bool surfacePointWithExclusionRegion::inExclusionZone(const SPoint2 &p)
{
double mat[2][2];
double b[2], uv[2];
mat[0][0] = _q[1].x() - _q[0].x();
mat[0][1] = _q[2].x() - _q[0].x();
mat[1][0] = _q[1].y() - _q[0].y();
mat[1][1] = _q[2].y() - _q[0].y();
b[0] = p.x() - _q[0].x();
b[1] = p.y() - _q[0].y();
sys2x2(mat, b, uv);
// printf("inversion 1 : %g %g \n",uv[0],uv[1]);
if(uv[0] >= 0 && uv[1] >= 0 && 1. - uv[0] - uv[1] >= 0) return true;
mat[0][0] = _q[3].x() - _q[2].x();
mat[0][1] = _q[0].x() - _q[2].x();
mat[1][0] = _q[3].y() - _q[2].y();
mat[1][1] = _q[0].y() - _q[2].y();
b[0] = p.x() - _q[2].x();
b[1] = p.y() - _q[2].y();
sys2x2(mat, b, uv);
// printf("inversion 2 : %g %g \n",uv[0],uv[1]);
if(uv[0] >= 0 && uv[1] >= 0 && 1. - uv[0] - uv[1] >= 0) return true;
return false;
}
GPoint gmshFace::closestPoint(const SPoint3 & qp, const double initialGuess[2]) const
{
#if defined(HAVE_BFGS)
return GFace::closestPoint(qp, initialGuess);
#endif
if (s->Typ == MSH_SURF_PLAN && !s->geometry){
double XP = qp.x();
double YP = qp.y();
double ZP = qp.z();
double VX[3], VY[3], x, y, z;
getMeanPlaneData(VX, VY, x, y, z);
double M[3][2] = {{VX[0], VY[0]}, {VX[1], VY[1]}, {VX[2], VY[2]}};
double MN[2][2];
double B[3] = {XP - x, YP - y, ZP - z};
double BN[2], UV[2];
for (int i = 0; i < 2; i++){
BN[i] = 0;
for (int k = 0; k < 3; k++){
BN[i] += B[k] * M[k][i];
}
}
for (int i = 0; i < 2; i++){
for (int j = 0; j < 2; j++){
MN[i][j] = 0;
for (int k = 0; k < 3; k++){
MN[i][j] += M[k][i] * M[k][j];
}
}
}
sys2x2(MN, BN, UV);
return GPoint(XP, YP, ZP, this, UV);
}
Vertex v;
v.Pos.X = qp.x();
v.Pos.Y = qp.y();
v.Pos.Z = qp.z();
double u[2] = {initialGuess[0], initialGuess[1]};
bool result = ProjectPointOnSurface(s, v, u);
if (!result)
return GPoint(-1.e22, -1.e22, -1.e22, 0, u);
return GPoint(v.Pos.X, v.Pos.Y, v.Pos.Z, this, u);
}
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;
}
