 1; j++){
	MQuadrangle *q = new MQuadrangle(gf->mesh_vertices[i * N + j],
					 gf->mesh_vertices[(i + 1) * N + j],
					 gf->mesh_vertices[(i + 1) * N + (j + 1)],
					 gf->mesh_vertices[i * N + (j + 1)]);
	//if(FM->GetOrientation(gf->tag()) < 0) q->revert();
	gf->quadrangles.push_back(q);
      }
    }
  }
};

class meshGmsh{
public:
  void operator() (GFace *gf)
  {  
    fourierFace *ff = dynamic_cast<fourierFace*>(gf);
    if(!ff) {
      Msg(GERROR, "face %d is not Fourier", gf->tag());
      return;
    }
    ff->meshBoundary();
    meshGFace mesh; 
    mesh(ff);
  }
};

class computePartitionOfUnity{
public:
  void operator() (GFace *gf)
  {  
    // we only normalize the partition of unity amongst patches that
    // overlap; we don't normalize across hard edges
    std::vector<int> overlaps;
    FM->GetNeighbor(gf->tag(), overlaps);
    for(unsigned int i = 0; i < gf->mesh_vertices.size(); i++){
      MVertex *v = gf->mesh_vertices[i];
      std::vector<std::pair<GFace*, SPoint2> > param;
      for(unsigned int j = 0; j < overlaps.size(); j++){
	GFace *gf2 = gf->model()->faceByTag(overlaps[j]);
	SPoint2 uv2 = gf2->parFromPoint(SPoint3(v->x(), v->y(), v->z()));
	if(gf2->containsParam(uv2)){
	  GPoint xyz2 = gf2->point(uv2);
	  const double tol = 1.e-2; // Warning: tolerance
	  if(fabs(xyz2.x() - v->x()) < tol && 
	     fabs(xyz2.y() - v->y()) < tol && 
	     fabs(xyz2.z() - v->z()) < tol)
	    param.push_back(std::pair<GFace*, SPoint2>(gf2, uv2));
	}
      }
      if(param.empty()){
      	Msg(GERROR, "Vertex %d does not belong to any patch", v->getNum());
      }
      else{
	double allPou = 0.;
	for(unsigned int i = 0; i < param.size(); i++){
	  double u2 = param[i].second[0], v2 = param[i].second[1];
	  double pou2=1;
	  //FM->GetPou(param[i].first->tag(), u2, v2, pou2);
	  allPou += pou2;
	}
	if(v->getData()){
	  double *pou = (double*)v->getData();
	  *pou = *pou / allPou;
	}
	else{
	  Msg(GERROR, "Vertex %d has no POU data", v->getNum());
	}
      }
    }

    //debugElements(gf->quadrangles, "pou", false, gf->tag());
  }
};

class createGroove{
public:
  void operator() (GFace *gf)
  {  
    // mark elements in the groove with '-1' visibility tag
    for(unsigned int i = 0; i < gf->quadrangles.size(); i++){
      MElement *e = gf->quadrangles[i];
      for(int j = 0; j < e->getNumVertices(); j++){
	void *data = e->getVertex(j)->getData();
	if(data){
	  double pou = *(double*)data;
	  if(pou < 0.51)
	    e->setVisibility(-1);
	}
      }
    }

    // remove elements in the groove
    std::vector<MQuadrangle*> newq;
    for(unsigned int i = 0; i < gf->quadrangles.size(); i++)
      if(gf->quadrangles[i]->getVisibility() < 0) 
	delete gf->quadrangles[i];
      else
	newq.push_back(gf->quadrangles[i]);
    gf->quadrangles = newq;

    // remove vertices in the groove
    std::vector<MVertex*> newv;
    for(unsigned int i = 0; i < gf->mesh_vertices.size(); i++)
      gf->mesh_vertices[i]->setVisibility(-1);
    for(unsigned int i = 0; i < gf->quadrangles.size(); i++)
      for(int j = 0; j < gf->quadrangles[i]->getNumVertices(); j++)
	gf->quadrangles[i]->getVertex(j)->setVisibility(1);
    for(unsigned int i = 0; i < gf->mesh_vertices.size(); i++)
      if(gf->mesh_vertices[i]->getVisibility() < 0) 
	delete gf->mesh_vertices[i];
      else
	newv.push_back(gf->mesh_vertices[i]);
    gf->mesh_vertices = newv;
  }
};

void getOrderedBoundaryLoops(std::vector<MElement*> &elements, 
			     std::vector<std::vector<MVertex*> > &loops)
{
  typedef std::pair<MVertex*, MVertex*> vpair;
  std::map<vpair, vpair> edges;
  for(unsigned int i = 0; i < elements.size(); i++){
    for(int j = 0; j < elements[i]->getNumEdges(); j++){
      MEdge e = elements[i]->getEdge(j);
      vpair p(e.getMinVertex(), e.getMaxVertex());
      if(edges.count(p)) edges.erase(p);
      else edges[p] = vpair(e.getVertex(0), e.getVertex(1));
    }
  }

  std::map<MVertex*, MVertex*> connect;
  for(std::map<vpair, vpair>::iterator it = edges.begin(); it != edges.end(); it++)
    connect[it->second.first] = it->second.second;

  loops.resize(1);
  while(connect.size()){
    if(loops[loops.size() - 1].empty()) 
      loops[loops.size() - 1].push_back(connect.begin()->first);
    MVertex *prev = loops[loops.size() - 1][loops[loops.size() - 1].size() - 1];
    MVertex *next = connect[prev];
    connect.erase(prev);
    loops[loops.size() - 1].push_back(next);
    if(next == loops[loops.size() - 1][0])
      loops.resize(loops.size() + 1);
  }

  if(loops[loops.size() - 1].empty())
    loops.pop_back();
  
  Msg(INFO, "Found %d loop(s) in boundary", loops.size());
}

void classifyFaces(GFace *gf, std::set<GFace*> &connected, std::set<GFace*> &other)
{
  connected.insert(gf); 
  std::set<MVertex*> verts;
  for(unsigned int i = 0; i < gf->mesh_vertices.size(); i++)
    verts.insert(gf->mesh_vertices[i]);

  for(int i = 0; i < gf->model()->numFace() - 1; i++){ // worst case
    for(GModel::fiter it = gf->model()->firstFace(); it != gf->model()->lastFace(); it++){
      if(connected.find(*it) == connected.end()){
	for(unsigned int j = 0; j < (*it)->mesh_vertices.size(); j++){
	  if(std::find(verts.begin(), verts.end(), (*it)->mesh_vertices[j]) != verts.end()){
	    connected.insert(*it);
	    for(unsigned int k = 0; k < (*it)->mesh_vertices.size(); k++)
	      verts.insert((*it)->mesh_vertices[k]);
	    break;
	  }
	}
      }
    }
  }

  for(GModel::fiter it = gf->model()->firstFace(); it != gf->model()->lastFace(); it++)
    if(connected.find(*it) == connected.end()) 
      other.insert(*it);

  Msg(INFO, "Found %d face(s) connected to face %d", (int)connected.size(), gf->tag());
  for(std::set<GFace*>::iterator it = connected.begin(); it != connected.end(); it++)
    Msg(INFO, "   %d", (*it)->tag());
}

void getIntersectingBoundaryParts(GFace *gf, std::vector<MElement*> &elements,
				  std::vector<std::vector<std::vector<MVertex*> > > &parts)
{
  std::vector<std::vector<MVertex*> > loops;
  getOrderedBoundaryLoops(elements, loops);
  parts.resize(loops.size());

  for(unsigned int i = 0; i < loops.size(); i++){
    // last vertex in loop is equal to the first vertex
    bool newpart = true;
    for(unsigned int j = 0; j < loops[i].size() - 1; j++){
      MVertex *v = loops[i][j];
      SPoint2 uv = gf->parFromPoint(SPoint3(v->x(), v->y(), v->z()));
      if(gf->containsParam(uv)){
	GPoint xyz = gf->point(uv);
	const double tol = 1.e-2; // Warning: tolerance
	if(fabs(xyz.x() - v->x()) < tol && 
	   fabs(xyz.y() - v->y()) < tol && 
	   fabs(xyz.z() - v->z()) < tol){
	  if(newpart){
	    parts[i].resize(parts[i].size() + 1);
	    newpart = false;
	  }
	  v->setParameter(0, uv[0]);
	  v->setParameter(1, uv[1]);
	  parts[i][parts[i].size() - 1].push_back(v);
	}
	else{
	  newpart = true;
	}
      }
      else{
	newpart = true;
      }
    }
  }

#if 0
  static int nn = 0;
  debugElements(elements, "elements", false, nn++);
  for(unsigned int i = 0; i < loops.size(); i++)
    debugVertices(loops[i], "loops", false, nn++);
  for(unsigned int i = 0; i < parts.size(); i++)
    for(unsigned int j = 0; j < parts[i].size(); j++)
      debugVertices(parts[i][j], "parts", false, nn++);
#endif
}

void meshGrout(GFace *gf, std::vector<MVertex*> &loop, std::vector<MVertex*> &hole)
{ 
  debugVertices(hole, "hole", true, gf->tag());
  debugVertices(loop, "loop", true, gf->tag());

  fourierFace *grout = new fourierFace(gf, loop, hole);
  meshGFace mesh; 
  mesh(grout);
  orientMeshGFace orient; 
  orient(grout);
  //debugElements(grout->triangles, "grout", true);
  for(unsigned int i = 0; i < grout->triangles.size(); i++)
    gf->triangles.push_back(grout->triangles[i]);
  for(unsigned int i = 0; i < loop.size(); i++)
    gf->mesh_vertices.push_back(loop[i]);
  for(unsigned int i = 0; i < hole.size(); i++)
    gf->mesh_vertices.push_back(hole[i]);
  for(unsigned int i = 0; i < grout->mesh_vertices.size(); i++)
    gf->mesh_vertices.push_back(grout->mesh_vertices[i]);
  delete grout;
}

void meshGroutWithHole(GFace *gf,
		       std::vector<std::vector<std::vector<MVertex*> > > &inside,
		       std::vector<std::vector<std::vector<MVertex*> > > &outside)
{		       
  std::vector<MVertex*> hole, loop;

  // create hole
  SPoint2 ic(0., 0.);
  for(unsigned int i = 0; i < inside[0][0].size(); i++){
    hole.push_back(inside[0][0][i]);
    double u, v;
    inside[0][0][i]->getParameter(0, u);
    inside[0][0][i]->getParameter(1, v);
    ic += SPoint2(u, v);
  }
  ic *= 1. / (double)inside[0][0].size();
  hole.push_back(hole[0]);

  // order exterior parts and create exterior loop
  std::vector<std::pair<double, int> > angle;
  std::map<int, std::vector<MVertex*> > outside_flat;
  int part = 0;
  for(unsigned int i = 0; i < outside.size(); i++){
    for(unsigned int j = 0; j < outside[i].size(); j++){
      for(unsigned int k = 0; k < outside[i][j].size(); k++){
	outside_flat[part].push_back(outside[i][j][k]);
      }
      part++;
    }
  }
  std::map<int, std::vector<MVertex*> >::iterator it = outside_flat.begin();
  for(; it != outside_flat.end(); it++){
    SPoint2 oc(0., 0.);
    for(unsigned int i = 0; i < it->second.size(); i++){
      double u, v;
      it->second[i]->getParameter(0, u);
      it->second[i]->getParameter(1, v);
      oc += SPoint2(u, v);
    }
    oc *= 1. / (double)it->second.size();
    double a = atan2(oc[1] - ic[1], oc[0] - ic[0]);
    angle.push_back(std::make_pair(a, it->first));
  }
  std::sort(angle.begin(), angle.end());
  for(unsigned int i = 0; i < angle.size(); i++){
    for(unsigned int j = 0; j < outside_flat[angle[i].second].size(); j++)
      loop.push_back(outside_flat[angle[i].second][j]);
  }
  loop.push_back(hole[0]);

  // mesh the grout
  meshGrout(gf, loop, hole);
}

bool onHardEdge(GFace *gf, MVertex *vertex)
{
  std::vector<int> edges;
  FM->GetEdge(gf->tag(), edges);
  if(edges.empty()) return false;
  double u, v;
  vertex->getParameter(0, u);
  vertex->getParameter(1, v);
  for(unsigned int i = 0; i < edges.size(); i++){
    switch(edges[i]){
    case 0: if(u == 0.) return true;
    case 1: if(u == 1.) return true;
    case 2: if(v == 0.) return true;
    case 3: if(v == 1.) return true;
    }
  }
  return false;
}

bool removeHardEdges(GFace *gf, std::vector<MVertex*> &loop,
		     std::vector<std::vector<MVertex*> > &subloops)
{
  subloops.resize(1);
  subloops[0].push_back(loop[0]);
  for(unsigned int i = 1; i < loop.size() - 1; i++){
    if(onHardEdge(gf, loop[i - 1]) && 
       onHardEdge(gf, loop[i]) &&
       onHardEdge(gf, loop[i + 1])){
      // skip + create new path
      subloops.resize(subloops.size() + 1);
    }
    else{
      subloops[subloops.size() - 1].push_back(loop[i]);
    }
  }
  subloops[subloops.size() - 1].push_back(loop[loop.size() - 1]);

  if(subloops.size() > 1){
    for(unsigned int i = 0; i < subloops.size(); i++){
      //if(subloops[i].size()) debugVertices(subloops[i], "x", false, i);
    }
    Msg(INFO, "HAVE SUBLOOPS!");
    return true;
  }
  return false;
}

void meshGroutWithoutHole(GFace *gf,
			  std::vector<std::vector<MVertex*> > &inside)
{
  std::vector<MVertex*> hole, tmp;
  std::vector<std::vector<MVertex*> > loops;

  for(unsigned int i = 0; i < inside.size(); i++)
    for(unsigned int j = 0; j < inside[i].size(); j++)
      tmp.push_back(inside[i][j]);
  tmp.push_back(tmp[0]);

  if(removeHardEdges(gf, tmp, loops)){
    //for(unsigned int i = 0; i < loops.size(); i++)
      //meshGrout(gf, loops[i], hole);
  }
  else{
    meshGrout(gf, tmp, hole);
  }
}

class createGrout{
public:
  void operator() (GFace *gf)
  {  
    if(gf->tag() > 2) return;

    Msg(INFO, "Processing grout for face %d", gf->tag());

    std::set<GFace*> connected, other;
    classifyFaces(gf, connected, other);

    std::vector<MElement*> connectedElements;
    for(std::set<GFace*>::iterator it = connected.begin(); it != connected.end(); it++){
      for(unsigned int i = 0; i < (*it)->triangles.size(); i++)
	connectedElements.push_back((*it)->triangles[i]);
      for(unsigned int i = 0; i < (*it)->quadrangles.size(); i++)
	connectedElements.push_back((*it)->quadrangles[i]);
    }

    std::vector<MElement*> otherElements;
    for(std::set<GFace*>::iterator it = other.begin(); it != other.end(); it++){
      for(unsigned int i = 0; i < (*it)->triangles.size(); i++)
	otherElements.push_back((*it)->triangles[i]);
      for(unsigned int i = 0; i < (*it)->quadrangles.size(); i++)
	otherElements.push_back((*it)->quadrangles[i]);
    }

    std::vector<std::vector<std::vector<MVertex*> > > inside;
    getIntersectingBoundaryParts(gf, connectedElements, inside);
    Msg(INFO, "%d inside loop(s)", (int)inside.size());
    for(unsigned int i = 0; i < inside.size(); i++)
      Msg(INFO, "   inside loop %d intersect has %d part(s)", i, (int)inside[i].size());

    std::vector<std::vector<std::vector<MVertex*> > > outside;
    getIntersectingBoundaryParts(gf, otherElements, outside);
    Msg(INFO, "%d outside loop(s)", (int)outside.size());
    for(unsigned int i = 0; i < outside.size(); i++)
      Msg(INFO, "   outside loop %d intersect has %d part(s)", i, (int)outside[i].size());

    if(inside.size() == 1 && inside[0].size() == 1){
      Msg(INFO, "*** CASE 1: grout has a single hole in one part ***");
      meshGroutWithHole(gf, inside, outside);
    }
    else if(!outside.size()){
      Msg(INFO, "*** CASE 2: grout has no outside contributions ***");
      for(unsigned int i = 0; i < inside.size(); i++)
	meshGroutWithoutHole(gf, inside[i]);
    }
    else{
      Msg(WARNING, "*** TODO: UNKNOWN CASE ***");
    }
  }
};

fourierEdge::fourierEdge(GModel *model, int num, GVertex *v1, GVertex *v2)
  : GEdge(model, num, v1, v2)
{
}

fourierFace::fourierFace(GModel *m, int num)
  : GFace(m, num)
{
  for(int i = 0; i < 4; i++){ _v[i] = 0; _e[i] = 0; }
  _discrete = 1;
  _plane = 0;
}

fourierFace::fourierFace(GFace *f, std::vector<MVertex*> &loop, std::vector<MVertex*> &hole)
  : GFace(f->model(), f->tag())
{
  for(int i = 0; i < 4; i++){ _v[i] = 0; _e[i] = 0; }
  _discrete = 0;
  _plane = 0;

  if(!loop.size()){
    Msg(GERROR, "No vertices in exterior loop");
    return; 
  }
  
  _v[0] = new fourierVertex(f->model(), loop[0]);
  _v[1] = new fourierVertex(f->model(), loop[loop.size() - 2]);
  _e[0] = new fourierEdge(f->model(), 1, _v[0], _v[1]);
  _e[0]->addFace(this);
  _e[1] = new fourierEdge(f->model(), 2, _v[1], _v[0]);
  _e[1]->addFace(this);
  for(unsigned int i = 1; i < loop.size() - 2; i++)
    _e[0]->mesh_vertices.push_back(loop[i]);

  l_edges.push_back(_e[0]); l_dirs.push_back(-1);
  l_edges.push_back(_e[1]); l_dirs.push_back(-1);

  if(hole.size()){
    _v[2] = new fourierVertex(f->model(), hole[0]);
    _v[3] = new fourierVertex(f->model(), hole[hole.size() - 2]);
    _e[2] = new fourierEdge(f->model(), 3, _v[2], _v[3]);
    _e[2]->addFace(this);
    _e[3] = new fourierEdge(f->model(), 4, _v[3], _v[2]);
    _e[3]->addFace(this);
    for(unsigned int i = 1; i < hole.size() - 2; i++)
      _e[2]->mesh_vertices.push_back(hole[i]);

    l_edges.push_back(_e[2]); l_dirs.push_back(1);
    l_edges.push_back(_e[3]); l_dirs.push_back(1);
  }
}

fourierFace::~fourierFace()
{
  if(!_discrete){
    // this face was just used temporarily for meshing, so don't
    // delete the mesh vertices or the mesh elements: they have been
    // transferred elsewhere
    for(int i = 0; i < 4; i++){ 
      if(_e[i]){
	_e[i]->mesh_vertices.clear();
	delete _e[i];
      }
    }
    for(int i = 0; i < 4; i++){ 
      if(_v[i]){
	_v[i]->mesh_vertices.clear();
	delete _v[i];
      }
    }
    triangles.clear();
    quadrangles.clear();
    mesh_vertices.clear();
    l_edges.clear();
  }
}

void fourierFace::meshBoundary()
{
  const double tol = 1.e-6;

  _discrete = 0;

  int nu=0, nv=0;
  FM->GetNum(tag(), nu, nv);

  std::vector<double> u, v;
  FM->GetBoundary_Points(tag(), u, v);

  if(2*nu+2*nv != u.size()){
    Msg(INFO, "Special planar patch from YoungAe: %d", tag());
#if 1 // transfinite, by hand -- WARNING
    _plane = 1; // to enable smoothing of transfinite meshes
    nu = 14;
    nv = 9;
    // remove duplicates
    std::vector<MVertex*> verts;
    for(unsigned int i = 0; i < u.size() - 1; i++){
      if(!i || fabs(u[i]-u[i-1]) > tol || fabs(v[i]-v[i-1]) > tol){
	GPoint p = point(u[i], v[i]);
	verts.push_back(new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]));
      }
    }
    int corners[4] = {0, nu - 1, nu + nv - 2,  2 * nu + nv - 3};
    for(int i = 0; i < 4; i++)
      _v[i] = new fourierVertex(model(), verts[corners[i]]);
    meshAttributes.Method = TRANSFINI;
    meshAttributes.recombine = 1;
    meshAttributes.transfiniteArrangement = 1;
    meshAttributes.corners.clear();
    for(int i = 0; i < 4; i++)
      meshAttributes.corners.push_back(_v[i]);
    _e[0] = new fourierEdge(model(), 1, _v[0], _v[1]);
    _e[0]->addFace(this);
    _e[1] = new fourierEdge(model(), 2, _v[1], _v[2]);
    _e[1]->addFace(this);
    _e[2] = new fourierEdge(model(), 3, _v[2], _v[3]);
    _e[2]->addFace(this);
    _e[3] = new fourierEdge(model(), 4, _v[3], _v[0]);
    _e[3]->addFace(this);
    for(unsigned int i = corners[0] + 1; i < corners[1]; i++)
      _e[0]->mesh_vertices.push_back(verts[i]);
    for(unsigned int i = corners[1] + 1; i < corners[2]; i++)
      _e[1]->mesh_vertices.push_back(verts[i]);
    for(unsigned int i = corners[2] + 1; i < corners[3]; i++)
      _e[2]->mesh_vertices.push_back(verts[i]);
    for(unsigned int i = corners[3] + 1; i < verts.size(); i++)
      _e[3]->mesh_vertices.push_back(verts[i]);
    l_edges.push_back(_e[0]); l_dirs.push_back(1);
    l_edges.push_back(_e[1]); l_dirs.push_back(1);
    l_edges.push_back(_e[2]); l_dirs.push_back(1);
    l_edges.push_back(_e[3]); l_dirs.push_back(1);
#else // unstructured
    GPoint p0 = point(u[0], v[0]);
    GPoint p1 = point(u[1], v[1]);
    MVertex *v0 = new MFaceVertex(p0.x(), p0.y(), p0.z(), this, u[0], v[0]);
    MVertex *v1 = new MFaceVertex(p1.x(), p1.y(), p1.z(), this, u[1], v[1]);
    _v[0] = new fourierVertex(model(), v0);
    _v[1] = new fourierVertex(model(), v1);
    _e[0] = new fourierEdge(model(), 1, _v[0], _v[1]);
    _e[0]->addFace(this);
    _e[1] = new fourierEdge(model(), 2, _v[1], _v[0]);
    _e[1]->addFace(this);
    for(unsigned int i = 2; i < u.size() - 1; i++){
      if(fabs(u[i]-u[i-1]) > tol || fabs(v[i]-v[i-1]) > tol){
	GPoint p = point(u[i], v[i]);
	MVertex *vv = new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]);
	_e[1]->mesh_vertices.push_back(vv);
      }
    }
    l_edges.push_back(_e[0]); l_dirs.push_back(1);
    l_edges.push_back(_e[1]); l_dirs.push_back(1);
#endif
    return;
  }
  
  int corners[4] = {0, nu, nu + nv, 2 * nu + nv};
  for(int i = 0; i < 4; i++){
    double uu = u[corners[i]], vv = v[corners[i]];
    GPoint p = point(uu, vv);
    MVertex *newv = new MFaceVertex(p.x(), p.y(), p.z(), this, uu, vv);
    _v[i] = new fourierVertex(model(), newv);
  }
  
  meshAttributes.Method = TRANSFINI;
  meshAttributes.recombine = 1;
  meshAttributes.transfiniteArrangement = 1;
  meshAttributes.corners.clear();
  for(int i = 0; i < 4; i++)
    meshAttributes.corners.push_back(_v[i]);
      
  _e[0] = new fourierEdge(model(), 1, _v[0], _v[1]);
  _e[0]->addFace(this);
  _e[1] = new fourierEdge(model(), 2, _v[1], _v[2]);
  _e[1]->addFace(this);
  _e[2] = new fourierEdge(model(), 3, _v[2], _v[3]);
  _e[2]->addFace(this);
  _e[3] = new fourierEdge(model(), 4, _v[3], _v[0]);
  _e[3]->addFace(this);

  for(unsigned int i = corners[0] + 1; i < corners[1] - 1; i++){
    GPoint p = point(u[i], v[i]);
    _e[0]->mesh_vertices.push_back(new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]));
  }
  for(unsigned int i = corners[1] + 1; i < corners[2] - 1; i++){
    GPoint p = point(u[i], v[i]);
    _e[1]->mesh_vertices.push_back(new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]));
  }
  for(unsigned int i = corners[2] + 1; i < corners[3] - 1; i++){
    GPoint p = point(u[i], v[i]);
    _e[2]->mesh_vertices.push_back(new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]));
  }
  for(unsigned int i = corners[3] + 1; i < u.size() - 1; i++){
    GPoint p = point(u[i], v[i]);
    _e[3]->mesh_vertices.push_back(new MFaceVertex(p.x(), p.y(), p.z(), this, u[i], v[i]));
  }

  l_edges.push_back(_e[0]); l_dirs.push_back(1);
  l_edges.push_back(_e[1]); l_dirs.push_back(1);
  l_edges.push_back(_e[2]); l_dirs.push_back(1);
  l_edges.push_back(_e[3]); l_dirs.push_back(1);
}

Range<double> fourierFace::parBounds(int i) const
{
  double min, max;
  FM->GetParamBounds(tag(), i, min, max);
  return Range<double>(min, max);
}
  
GPoint fourierFace::point(double par1, double par2) const
{
  double x, y, z;
  FM->GetPoint(tag(), par1, par2, x, y, z);
  return GPoint(x, y, z);
}

GPoint fourierFace::point(const SPoint2 &pt) const
{
  return point(pt[0], pt[1]);
}

GPoint fourierFace::closestPoint(const SPoint3 & queryPoint) const
{
  throw;
}
  
int fourierFace::containsPoint(const SPoint3 &pt) const
{
  throw;
}

int fourierFace::containsParam(const SPoint2 &pt) const
{
  double umin, umax, vmin, vmax;
  FM->GetParamBounds(tag(), 0, umin, umax);
  FM->GetParamBounds(tag(), 1, vmin, vmax);
  const double tol = 1.e-6;
  if(pt[0] < umin - tol || pt[0] > umax + tol) return 0;
  if(pt[1] < vmin - tol || pt[1] > vmax + tol) return 0;
  return 1;
}
  
SVector3 fourierFace::normal(const SPoint2 &param) const
{
  throw;
}

GEntity::GeomType fourierFace::geomType() const
{
  if(_discrete)
    return  GEntity::DiscreteSurface;
  else if(_plane)
    return  GEntity::Plane;
  else
    return GEntity::Unknown;
}

SPoint2 fourierFace::parFromPoint(const SPoint3 &p) const
{
  double u, v;
  FM->GetParamFromPoint(tag(), p.x(), p.y(), p.z(), u, v);
  return SPoint2(u, v);
}

int GModel::readFourier(const std::string &name)
{
  FM = new model(name);

  CTX.terminal = 1;
  
  Msg(INFO, "Fourier model created: %d patches", FM->GetNumPatches());

  // create one face per patch
  for(int i = 0; i < FM->GetNumPatches(); i++)
    add(new fourierFace(this, i));

  // mesh each face with quads
  //std::for_each(firstFace(), lastFace(), meshCartesian());
  //return 1;

  // mesh each face using the standard gmsh algorithms
  setMeshSize(0.05);
  std::for_each(firstFace(), lastFace(), meshGmsh());
  return 1;

  // compute partition of unity
  std::for_each(firstFace(), lastFace(), computePartitionOfUnity());

  // create grooves
  std::for_each(firstFace(), lastFace(), createGroove());

  // create grout
  std::for_each(firstFace(), lastFace(), createGrout());

  // remove any duplicate vertices on hard edges

  // Here's an alternative approach that might be worth investigating:
  // - compute and store the pou of each overlapping patch in the nodes of
  //   all the patches
  // - for each pair of overlapping patches, find the line pou1=pou2 by
  //   interpolation on the overlapping grids
  // - compute the intersections of these lines
  // This should define a non-overlapping partitioning of the grid, which
  // could be used as the boundary constrain for the unstructured algo

  CTX.terminal = 0;

  CTX.mesh.changed = ENT_ALL;

  return 1;
}

#else

int GModel::readFourier(const std::string &name)
{
  Msg(GERROR, "Fourier model is not compiled in this version of Gmsh");
  return 1;
}

#endif