bool GEdge::XYZToU(const double X, const double Y, const double Z,
double &u, const double relax) const
{
const int MaxIter = 25;
const int NumInitGuess = 11;
double err;//, err2;
int iter;
Range<double> uu = parBounds(0);
double uMin = uu.low();
double uMax = uu.high();
SVector3 Q(X, Y, Z), P;
double init[NumInitGuess];
for (int i = 0; i < NumInitGuess; i++)
init[i] = uMin + (uMax - uMin) / (NumInitGuess - 1) * i;
for(int i = 0; i < NumInitGuess; i++){
u = init[i];
double uNew = u;
//err2 = 1.0;
iter = 1;
SVector3 dPQ = P - Q;
err = dPQ.norm();
if (err < 1.e-8 * CTX::instance()->lc) return true;
while(iter++ < MaxIter && err > 1e-8 * CTX::instance()->lc) {
SVector3 der = firstDer(u);
uNew = u - relax * dot(dPQ,der) / dot(der,der);
uNew = std::min(uMax,std::max(uMin,uNew));
P = position(uNew);
dPQ = P - Q;
err = dPQ.norm();
//err2 = fabs(uNew - u);
u = uNew;
}
if (err < 1e-8 * CTX::instance()->lc) return true;
}
if(relax > 1.e-2) {
// Msg::Info("point %g %g %g on edge %d : Relaxation factor = %g",
// Q.x(), Q.y(), Q.z(), 0.75 * relax);
return XYZToU(Q.x(), Q.y(), Q.z(), u, 0.75 * relax);
}
// Msg::Error("Could not converge reparametrisation of point (%e,%e,%e) on edge %d",
// Q.x(), Q.y(), Q.z(), tag());
return false;
}
double distMaxStraight(MElement *el)
{
const polynomialBasis *lagrange = (polynomialBasis*)el->getFunctionSpace();
const polynomialBasis *lagrange1 = (polynomialBasis*)el->getFunctionSpace(1);
int nV = lagrange->points.size1();
int nV1 = lagrange1->points.size1();
int dim = lagrange1->dimension;
SPoint3 sxyz[256];
for (int i = 0; i < nV1; ++i) {
sxyz[i] = el->getVertex(i)->point();
}
for (int i = nV1; i < nV; ++i) {
double f[256];
lagrange1->f(lagrange->points(i, 0), lagrange->points(i, 1),
dim < 3 ? 0 : lagrange->points(i, 2), f);
for (int j = 0; j < nV1; ++j)
sxyz[i] += sxyz[j] * f[j];
}
double maxdx = 0.0;
for (int iV = nV1; iV < nV; iV++) {
SVector3 d = el->getVertex(iV)->point()-sxyz[iV];
double dx = d.norm();
if (dx > maxdx) maxdx = dx;
}
return maxdx;
}
double angle3Vertices(const MVertex *p1, const MVertex *p2, const MVertex *p3)
{
SVector3 a(p1->x() - p2->x(), p1->y() - p2->y(), p1->z() - p2->z());
SVector3 b(p3->x() - p2->x(), p3->y() - p2->y(), p3->z() - p2->z());
SVector3 c = crossprod(a, b);
double sinA = c.norm();
double cosA = dot(a, b);
return atan2 (sinA, cosA);
}
double goldenSectionSearch(const GEdge *ge, const SPoint3 &q, double x1,
double x2, double x3, double tau)
{
// Create a new possible center in the area between x2 and x3, closer to x2
double x4 = x2 + GOLDEN2 * (x3 - x2);
// Evaluate termination criterion
if (fabs(x3 - x1) < tau * (fabs(x2) + fabs(x4)))
return (x3 + x1) / 2;
const SVector3 dp4 = q - ge->position(x4);
const SVector3 dp2 = q - ge->position(x2);
const double d4 = dp4.norm();
const double d2 = dp2.norm();
if (d4 < d2)
return goldenSectionSearch(ge, q, x2, x4, x3, tau);
else
return goldenSectionSearch(ge,q , x4, x2, x1, tau);
}
GPoint GEdge::closestPoint(const SPoint3 &q, double &t) const
{
// printf("looking for closest point in curve %d to point %g %g\n",tag(),q.x(),q.y());
const int nbSamples = 100;
Range<double> interval = parBounds(0);
double tMin = std::min(interval.high(), interval.low());
double tMax = std::max(interval.high(), interval.low());
double DMIN = 1.e22;
double topt = tMin;
const double DT = (tMax - tMin) / (nbSamples - 1.) ;
for (int i = 0; i < nbSamples; i++){
t = tMin + i * DT;
const SVector3 dp = q - position(t);
const double D = dp.norm();
if (D < DMIN) {
topt = t;
DMIN = D;
}
}
// printf("parameter %g as an initial guess (dist = %g)\n",topt,DMIN);
if (topt == tMin)
t = goldenSectionSearch (this, q, topt, topt + DT/2, topt + DT, 1.e-9);
else if (topt == tMax)
t = goldenSectionSearch (this, q, topt - DT, topt - DT/2 , topt, 1.e-9);
else
t = goldenSectionSearch (this, q, topt - DT, topt, topt + DT, 1.e-9);
const SVector3 dp = q - position(t);
// const double D = dp.norm();
// printf("after golden section parameter %g (dist = %g)\n",t,D);
return point(t);
}
void meshGEdge::operator() (GEdge *ge)
{
#if defined(HAVE_ANN)
FieldManager *fields = ge->model()->getFields();
BoundaryLayerField *blf = 0;
Field *bl_field = fields->get(fields->getBoundaryLayerField());
blf = dynamic_cast<BoundaryLayerField*> (bl_field);
#else
bool blf = false;
#endif
ge->model()->setCurrentMeshEntity(ge);
if(ge->geomType() == GEntity::DiscreteCurve) return;
if(ge->geomType() == GEntity::BoundaryLayerCurve) return;
if(ge->meshAttributes.method == MESH_NONE) return;
if(CTX::instance()->mesh.meshOnlyVisible && !ge->getVisibility()) return;
// look if we are doing the STL triangulation
std::vector<MVertex*> &mesh_vertices = ge->mesh_vertices ;
std::vector<MLine*> &lines = ge->lines ;
deMeshGEdge dem;
dem(ge);
if(MeshExtrudedCurve(ge)) return;
if (ge->meshMaster() != ge){
GEdge *gef = dynamic_cast<GEdge*> (ge->meshMaster());
if (gef->meshStatistics.status == GEdge::PENDING) return;
Msg::Info("Meshing curve %d (%s) as a copy of %d", ge->tag(),
ge->getTypeString().c_str(), ge->meshMaster()->tag());
copyMesh(gef, ge, ge->masterOrientation);
ge->meshStatistics.status = GEdge::DONE;
return;
}
Msg::Info("Meshing curve %d (%s)", ge->tag(), ge->getTypeString().c_str());
// compute bounds
Range<double> bounds = ge->parBounds(0);
double t_begin = bounds.low();
double t_end = bounds.high();
// first compute the length of the curve by integrating one
double length;
std::vector<IntPoint> Points;
if(ge->geomType() == GEntity::Line &&
ge->getBeginVertex() == ge->getEndVertex() &&
//do not consider closed lines as degenerated
(ge->position(0.5) - ge->getBeginVertex()->xyz()).norm() < CTX::instance()->geom.tolerance)
length = 0.; // special case t avoid infinite loop in integration
else
length = Integration(ge, t_begin, t_end, F_One, Points, 1.e-8 * CTX::instance()->lc);
ge->setLength(length);
Points.clear();
if(length < CTX::instance()->mesh.toleranceEdgeLength){
ge->setTooSmall(true);
}
// Integrate detJ/lc du
double a;
int N;
if(length == 0. && CTX::instance()->mesh.toleranceEdgeLength == 0.){
Msg::Warning("Curve %d has a zero length", ge->tag());
a = 0.;
N = 1;
}
else if(ge->degenerate(0)){
a = 0.;
N = 1;
}
else if(ge->meshAttributes.method == MESH_TRANSFINITE){
a = Integration(ge, t_begin, t_end, F_Transfinite, Points,
CTX::instance()->mesh.lcIntegrationPrecision);
N = ge->meshAttributes.nbPointsTransfinite;
if(CTX::instance()->mesh.flexibleTransfinite && CTX::instance()->mesh.lcFactor)
N /= CTX::instance()->mesh.lcFactor;
}
else{
if (CTX::instance()->mesh.algo2d == ALGO_2D_BAMG || blf){
a = Integration(ge, t_begin, t_end, F_Lc_aniso, Points,
CTX::instance()->mesh.lcIntegrationPrecision);
}
else{
a = Integration(ge, t_begin, t_end, F_Lc, Points,
CTX::instance()->mesh.lcIntegrationPrecision);
}
// we should maybe provide an option to disable the smoothing
for (unsigned int i = 0; i < Points.size(); i++){
IntPoint &pt = Points[i];
SVector3 der = ge->firstDer(pt.t);
pt.xp = der.norm();
}
a = smoothPrimitive(ge, sqrt(CTX::instance()->mesh.smoothRatio), Points);
N = std::max(ge->minimumMeshSegments() + 1, (int)(a + 1.99));
}
// force odd number of points if blossom is used for recombination
if((ge->meshAttributes.method != MESH_TRANSFINITE ||
CTX::instance()->mesh.flexibleTransfinite) &&
CTX::instance()->mesh.algoRecombine != 0){
if(CTX::instance()->mesh.recombineAll){
if (N % 2 == 0) N++;
if (CTX::instance()->mesh.algoRecombine == 2)
N = increaseN(N);
}
else{
std::list<GFace*> faces = ge->faces();
for(std::list<GFace*>::iterator it = faces.begin(); it != faces.end(); it++){
if((*it)->meshAttributes.recombine){
if (N % 2 == 0) N ++;
if (CTX::instance()->mesh.algoRecombine == 2)
N = increaseN(N);
break;
}
}
}
}
// printFandPrimitive(ge->tag(),Points);
// if the curve is periodic and if the begin vertex is identical to
// the end vertex and if this vertex has only one model curve
// adjacent to it, then the vertex is not connecting any other
// curve. So, the mesh vertex and its associated geom vertex are not
// necessary at the same location
GPoint beg_p, end_p;
if(ge->getBeginVertex() == ge->getEndVertex() &&
ge->getBeginVertex()->edges().size() == 1){
end_p = beg_p = ge->point(t_begin);
Msg::Debug("Meshing periodic closed curve");
}
else{
MVertex *v0 = ge->getBeginVertex()->mesh_vertices[0];
MVertex *v1 = ge->getEndVertex()->mesh_vertices[0];
beg_p = GPoint(v0->x(), v0->y(), v0->z());
end_p = GPoint(v1->x(), v1->y(), v1->z());
}
// do not consider the first and the last vertex (those are not
// classified on this mesh edge)
if(N > 1){
const double b = a / (double)(N - 1);
int count = 1, NUMP = 1;
IntPoint P1, P2;
mesh_vertices.resize(N - 2);
while(NUMP < N - 1) {
P1 = Points[count - 1];
P2 = Points[count];
const double d = (double)NUMP * b;
if((fabs(P2.p) >= fabs(d)) && (fabs(P1.p) < fabs(d))) {
double dt = P2.t - P1.t;
double dlc = P2.lc - P1.lc;
double dp = P2.p - P1.p;
double t = P1.t + dt / dp * (d - P1.p);
SVector3 der = ge->firstDer(t);
const double d = norm(der);
double lc = d/(P1.lc + dlc / dp * (d - P1.p));
GPoint V = ge->point(t);
mesh_vertices[NUMP - 1] = new MEdgeVertex(V.x(), V.y(), V.z(), ge, t, lc);
NUMP++;
}
else {
count++;
}
}
mesh_vertices.resize(NUMP - 1);
}
for(unsigned int i = 0; i < mesh_vertices.size() + 1; i++){
MVertex *v0 = (i == 0) ?
ge->getBeginVertex()->mesh_vertices[0] : mesh_vertices[i - 1];
MVertex *v1 = (i == mesh_vertices.size()) ?
ge->getEndVertex()->mesh_vertices[0] : mesh_vertices[i];
lines.push_back(new MLine(v0, v1));
}
if(ge->getBeginVertex() == ge->getEndVertex() &&
ge->getBeginVertex()->edges().size() == 1){
MVertex *v0 = ge->getBeginVertex()->mesh_vertices[0];
v0->x() = beg_p.x();
v0->y() = beg_p.y();
v0->z() = beg_p.z();
}
ge->meshStatistics.status = GEdge::DONE;
}