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Operation_HPDDM.cpp
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Christophe Geuzaine authoredChristophe Geuzaine authored
BackgroundMesh.cpp 35.83 KiB
// Gmsh - Copyright (C) 1997-2014 C. Geuzaine, J.-F. Remacle
//
// See the LICENSE.txt file for license information. Please report all
// bugs and problems to the public mailing list <gmsh@geuz.org>.
#include "GmshMessage.h"
#include "BackgroundMesh.h"
#include "Numeric.h"
#include "Context.h"
#include "GVertex.h"
#include "GEdge.h"
#include "GEdgeCompound.h"
#include "GFace.h"
#include "GFaceCompound.h"
#include "GModel.h"
#include "OS.h"
#include "Field.h"
#include "MElement.h"
#include "MElementOctree.h"
#include "MLine.h"
#include "MTriangle.h"
#include "MQuadrangle.h"
#include "MVertex.h"
#if defined(HAVE_SOLVER)
#include "dofManager.h"
#include "laplaceTerm.h"
#include "linearSystemGMM.h"
#include "linearSystemCSR.h"
#include "linearSystemFull.h"
#include "linearSystemPETSc.h"
#endif
// computes the characteristic length of the mesh at a vertex in order
// to have the geometry captured with accuracy. A parameter called
// CTX::instance()->mesh.minCircPoints tells the minimum number of points per
// radius of curvature
#if defined(HAVE_ANN)
static int _NBANN = 2;
#endif
SMetric3 buildMetricTangentToCurve(SVector3 &t, double l_t, double l_n)
{
if (l_t == 0.0) return SMetric3(1.e-22);
SVector3 a;
if (fabs(t(0)) <= fabs(t(1)) && fabs(t(0)) <= fabs(t(2))){
a = SVector3(1,0,0);
}
else if (fabs(t(1)) <= fabs(t(0)) && fabs(t(1)) <= fabs(t(2))){
a = SVector3(0,1,0);
}
else{
a = SVector3(0,0,1);
}
SVector3 b = crossprod (t,a);
SVector3 c = crossprod (b,t);
b.normalize();
c.normalize();
t.normalize();
SMetric3 Metric (1./(l_t*l_t),1./(l_n*l_n),1./(l_n*l_n),t,b,c);
// printf("bmttc %g %g %g %g %g\n",l_t,l_n,Metric(0,0),Metric(0,1),Metric(1,1));
return Metric;
}
SMetric3 buildMetricTangentToSurface(SVector3 &t1, SVector3 &t2,
double l_t1, double l_t2, double l_n)
{
t1.normalize();
t2.normalize();
SVector3 n = crossprod (t1,t2);
n.normalize();
l_t1 = std::max(l_t1, CTX::instance()->mesh.lcMin);
l_t2 = std::max(l_t2, CTX::instance()->mesh.lcMin);
l_t1 = std::min(l_t1, CTX::instance()->mesh.lcMax);
l_t2 = std::min(l_t2, CTX::instance()->mesh.lcMax);
SMetric3 Metric (1./(l_t1*l_t1),1./(l_t2*l_t2),1./(l_n*l_n),t1,t2,n);
return Metric;
}
SMetric3 max_edge_curvature_metric(const GVertex *gv)
{
SMetric3 val (1.e-12);
std::list<GEdge*> l_edges = gv->edges();
for (std::list<GEdge*>::const_iterator ite = l_edges.begin();
ite != l_edges.end(); ++ite){
GEdge *_myGEdge = *ite;
Range<double> range = _myGEdge->parBounds(0);
SMetric3 cc;
if (gv == _myGEdge->getBeginVertex()) {
SVector3 t = _myGEdge->firstDer(range.low());
t.normalize();
double l_t = ((2 * M_PI) /( fabs(_myGEdge->curvature(range.low()))
* CTX::instance()->mesh.minCircPoints ));
double l_n = 1.e12;
cc = buildMetricTangentToCurve(t,l_t,l_n);
}
else {
SVector3 t = _myGEdge->firstDer(range.high());
t.normalize();
double l_t = ((2 * M_PI) /( fabs(_myGEdge->curvature(range.high()))
* CTX::instance()->mesh.minCircPoints ));
double l_n = 1.e12;
cc = buildMetricTangentToCurve(t,l_t,l_n);
}
val = intersection(val,cc);
}
return val;
}
SMetric3 max_edge_curvature_metric(const GEdge *ge, double u)
{
SVector3 t = ge->firstDer(u);
t.normalize();
double l_t = ((2 * M_PI) /( fabs(ge->curvature(u))
* CTX::instance()->mesh.minCircPoints ));
double l_n = 1.e12;
return buildMetricTangentToCurve(t,l_t,l_n);
}
static double max_edge_curvature(const GVertex *gv)
{
double val = 0;
std::list<GEdge*> l_edges = gv->edges();
for (std::list<GEdge*>::const_iterator ite = l_edges.begin();
ite != l_edges.end(); ++ite){
GEdge *_myGEdge = *ite;
Range<double> range = _myGEdge->parBounds(0);
double cc;
if (gv == _myGEdge->getBeginVertex()) cc = _myGEdge->curvature(range.low());
else cc = _myGEdge->curvature(range.high());
val = std::max(val, cc);
}
return val;
}
static double max_surf_curvature(const GEdge *ge, double u)
{
double val = 0;
std::list<GFace *> faces = ge->faces();
std::list<GFace *>::iterator it = faces.begin();
while(it != faces.end()){
if ((*it)->geomType() != GEntity::CompoundSurface &&
(*it)->geomType() != GEntity::DiscreteSurface){
SPoint2 par = ge->reparamOnFace((*it), u, 1);
double cc = (*it)->curvature(par);
val = std::max(cc, val);
}
++it;
}
return val;
}
// static double max_surf_curvature_vertex(const GVertex *gv)
// {
// double val = 0;
// std::list<GEdge*> l_edges = gv->edges();
// for (std::list<GEdge*>::const_iterator ite = l_edges.begin();
// ite != l_edges.end(); ++ite){
// GEdge *_myGEdge = *ite;
// Range<double> bounds = _myGEdge->parBounds(0);
// if (gv == _myGEdge->getBeginVertex())
// val = std::max(val, max_surf_curvature(_myGEdge, bounds.low()));
// else
// val = std::max(val, max_surf_curvature(_myGEdge, bounds.high()));
// }
// return val;
// }
SMetric3 metric_based_on_surface_curvature(const GFace *gf, double u, double v,
bool surface_isotropic,
double d_normal ,
double d_tangent_max)
{
if (gf->geomType() == GEntity::Plane)return SMetric3(1.e-12);
double cmax, cmin;
SVector3 dirMax,dirMin;
cmax = gf->curvatures(SPoint2(u, v),&dirMax, &dirMin, &cmax,&cmin);
if (cmin == 0)cmin =1.e-12;
if (cmax == 0)cmax =1.e-12;
double lambda1 = ((2 * M_PI) /( fabs(cmin) * CTX::instance()->mesh.minCircPoints ) );
double lambda2 = ((2 * M_PI) /( fabs(cmax) * CTX::instance()->mesh.minCircPoints ) );
SVector3 Z = crossprod(dirMax,dirMin);
if (surface_isotropic) lambda2 = lambda1 = std::min(lambda2,lambda1);
dirMin.normalize();
dirMax.normalize();
Z.normalize();
lambda1 = std::max(lambda1, CTX::instance()->mesh.lcMin);
lambda2 = std::max(lambda2, CTX::instance()->mesh.lcMin);
lambda1 = std::min(lambda1, CTX::instance()->mesh.lcMax);
lambda2 = std::min(lambda2, CTX::instance()->mesh.lcMax);
double lambda3 = std::min(d_normal, CTX::instance()->mesh.lcMax);
lambda3 = std::max(lambda3, CTX::instance()->mesh.lcMin);
lambda1 = std::min(lambda1, d_tangent_max);
lambda2 = std::min(lambda2, d_tangent_max);
SMetric3 curvMetric (1./(lambda1*lambda1),1./(lambda2*lambda2),
1./(lambda3*lambda3),
dirMin, dirMax, Z );
return curvMetric;
}
static SMetric3 metric_based_on_surface_curvature(const GEdge *ge, double u, bool iso_surf)
{
const GEdgeCompound* ptrCompoundEdge = dynamic_cast<const GEdgeCompound*>(ge);
if (ptrCompoundEdge){
double cmax, cmin;
SVector3 dirMax,dirMin;
cmax = ptrCompoundEdge->curvatures(u,&dirMax, &dirMin, &cmax,&cmin);
if (cmin == 0)cmin =1.e-12;
if (cmax == 0)cmax =1.e-12;
double lambda2 = ((2 * M_PI) /( fabs(cmax) * CTX::instance()->mesh.minCircPoints ) );
double lambda1 = ((2 * M_PI) /( fabs(cmin) * CTX::instance()->mesh.minCircPoints ) );
SVector3 Z = crossprod(dirMax,dirMin);
lambda1 = std::max(lambda1, CTX::instance()->mesh.lcMin);
lambda2 = std::max(lambda2, CTX::instance()->mesh.lcMin);
lambda1 = std::min(lambda1, CTX::instance()->mesh.lcMax);
lambda2 = std::min(lambda2, CTX::instance()->mesh.lcMax);
SMetric3 curvMetric (1. / (lambda1 * lambda1), 1. / (lambda2 * lambda2),
1.e-12, dirMin, dirMax, Z);
return curvMetric;
}
else{
SMetric3 mesh_size(1.e-12);
std::list<GFace *> faces = ge->faces();
std::list<GFace *>::iterator it = faces.begin();
// we choose the metric eigenvectors to be the ones
// related to the edge ...
SMetric3 curvMetric = max_edge_curvature_metric(ge, u);
while(it != faces.end()){
if (((*it)->geomType() != GEntity::CompoundSurface) &&
((*it)->geomType() != GEntity::DiscreteSurface)){
SPoint2 par = ge->reparamOnFace((*it), u, 1);
SMetric3 m = metric_based_on_surface_curvature (*it, par.x(), par.y(), iso_surf);
curvMetric = intersection_conserveM1(curvMetric,m);
}
++it;
}
return curvMetric;
}
}
static SMetric3 metric_based_on_surface_curvature(const GVertex *gv, bool iso_surf)
{
SMetric3 mesh_size(1.e-15);
std::list<GEdge*> l_edges = gv->edges();
for (std::list<GEdge*>::const_iterator ite = l_edges.begin();
ite != l_edges.end(); ++ite){
GEdge *_myGEdge = *ite;
Range<double> bounds = _myGEdge->parBounds(0);
// ES: Added extra if condition to use the code below only with compund curves
// This is because we want to call the function
// metric_based_on_surface_curvature(const GEdge *ge, double u) for the case when
// ge is a compound edge
if (_myGEdge->geomType() == GEntity::CompoundCurve){
if (gv == _myGEdge->getBeginVertex())
mesh_size = intersection
(mesh_size,
metric_based_on_surface_curvature(_myGEdge, bounds.low(), iso_surf));
else
mesh_size = intersection
(mesh_size,
metric_based_on_surface_curvature(_myGEdge, bounds.high(), iso_surf));
}
}
return mesh_size;
}
// the mesh vertex is classified on a model vertex. we compute the
// maximum of the curvature of model faces surrounding this point if
// it is classified on a model edge, we do the same for all model
// faces surrounding it if it is on a model face, we compute the
// curvature at this location
static double LC_MVertex_CURV(GEntity *ge, double U, double V)
{
double Crv = 0;
switch(ge->dim()){
case 0:
Crv = max_edge_curvature((const GVertex *)ge);
//Crv = std::max(max_surf_curvature_vertex((const GVertex *)ge), Crv);
// Crv = max_surf_curvature((const GVertex *)ge);
break;
case 1:
{
GEdge *ged = (GEdge *)ge;
Crv = ged->curvature(U);
Crv = std::max(Crv, max_surf_curvature(ged, U));
// Crv = max_surf_curvature(ged, U);
}
break;
case 2:
{
GFace *gf = (GFace *)ge;
Crv = gf->curvature(SPoint2(U, V));
}
break;
}
double lc = Crv > 0 ? 2 * M_PI / Crv / CTX::instance()->mesh.minCircPoints : MAX_LC;
return lc;
}
SMetric3 LC_MVertex_CURV_ANISO(GEntity *ge, double U, double V)
{
bool iso_surf = CTX::instance()->mesh.lcFromCurvature == 2;
switch(ge->dim()){
case 0: return metric_based_on_surface_curvature((const GVertex *)ge, iso_surf);
case 1: return metric_based_on_surface_curvature((const GEdge *)ge, U, iso_surf);
case 2: return metric_based_on_surface_curvature((const GFace *)ge, U, V, iso_surf);
}
Msg::Error("Curvature control impossible to compute for a volume!");
return SMetric3();
}
// compute the mesh size at a given vertex due to prescribed sizes at
// mesh vertices
static double LC_MVertex_PNTS(GEntity *ge, double U, double V)
{
switch(ge->dim()){
case 0:
{
GVertex *gv = (GVertex *)ge;
double lc = gv->prescribedMeshSizeAtVertex();
// FIXME we might want to remove this to make all lc treatment consistent
if(lc >= MAX_LC) return CTX::instance()->lc / 10.;
return lc;
}
case 1:
{
GEdge *ged = (GEdge *)ge;
GVertex *v1 = ged->getBeginVertex();
GVertex *v2 = ged->getEndVertex();
if (v1 && v2){
Range<double> range = ged->parBounds(0);
double a = (U - range.low()) / (range.high() - range.low());
double lc = (1 - a) * v1->prescribedMeshSizeAtVertex() +
(a) * v2->prescribedMeshSizeAtVertex() ;
// FIXME we might want to remove this to make all lc treatment consistent
if(lc >= MAX_LC) return CTX::instance()->lc / 10.;
return lc;
}
else
return MAX_LC;
}
default:
return MAX_LC;
}
}
// This is the only function that is used by the meshers
double BGM_MeshSize(GEntity *ge, double U, double V,
double X, double Y, double Z)
{
// default lc (mesh size == size of the model)
double l1 = CTX::instance()->lc;
// lc from points
double l2 = MAX_LC;
if(CTX::instance()->mesh.lcFromPoints && ge->dim() < 2)
l2 = LC_MVertex_PNTS(ge, U, V);
// lc from curvature
double l3 = MAX_LC;
if(CTX::instance()->mesh.lcFromCurvature && ge->dim() < 3)
l3 = LC_MVertex_CURV(ge, U, V);
// lc from fields
double l4 = MAX_LC;
FieldManager *fields = ge->model()->getFields();
if(fields->getBackgroundField() > 0){
Field *f = fields->get(fields->getBackgroundField());
if(f) l4 = (*f)(X, Y, Z, ge);
}
// take the minimum, then constrain by lcMin and lcMax
double lc = std::min(std::min(std::min(l1, l2), l3), l4);
lc = std::max(lc, CTX::instance()->mesh.lcMin);
lc = std::min(lc, CTX::instance()->mesh.lcMax);
if(lc <= 0.){
Msg::Error("Wrong mesh element size lc = %g (lcmin = %g, lcmax = %g)",
lc, CTX::instance()->mesh.lcMin, CTX::instance()->mesh.lcMax);
lc = l1;
}
//Msg::Debug("BGM X,Y,Z=%g,%g,%g L4=%g L3=%g L2=%g L1=%g LC=%g LFINAL=%g DIM =%d ",
//X, Y, Z, l4, l3, l2, l1, lc, lc * CTX::instance()->mesh.lcFactor, ge->dim());
//Emi fix
//if (lc == l1) lc /= 10.;
return lc * CTX::instance()->mesh.lcFactor;
}
// anisotropic version of the background field
SMetric3 BGM_MeshMetric(GEntity *ge,
double U, double V,
double X, double Y, double Z)
{
// Metrics based on element size
// Element size = min. between default lc and lc from point (if applicable), constrained by lcMin and lcMax
double lc = CTX::instance()->lc;
if(CTX::instance()->mesh.lcFromPoints && ge->dim() < 2) lc = std::min(lc, LC_MVertex_PNTS(ge, U, V));
lc = std::max(lc, CTX::instance()->mesh.lcMin);
lc = std::min(lc, CTX::instance()->mesh.lcMax);
if(lc <= 0.){
Msg::Error("Wrong mesh element size lc = %g (lcmin = %g, lcmax = %g)",
lc, CTX::instance()->mesh.lcMin, CTX::instance()->mesh.lcMax);
lc = CTX::instance()->lc;
}
SMetric3 m0(1./(lc*lc));
// Intersect with metrics from fields if applicable
FieldManager *fields = ge->model()->getFields();
SMetric3 m1 = m0;
if(fields->getBackgroundField() > 0){
Field *f = fields->get(fields->getBackgroundField());
if(f) {
SMetric3 l4;
if (!f->isotropic()) (*f)(X, Y, Z, l4, ge);
else {
const double L = (*f)(X, Y, Z, ge);
l4 = SMetric3(1/(L*L));
}
m1 = intersection(l4, m0);
}
}
// Intersect with metrics from curvature if applicable
SMetric3 m = (CTX::instance()->mesh.lcFromCurvature && ge->dim() < 3) ?
intersection(m1, LC_MVertex_CURV_ANISO(ge, U, V)) : m1;
return m;
}
bool Extend1dMeshIn2dSurfaces()
{
return CTX::instance()->mesh.lcExtendFromBoundary ? true : false;
}
bool Extend2dMeshIn3dVolumes()
{
return CTX::instance()->mesh.lcExtendFromBoundary ? true : false;
}
void backgroundMesh::set(GFace *gf)
{
if (_current) delete _current;
_current = new backgroundMesh(gf);
}
void backgroundMesh::setCrossFieldsByDistance(GFace *gf)
{
if (_current) delete _current;
_current = new backgroundMesh(gf, true);
}
void backgroundMesh::unset()
{
if (_current) delete _current;
_current = 0;
}
double backgroundMesh::sizeFactor = 1.0;
backgroundMesh::backgroundMesh(GFace *_gf, bool cfd)
#if defined(HAVE_ANN)
: _octree(0), uv_kdtree(0), nodes(0), angle_nodes(0), angle_kdtree(0)
#endif
{
if (cfd){
Msg::Info("Building A Cross Field Using Closest Distance");
propagateCrossFieldByDistance(_gf);
return;
}
// create a bunch of triangles on the parametric space
// those triangles are local to the backgroundMesh so that
// they do not depend on the actual mesh that can be deleted
std::set<SPoint2> myBCNodes;
for (unsigned int i = 0; i < _gf->triangles.size(); i++){
MTriangle *e = _gf->triangles[i];
MVertex *news[3];
for (int j=0;j<3;j++){
MVertex *v = e->getVertex(j);
std::map<MVertex*,MVertex*>::iterator it = _3Dto2D.find(v);
MVertex *newv =0;
if (it == _3Dto2D.end()){
SPoint2 p;
reparamMeshVertexOnFace(v, _gf, p);
newv = new MVertex (p.x(), p.y(), 0.0);
_vertices.push_back(newv);
_3Dto2D[v] = newv;
_2Dto3D[newv] = v;
if(v->onWhat()->dim()<2) myBCNodes.insert(p);
}
else newv = it->second;
news[j] = newv;
}
MTriangle *T2D = new MTriangle(news[0],news[1],news[2]);
_triangles.push_back(T2D);
}
#if defined(HAVE_ANN)
//printf("creating uv kdtree %d \n", myBCNodes.size());
index = new ANNidx[2];
dist = new ANNdist[2];
nodes = annAllocPts(myBCNodes.size(), 3);
std::set<SPoint2>::iterator itp = myBCNodes.begin();
int ind = 0;
while (itp != myBCNodes.end()){
SPoint2 pt = *itp;
//fprintf(of, "SP(%g,%g,%g){%g};\n", pt.x(), pt.y(), 0.0, 10000);
nodes[ind][0] = pt.x();
nodes[ind][1] = pt.y();
nodes[ind][2] = 0.0;
itp++; ind++;
}
uv_kdtree = new ANNkd_tree(nodes, myBCNodes.size(), 3);
#endif
// build a search structure
_octree = new MElementOctree(_triangles);
// compute the mesh sizes at nodes
if (CTX::instance()->mesh.lcFromPoints){
propagate1dMesh(_gf);
}
else {
std::map<MVertex*, MVertex*>::iterator itv2 = _2Dto3D.begin();
for ( ; itv2 != _2Dto3D.end(); ++itv2){
_sizes[itv2->first] = CTX::instance()->mesh.lcMax;
}
}
// ensure that other criteria are fullfilled
updateSizes(_gf);
// compute optimal mesh orientations
propagateCrossField(_gf);
_3Dto2D.clear();
_2Dto3D.clear();
}
backgroundMesh::~backgroundMesh()
{
for (unsigned int i = 0; i < _vertices.size(); i++) delete _vertices[i];
for (unsigned int i = 0; i < _triangles.size(); i++) delete _triangles[i];
if (_octree)delete _octree;
#if defined(HAVE_ANN)
if(uv_kdtree) delete uv_kdtree;
if(angle_kdtree) delete angle_kdtree;
if(nodes) annDeallocPts(nodes);
if(angle_nodes) annDeallocPts(angle_nodes);
delete[]index;
delete[]dist;
#endif
}
static void propagateValuesOnFace(GFace *_gf,
std::map<MVertex*,double> &dirichlet,
simpleFunction<double> *ONE,
bool in_parametric_plane = false)
{
#if defined(HAVE_SOLVER)
linearSystem<double> *_lsys = 0;
#if defined(HAVE_PETSC) && !defined(HAVE_TAUCS)
_lsys = new linearSystemPETSc<double>;
#elif defined(HAVE_GMM) && !defined(HAVE_TAUCS)
linearSystemGmm<double> *_lsysb = new linearSystemGmm<double>;
_lsysb->setGmres(1);
_lsys = _lsysb;
#elif defined(HAVE_TAUCS)
_lsys = new linearSystemCSRTaucs<double>;
#else
_lsys = new linearSystemFull<double>;
#endif
dofManager<double> myAssembler(_lsys);
// fix boundary conditions
std::map<MVertex*, double>::iterator itv = dirichlet.begin();
for ( ; itv != dirichlet.end(); ++itv){
myAssembler.fixVertex(itv->first, 0, 1, itv->second);
}
// Number vertices
std::set<MVertex*> vs;
for (unsigned int k = 0; k < _gf->triangles.size(); k++)
for (int j=0;j<3;j++)vs.insert(_gf->triangles[k]->getVertex(j));
for (unsigned int k = 0; k < _gf->quadrangles.size(); k++)
for (int j=0;j<4;j++)vs.insert(_gf->quadrangles[k]->getVertex(j));
std::map<MVertex*,SPoint3> theMap;
if ( in_parametric_plane) {
for (std::set<MVertex*>::iterator it = vs.begin(); it != vs.end(); ++it){
SPoint2 p;
reparamMeshVertexOnFace ( *it, _gf, p);
theMap[*it] = SPoint3((*it)->x(),(*it)->y(),(*it)->z());
(*it)->setXYZ(p.x(),p.y(),0.0);
}
}
for (std::set<MVertex*>::iterator it = vs.begin(); it != vs.end(); ++it)
myAssembler.numberVertex(*it, 0, 1);
// Assemble
laplaceTerm l(0, 1, ONE);
for (unsigned int k = 0; k < _gf->triangles.size(); k++){
MTriangle *t = _gf->triangles[k];
SElement se(t);
l.addToMatrix(myAssembler, &se);
}
// Solve
if (myAssembler.sizeOfR()){
_lsys->systemSolve();
}
// save solution
for (std::set<MVertex*>::iterator it = vs.begin(); it != vs.end(); ++it){
myAssembler.getDofValue(*it, 0, 1, dirichlet[*it]);
}
if ( in_parametric_plane) {
for (std::set<MVertex*>::iterator it = vs.begin(); it != vs.end(); ++it){
SPoint3 p = theMap[(*it)];
(*it)->setXYZ(p.x(),p.y(),p.z());
}
}
delete _lsys;
#endif
}
void backgroundMesh::propagate1dMesh(GFace *_gf)
{
std::list<GEdge*> e;// = _gf->edges();
replaceMeshCompound(_gf, e);
std::list<GEdge*>::const_iterator it = e.begin();
std::map<MVertex*,double> sizes;
for( ; it != e.end(); ++it ){
if (!(*it)->isSeam(_gf)){
for(unsigned int i = 0; i < (*it)->lines.size(); i++ ){
MVertex *v1 = (*it)->lines[i]->getVertex(0);
MVertex *v2 = (*it)->lines[i]->getVertex(1);
if (v1 != v2){
double d = sqrt((v1->x() - v2->x()) * (v1->x() - v2->x()) +
(v1->y() - v2->y()) * (v1->y() - v2->y()) +
(v1->z() - v2->z()) * (v1->z() -v2->z()));
for (int k=0;k<2;k++){
MVertex *v = (*it)->lines[i]->getVertex(k);
std::map<MVertex*, double>::iterator itv = sizes.find(v);
if (itv == sizes.end())
sizes[v] = log(d);
else
itv->second = 0.5 * (itv->second + log(d));
}
}
}
}
}
simpleFunction<double> ONE(1.0);
propagateValuesOnFace(_gf, sizes,&ONE);
std::map<MVertex*,MVertex*>::iterator itv2 = _2Dto3D.begin();
for ( ; itv2 != _2Dto3D.end(); ++itv2){
MVertex *v_2D = itv2->first;
MVertex *v_3D = itv2->second;
_sizes[v_2D] = exp(sizes[v_3D]);
}
}
crossField2d::crossField2d(MVertex* v, GEdge* ge)
{
double p;
bool success = reparamMeshVertexOnEdge(v, ge, p);
if (!success){
Msg::Warning("cannot reparametrize a point in crossField");
_angle = 0;
return;
}
SVector3 t = ge->firstDer (p);
t.normalize();
_angle = atan2 (t.y(),t.x());
crossField2d::normalizeAngle (_angle);
}
void backgroundMesh::propagateCrossFieldByDistance(GFace *_gf)
{
std::list<GEdge*> e;
replaceMeshCompound(_gf, e);
std::list<GEdge*>::const_iterator it = e.begin();
std::map<MVertex*,double> _cosines4,_sines4;
std::map<MVertex*,SPoint2> _param;
for( ; it != e.end(); ++it ){
if (!(*it)->isSeam(_gf)){
for(unsigned int i = 0; i < (*it)->lines.size(); i++ ){
MVertex *v[2];
v[0] = (*it)->lines[i]->getVertex(0);
v[1] = (*it)->lines[i]->getVertex(1);
SPoint2 p1,p2;
reparamMeshEdgeOnFace(v[0],v[1],_gf,p1,p2);
/* a correct way of computing angles */
Pair<SVector3, SVector3> der = _gf->firstDer((p1+p2)*.5);
SVector3 t1 = der.first();
SVector3 t2 (v[1]->x()-v[0]->x(),v[1]->y()-v[0]->y(),v[1]->z()-v[0]->z());
t1.normalize();
t2.normalize();
double _angle = angle (t1,t2);
// double angle = atan2 ( p1.y()-p2.y() , p1.x()-p2.x() );
crossField2d::normalizeAngle (_angle);
for (int i=0;i<2;i++){
std::map<MVertex*,double>::iterator itc = _cosines4.find(v[i]);
std::map<MVertex*,double>::iterator its = _sines4.find(v[i]);
if (itc != _cosines4.end()){
itc->second = 0.5*(itc->second + cos(4*_angle));
its->second = 0.5*(its->second + sin(4*_angle));
}
else {
_param[v[i]] = (i==0) ? p1 : p2;
_cosines4[v[i]] = cos(4*_angle);
_sines4[v[i]] = sin(4*_angle);
}
}
}
}
}
#if defined(HAVE_ANN)
index = new ANNidx[_NBANN];
dist = new ANNdist[_NBANN];
angle_nodes = annAllocPts(_cosines4.size(), 3);
std::map<MVertex*,double>::iterator itp = _cosines4.begin();
int ind = 0;
_sin.clear();
_cos.clear();
while (itp != _cosines4.end()){
MVertex *v = itp->first;
double c = itp->second;
SPoint2 pt = _param[v];
double s = _sines4[v];
angle_nodes[ind][0] = pt.x();
angle_nodes[ind][1] = pt.y();
angle_nodes[ind][2] = 0.0;
_cos.push_back(c);
_sin.push_back(s);
itp++;ind++;
}
angle_kdtree = new ANNkd_tree(angle_nodes, _cosines4.size(), 3);
#endif
}
inline double myAngle (const SVector3 &a, const SVector3 &b, const SVector3 &d){
double cosTheta = dot(a,b);
double sinTheta = dot(crossprod(a,b),d);
return atan2 (sinTheta,cosTheta);
}
// smoothness = h * (|grad (cos 4 a)| + |grad (sin 4 a)|)
// smoothness is of order 1 if not smooth
// smoothness is of order h/L if smooth
// h --> mesh size
// L --> domain size
double backgroundMesh::getSmoothness(MElement *e)
{
MVertex *v0 = _3Dto2D[e->getVertex(0)];
MVertex *v1 = _3Dto2D[e->getVertex(1)];
MVertex *v2 = _3Dto2D[e->getVertex(2)];
std::map<MVertex*,double> :: const_iterator i0 = _angles.find (v0);
std::map<MVertex*,double> :: const_iterator i1 = _angles.find (v1);
std::map<MVertex*,double> :: const_iterator i2 = _angles.find (v2);
double a[3] = {cos(4*i0->second),cos(4*i1->second),cos(4*i2->second)};
double b[3] = {sin(4*i0->second),sin(4*i1->second),sin(4*i2->second)};
// printf("coucou\n");
double f[3];
e->interpolateGrad(a,0,0,0,f);
const double gradcos = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
e->interpolateGrad(b,0,0,0,f);
const double gradsin = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
const double h = e->maxEdge();
return (gradcos /*+ gradsin*/) * h;
}
double backgroundMesh::getSmoothness(double u, double v, double w)
{
MElement *e = _octree->find(u, v, w, 2, true);
if (!e) return -1.0;
MVertex *v0 = e->getVertex(0);
MVertex *v1 = e->getVertex(1);
MVertex *v2 = e->getVertex(2);
std::map<MVertex*,double> :: const_iterator i0 = _angles.find (v0);
std::map<MVertex*,double> :: const_iterator i1 = _angles.find (v1);
std::map<MVertex*,double> :: const_iterator i2 = _angles.find (v2);
double a[3] = {cos(4*i0->second),cos(4*i1->second),cos(4*i2->second)};
double b[3] = {sin(4*i0->second),sin(4*i1->second),sin(4*i2->second)};
// printf("coucou\n");
double f[3];
e->interpolateGrad(a,0,0,0,f);
const double gradcos = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
e->interpolateGrad(b,0,0,0,f);
const double gradsin = sqrt (f[0]*f[0]+f[1]*f[1]+f[2]*f[2]);
const double h = e->maxEdge();
return (gradcos /*+ gradsin*/) * h;
}
void backgroundMesh::propagateCrossField(GFace *_gf)
{
// printf("coucou\n");
propagateCrossFieldHJ (_gf);
// solve the non liear problem
constantPerElement<double> C;
int ITER = 0;
// int NSMOOTH = _gf->triangles.size();
while(0){
// int NSMOOTH_NOW = 0;
for (unsigned int i = 0; i < _gf->triangles.size(); i++){
double smoothness = getSmoothness (_gf->triangles[i]);
double val = smoothness < .5 ? 1.0 : 1.e-3 ;//exp(-absf/10);
C.set(_gf->triangles[i],val);
}
// if (NSMOOTH_NOW == NSMOOTH) break;
// NSMOOTH = NSMOOTH_NOW;
// break;
_angles.clear();
propagateCrossField (_gf,&C);
if (++ITER > 0)break;
}
// printf("converged in %d iterations\n",ITER);
char name[256];
sprintf(name,"cross-%d-%d.pos",_gf->tag(),ITER);
print(name,0,1);
sprintf(name,"smooth-%d-%d.pos",_gf->tag(),ITER);
print(name,_gf,2);
}
void backgroundMesh::propagateCrossFieldHJ(GFace *_gf)
{
simpleFunction<double> ONE(1.0);
propagateCrossField (_gf, &ONE);
}
void backgroundMesh::propagateCrossField(GFace *_gf, simpleFunction<double> *ONE)
{
std::map<MVertex*,double> _cosines4,_sines4;
std::list<GEdge*> e;
replaceMeshCompound(_gf, e);
std::list<GEdge*>::const_iterator it = e.begin();
for( ; it != e.end(); ++it ){
if (!(*it)->isSeam(_gf)){
for(unsigned int i = 0; i < (*it)->lines.size(); i++ ){
MVertex *v[2];
v[0] = (*it)->lines[i]->getVertex(0);
v[1] = (*it)->lines[i]->getVertex(1);
SPoint2 p1,p2;
reparamMeshEdgeOnFace(v[0],v[1],_gf,p1,p2);
Pair<SVector3, SVector3> der = _gf->firstDer((p1+p2)*.5);
SVector3 t1 = der.first();
SVector3 t2 = der.second();
SVector3 n = crossprod(t1,t2);
n.normalize();
SVector3 d1(v[1]->x()-v[0]->x(),v[1]->y()-v[0]->y(),v[1]->z()-v[0]->z());
t1.normalize();
d1.normalize();
double _angle = myAngle (t1,d1,n);
crossField2d::normalizeAngle (_angle);
for (int i=0;i<2;i++){
std::map<MVertex*,double>::iterator itc = _cosines4.find(v[i]);
std::map<MVertex*,double>::iterator its = _sines4.find(v[i]);
if (itc != _cosines4.end()){
itc->second = 0.5*(itc->second + cos(4*_angle));
its->second = 0.5*(its->second + sin(4*_angle));
}
else {
_cosines4[v[i]] = cos(4*_angle);
_sines4[v[i]] = sin(4*_angle);
}
}
}
}
}
propagateValuesOnFace(_gf,_cosines4,ONE,false);
propagateValuesOnFace(_gf,_sines4,ONE,false);
std::map<MVertex*,MVertex*>::iterator itv2 = _2Dto3D.begin();
for ( ; itv2 != _2Dto3D.end(); ++itv2){
MVertex *v_2D = itv2->first;
MVertex *v_3D = itv2->second;
double angle = atan2(_sines4[v_3D],_cosines4[v_3D]) / 4.0;
crossField2d::normalizeAngle (angle);
_angles[v_2D] = angle;
}
}
void backgroundMesh::updateSizes(GFace *_gf)
{
std::map<MVertex*,double>::iterator itv = _sizes.begin();
for ( ; itv != _sizes.end(); ++itv){
SPoint2 p;
MVertex *v = _2Dto3D[itv->first];
double lc;
if (v->onWhat()->dim() == 0){
lc = sizeFactor * BGM_MeshSize(v->onWhat(), 0,0,v->x(),v->y(),v->z());
}
else if (v->onWhat()->dim() == 1){
double u;
v->getParameter(0, u);
lc = sizeFactor * BGM_MeshSize(v->onWhat(), u, 0, v->x(), v->y(), v->z());
}
else{
reparamMeshVertexOnFace(v, _gf, p);
lc = sizeFactor * BGM_MeshSize(_gf, p.x(), p.y(), v->x(), v->y(), v->z());
}
// printf("2D -- %g %g 3D -- %g %g\n",p.x(),p.y(),v->x(),v->y());
itv->second = std::min(lc,itv->second);
itv->second = std::max(itv->second, sizeFactor * CTX::instance()->mesh.lcMin);
itv->second = std::min(itv->second, sizeFactor * CTX::instance()->mesh.lcMax);
}
// do not allow large variations in the size field
// (Int. J. Numer. Meth. Engng. 43, 1143-1165 (1998) MESH GRADATION
// CONTROL, BOROUCHAKI, HECHT, FREY)
std::set<MEdge,Less_Edge> edges;
for (unsigned int i = 0; i < _triangles.size(); i++){
for (int j = 0; j < _triangles[i]->getNumEdges(); j++){
edges.insert(_triangles[i]->getEdge(j));
}
}
const double _beta = 1.3;
for (int i=0;i<3;i++){
std::set<MEdge,Less_Edge>::iterator it = edges.begin();
for ( ; it != edges.end(); ++it){
MVertex *v0 = it->getVertex(0);
MVertex *v1 = it->getVertex(1);
MVertex *V0 = _2Dto3D[v0];
MVertex *V1 = _2Dto3D[v1];
std::map<MVertex*,double>::iterator s0 = _sizes.find(V0);
std::map<MVertex*,double>::iterator s1 = _sizes.find(V1);
if (s0->second < s1->second)s1->second = std::min(s1->second,_beta*s0->second);
else s0->second = std::min(s0->second,_beta*s1->second);
}
}
}
bool backgroundMesh::inDomain (double u, double v, double w) const
{
return _octree->find(u, v, w, 2, true) != 0;
}
double backgroundMesh::operator() (double u, double v, double w) const
{
double uv[3] = {u, v, w};
double uv2[3];
MElement *e = _octree->find(u, v, w, 2, true);
if (!e) {
#if defined(HAVE_ANN)
//printf("BGM octree not found --> find in kdtree \n");
double pt[3] = {u, v, 0.0};
uv_kdtree->annkSearch(pt, 2, index, dist);
SPoint3 p1(nodes[index[0]][0], nodes[index[0]][1], nodes[index[0]][2]);
SPoint3 p2(nodes[index[1]][0], nodes[index[1]][1], nodes[index[1]][2]);
SPoint3 pnew; double d;
signedDistancePointLine(p1, p2, SPoint3(u, v, 0.), d, pnew);
e = _octree->find(pnew.x(), pnew.y(), 0.0, 2, true);
#endif
if(!e){
Msg::Error("BGM octree: cannot find UVW=%g %g %g", u, v, w);
return -1000.0;//0.4;
}
}
e->xyz2uvw(uv, uv2);
std::map<MVertex*,double>::const_iterator itv1 = _sizes.find(e->getVertex(0));
std::map<MVertex*,double>::const_iterator itv2 = _sizes.find(e->getVertex(1));
std::map<MVertex*,double>::const_iterator itv3 = _sizes.find(e->getVertex(2));
return itv1->second * (1-uv2[0]-uv2[1]) + itv2->second * uv2[0] + itv3->second * uv2[1];
}
double backgroundMesh::getAngle(double u, double v, double w) const
{
// JFR :
// we can use closest point for computing
// cross field angles : this allow NOT to
// generate a spurious mesh and solve a PDE
if (!_octree){
#if defined(HAVE_ANN)
double pt[3] = {u,v,0.0};
angle_kdtree->annkSearch(pt, _NBANN, index, dist);
double SINE = 0.0 , COSINE = 0.0;
for (int i=0;i<_NBANN;i++){
SINE += _sin[index[i]];
COSINE += _cos[index[i]];
// printf("%2d %2d %12.5E %12.5E\n",i,index[i],_sin[index[i]],_cos[index[i]]);
}
double angle = atan2(SINE,COSINE)/4.0;
crossField2d::normalizeAngle (angle);
return angle;
#endif
}
// HACK FOR LEWIS
// h = 1+30(y-x^2)^2 + (1-x)^2
// double x = u;
// double y = v;
// double dhdx = 30 * 2 * (y-x*x) * (-2*x) - 2 * (1-x);
// double dhdy = 30 * 2 * (y-x*x);
// double angles = atan2(y,x*x);
// crossField2d::normalizeAngle (angles);
// return angles;
double uv[3] = {u, v, w};
double uv2[3];
MElement *e = _octree->find(u, v, w, 2, true);
if (!e) {
#if defined(HAVE_ANN)
//printf("BGM octree not found --> find in kdtree \n");
double pt[3] = {u,v,0.0};
uv_kdtree->annkSearch(pt, 2, index, dist);
SPoint3 p1(nodes[index[0]][0], nodes[index[0]][1], nodes[index[0]][2]);
SPoint3 p2(nodes[index[1]][0], nodes[index[1]][1], nodes[index[1]][2]);
SPoint3 pnew; double d;
signedDistancePointLine(p1, p2, SPoint3(u, v, 0.), d, pnew);
e = _octree->find(pnew.x(), pnew.y(), 0., 2, true);
#endif
if(!e){
Msg::Error("BGM octree angle: cannot find UVW=%g %g %g", u, v, w);
return -1000.0;
}
}
e->xyz2uvw(uv, uv2);
std::map<MVertex*,double>::const_iterator itv1 = _angles.find(e->getVertex(0));
std::map<MVertex*,double>::const_iterator itv2 = _angles.find(e->getVertex(1));
std::map<MVertex*,double>::const_iterator itv3 = _angles.find(e->getVertex(2));
double cos4 = cos (4*itv1->second) * (1-uv2[0]-uv2[1]) +
cos (4*itv2->second) * uv2[0] +
cos (4*itv3->second) * uv2[1] ;
double sin4 = sin (4*itv1->second) * (1-uv2[0]-uv2[1]) +
sin (4*itv2->second) * uv2[0] +
sin (4*itv3->second) * uv2[1] ;
double angle = atan2(sin4,cos4)/4.0;
crossField2d::normalizeAngle (angle);
return angle;
}
void backgroundMesh::print(const std::string &filename, GFace *gf,
const std::map<MVertex*,double> &_whatToPrint, int smooth)
{
FILE *f = Fopen (filename.c_str(),"w");
fprintf(f,"View \"Background Mesh\"{\n");
if (smooth){
for(unsigned int i=0;i<gf->triangles.size();i++){
MVertex *v1 = gf->triangles[i]->getVertex(0);
MVertex *v2 = gf->triangles[i]->getVertex(1);
MVertex *v3 = gf->triangles[i]->getVertex(2);
double x = getSmoothness (gf->triangles[i]);
fprintf(f,"ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n",
v1->x(),v1->y(),v1->z(),
v2->x(),v2->y(),v2->z(),
v3->x(),v3->y(),v3->z(),x,x,x);
}
}
else {
for(unsigned int i=0;i<_triangles.size();i++){
MVertex *v1 = _triangles[i]->getVertex(0);
MVertex *v2 = _triangles[i]->getVertex(1);
MVertex *v3 = _triangles[i]->getVertex(2);
std::map<MVertex*,double>::const_iterator itv1 = _whatToPrint.find(v1);
std::map<MVertex*,double>::const_iterator itv2 = _whatToPrint.find(v2);
std::map<MVertex*,double>::const_iterator itv3 = _whatToPrint.find(v3);
if (!gf){
fprintf(f,"ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n",
v1->x(),v1->y(),v1->z(),
v2->x(),v2->y(),v2->z(),
v3->x(),v3->y(),v3->z(),itv1->second,itv2->second,itv3->second);
}
else {
GPoint p1 = gf->point(SPoint2(v1->x(),v1->y()));
GPoint p2 = gf->point(SPoint2(v2->x(),v2->y()));
GPoint p3 = gf->point(SPoint2(v3->x(),v3->y()));
fprintf(f,"ST(%g,%g,%g,%g,%g,%g,%g,%g,%g) {%g,%g,%g};\n",
p1.x(),p1.y(),p1.z(),
p2.x(),p2.y(),p2.z(),
p3.x(),p3.y(),p3.z(),itv1->second,itv2->second,itv3->second);
}
}
}
fprintf(f,"};\n");
fclose(f);
}
MElementOctree* backgroundMesh::get_octree(){
return _octree;
}
MElement *backgroundMesh::getMeshElementByCoord(double u, double v, double w, bool strict)
{
if(!_octree){
Msg::Debug("Rebuilding BackgroundMesh element octree");
_octree = new MElementOctree(_triangles);
}
return _octree->find(u,v,w, 2, strict);
}
backgroundMesh* backgroundMesh::_current = 0;