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;
}
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();
}
// 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::min(lc, ge->getMeshSize());
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;
}
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;
}
void Centerline::operator() (double x, double y, double z, SMetric3 &metr, GEntity *ge)
{
if (update_needed){
std::ifstream input;
input.open(fileName.c_str());
if(StatFile(fileName))
Msg::Fatal("Centerline file '%s' does not exist", fileName.c_str());
importFile(fileName);
buildKdTree();
update_needed = false;
}
//take xyz = closest point on boundary in case we are on
//the planar IN/OUT FACES or in VOLUME
double xyz[3] = {x,y,z};
bool onTubularSurface = true;
double ds = 0.0;
bool isCompound = (ge->dim() == 2 && ge->geomType() == GEntity::CompoundSurface) ?
true : false;
bool onInOutlets = (ge->geomType() == GEntity::Plane) ? true: false;
std::list<GFace*> cFaces;
if (isCompound) cFaces = ((GFaceCompound*)ge)->getCompounds();
if ( ge->dim() == 3 || (ge->dim() == 2 && ge->geomType() == GEntity::Plane) ||
(isCompound && (*cFaces.begin())->geomType() == GEntity::Plane) ){
onTubularSurface = false;
}
ANNidx index[1];
ANNdist dist[1];
kdtreeR->annkSearch(xyz, 1, index, dist);
if (! onTubularSurface){
ANNpointArray nodesR = kdtreeR->thePoints();
ds = sqrt(dist[0]);
xyz[0] = nodesR[index[0]][0];
xyz[1] = nodesR[index[0]][1];
xyz[2] = nodesR[index[0]][2];
}
ANNidx index2[2];
ANNdist dist2[2];
kdtree->annkSearch(xyz, 2, index2, dist2);
double radMax = sqrt(dist2[0]);
ANNpointArray nodes = kdtree->thePoints();
SVector3 p0(nodes[index2[0]][0], nodes[index2[0]][1], nodes[index2[0]][2]);
SVector3 p1(nodes[index2[1]][0], nodes[index2[1]][1], nodes[index2[1]][2]);
//dir_a = direction along the centerline
//dir_n = normal direction of the disk
//dir_t = tangential direction of the disk
SVector3 dir_a = p1-p0; dir_a.normalize();
SVector3 dir_n(xyz[0]-p0.x(), xyz[1]-p0.y(), xyz[2]-p0.z()); dir_n.normalize();
SVector3 dir_cross = crossprod(dir_a,dir_n); dir_cross.normalize();
// if (ge->dim()==3){
// printf("coucou dim ==3 !!!!!!!!!!!!!!! \n");
// SVector3 d1,d2,d3;
// computeCrossField(x,y,z,d1,d2,d3);
// exit(1);
// }
//find discrete curvature at closest vertex
Curvature& curvature = Curvature::getInstance();
if( !Curvature::valueAlreadyComputed() ) {
Msg::Info("Need to compute discrete curvature");
Curvature::typeOfCurvature type = Curvature::RUSIN;
curvature.computeCurvature(current, type);
}
double curv, cMin, cMax;
SVector3 dMin, dMax;
int isAbs = 1.0;
curvature.vertexNodalValuesAndDirections(vertices[index[0]],&dMax, &dMin, &cMax, &cMin, isAbs);
curvature.vertexNodalValues(vertices[index[0]], curv, 1);
if (cMin == 0) cMin =1.e-12;
if (cMax == 0) cMax =1.e-12;
double rhoMin = 1./cMin;
double rhoMax = 1./cMax;
//double signMin = (rhoMin > 0.0) ? -1.0: 1.0;
//double signMax = (rhoMax > 0.0) ? -1.0: 1.0;
//user-defined parameters
//define h_n, h_t1, and h_t2
double thickness = radMax/3.;
double h_far = radMax/5.;
double beta = (ds <= thickness) ? 1.2 : 2.1; //CTX::instance()->mesh.smoothRatio;
double ddist = (ds <= thickness) ? ds: thickness;
double h_n_0 = thickness/20.;
double h_n = std::min( (h_n_0+ds*log(beta)), h_far);
double betaMin = 10.0;
double betaMax = 3.1;
double oneOverD2_min = 1./(2.*rhoMin*rhoMin*(betaMin*betaMin-1)) *
(sqrt(1+ (4.*rhoMin*rhoMin*(betaMin*betaMin-1))/(h_n*h_n))-1.);
double oneOverD2_max = 1./(2.*rhoMax*rhoMax*(betaMax*betaMax-1)) *
(sqrt(1+ (4.*rhoMax*rhoMax*(betaMax*betaMax-1))/(h_n*h_n))-1.);
double h_t1_0 = sqrt(1./oneOverD2_min);
double h_t2_0 = sqrt(1./oneOverD2_max);
//double h_t1 = h_t1_0*(rhoMin+signMin*ddist)/rhoMin ;
//double h_t2 = h_t2_0*(rhoMax+signMax*ddist)/rhoMax ;
double h_t1 = std::min( (h_t1_0+(ddist*log(beta))), radMax);
double h_t2 = std::min( (h_t2_0+(ddist*log(beta))), h_far);
double dCenter = radMax-ds;
double h_a_0 = 0.5*radMax;
double h_a = h_a_0 - (h_a_0-h_t1_0)/(radMax)*dCenter;
//length between min and max
double lcMin = ((2 * M_PI *radMax) /( 50*nbPoints )); //CTX::instance()->mesh.lcMin;
double lcMax = lcMin*2000.; //CTX::instance()->mesh.lcMax;
h_n = std::max(h_n, lcMin); h_n = std::min(h_n, lcMax);
h_t1 = std::max(h_t1, lcMin); h_t1 = std::min(h_t1, lcMax);
h_t2 = std::max(h_t2, lcMin); h_t2 = std::min(h_t2, lcMax);
//curvature metric
SMetric3 curvMetric, curvMetric1, curvMetric2;
SMetric3 centMetric1, centMetric2, centMetric;
if (onInOutlets){
metr = buildMetricTangentToCurve(dir_n,h_n,h_t2);
}
else {
//on surface and in volume boundary layer
if ( ds < thickness ){
metr = metricBasedOnSurfaceCurvature(dMin, dMax, cMin, cMax, h_n, h_t1, h_t2);
}
//in volume
else {
//curvMetric = metricBasedOnSurfaceCurvature(dMin, dMax, cMin, cMax, h_n, h_t1, h_t2);
metr = SMetric3( 1./(h_a*h_a), 1./(h_n*h_n), 1./(h_n*h_n), dir_a, dir_n, dir_cross);
//metr = intersection_conserveM1_bis(metr, curvMetric);
//metr = intersection_conserveM1(metr,curvMetric);
//metr = intersection_conserve_mostaniso(metr, curvMetric);
//metr = intersection(metr,curvMetric);
}
}
return;
}
bool frameFieldBackgroundMesh2D::compute_RK_infos(double u,double v, double x, double y, double z, RK_form &infos)
{
// check if point is in domain
if (!inDomain(u,v)) return false;
// get stored angle
double angle_current = angle(u,v);
// compute t1,t2: cross field directions
// get the unit normal at that point
GFace *face = dynamic_cast<GFace*>(gf);
if(!face) {
Msg::Error("Entity is not a face in background mesh");
return false;
}
Pair<SVector3, SVector3> der = face->firstDer(SPoint2(u,v));
SVector3 s1 = der.first();
SVector3 s2 = der.second();
SVector3 n = crossprod(s1,s2);
n.normalize();
SVector3 basis_u = s1;
basis_u.normalize();
SVector3 basis_v = crossprod(n,basis_u);
// normalize vector t1 that is tangent to gf at uv
SVector3 t1 = basis_u * cos(angle_current) + basis_v * sin(angle_current) ;
t1.normalize();
// compute the second direction t2 and normalize (t1,t2,n) is the tangent frame
SVector3 t2 = crossprod(n,t1);
t2.normalize();
// get metric
double L = size(u,v);
infos.metricField = SMetric3(1./(L*L));
FieldManager *fields = gf->model()->getFields();
if(fields->getBackgroundField() > 0) {
Field *f = fields->get(fields->getBackgroundField());
if (!f->isotropic()) {
(*f)(x,y,z, infos.metricField,gf);
}
else {
L = (*f)(x,y,z,gf);
infos.metricField = SMetric3(1./(L*L));
}
}
double M = dot(s1,s1);
double N = dot(s2,s2);
double E = dot(s1,s2);
// compute the first fundamental form i.e. the metric tensor at the point
// M_{ij} = s_i \cdot s_j
double metric[2][2] = {{M,E},{E,N}};
// get sizes
double size_1 = sqrt(1. / dot(t1,infos.metricField,t1));
double size_2 = sqrt(1. / dot(t2,infos.metricField,t2));
// compute covariant coordinates of t1 and t2 - cross field directions in parametric domain
double covar1[2],covar2[2];
// t1 = a s1 + b s2 -->
// t1 . s1 = a M + b E
// t1 . s2 = a E + b N --> solve the 2 x 2 system
// and get covariant coordinates a and b
double rhs1[2] = {dot(t1,s1),dot(t1,s2)};
bool singular = false;
if (!sys2x2(metric,rhs1,covar1)) {
Msg::Info("Argh surface %d %g %g %g -- %g %g %g -- %g %g",gf->tag(),s1.x(),s1.y(),s1.z(),s2.x(),s2.y(),s2.z(),size_1,size_2);
covar1[1] = 1.0;
covar1[0] = 0.0;
singular = true;
}
double rhs2[2] = {dot(t2,s1),dot(t2,s2)};
if (!sys2x2(metric,rhs2,covar2)) {
Msg::Info("Argh surface %d %g %g %g -- %g %g %g",gf->tag(),s1.x(),s1.y(),s1.z(),s2.x(),s2.y(),s2.z());
covar2[0] = 1.0;
covar2[1] = 0.0;
singular = true;
}
// transform the sizes with respect to the metric
// consider a vector v of size 1 in the parameter plane
// its length is sqrt (v^T M v) --> if I want a real size
// of size1 in direction v, it should be sqrt(v^T M v) * size1
double l1 = sqrt(covar1[0]*covar1[0]+covar1[1]*covar1[1]);
double l2 = sqrt(covar2[0]*covar2[0]+covar2[1]*covar2[1]);
covar1[0] /= l1;
covar1[1] /= l1;
covar2[0] /= l2;
covar2[1] /= l2;
double size_param_1 = size_1 / sqrt ( M*covar1[0]*covar1[0]+
2*E*covar1[1]*covar1[0]+
N*covar1[1]*covar1[1]);
double size_param_2 = size_2 / sqrt ( M*covar2[0]*covar2[0]+
2*E*covar2[1]*covar2[0]+
N*covar2[1]*covar2[1]);
if (singular) {
size_param_1 = size_param_2 = std::min (size_param_1,size_param_2);
}
// filling form...
infos.t1 = t1;
infos.h.first = size_1;
infos.h.second = size_2;
infos.paramh.first = size_param_1;
infos.paramh.second = size_param_2;
infos.paramt1 = SPoint2(covar1[0],covar1[1]);
infos.paramt2 = SPoint2(covar2[0],covar2[1]);
infos.angle = angle_current;
infos.localsize = L;
infos.normal = n;
return true;
}