// returns the cross field as a pair of othogonal vectors (NOT in parametric coordinates, but real 3D coordinates)
Pair<SVector3, SVector3> frameFieldBackgroundMesh2D::compute_crossfield_directions(double u, double v,
double angle_current)
{
// 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 Pair<SVector3,SVector3>(SVector3(), SVector3());
}
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();
return Pair<SVector3,SVector3>(SVector3(t1[0],t1[1],t1[2]),
SVector3(t2[0],t2[1],t2[2]));
}
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;
}
void frameFieldBackgroundMesh2D::computeCrossField(simpleFunction<double> &eval_diffusivity)
{
angles.clear();
DoubleStorageType _cosines4,_sines4;
list<GEdge*> e;
GFace *face = dynamic_cast<GFace*>(gf);
if(!face) {
Msg::Error("Entity is not a face in background mesh");
return;
}
replaceMeshCompound(face, e);
list<GEdge*>::const_iterator it = e.begin();
for( ; it != e.end(); ++it ) {
if (!(*it)->isSeam(face)) {
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],face,p1,p2);
Pair<SVector3, SVector3> der = face->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);
normalizeAngle (_angle);
for (int i=0; i<2; i++) {
DoubleStorageType::iterator itc = _cosines4.find(v[i]);
DoubleStorageType::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);
}
}
}
}
}
propagateValues(_cosines4,eval_diffusivity,false);
propagateValues(_sines4,eval_diffusivity,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;
normalizeAngle (angle);
angles[v_2D] = angle;
}
}
