// Implementation of knupp metric untangling
void knuppMetric::optimizeNodePosition(const scalar tolObsolete)
{
if( !bb_.contains(p_) )
p_ = 0.5 * (bb_.min() + bb_.max());
const scalar tol = Foam::sqr(2.0 * SMALL) * magSqr(bb_.min() - bb_.max());
label iterI, outerIter(0);
vector gradF, disp;
tensor gradGradF;
scalar func, lastFunc;
# ifdef DEBUGSmooth
forAll(normals_, nI)
{
const scalar fx = normals_[nI] & (p_ - centres_[nI]);
Info << "Tet " << nI << " has distance " << fx << " func "
<< Foam::sqr(mag(fx) - fx) << endl;
}
Info << "BoundBox size " << (bb_.max() - bb_.min()) << endl;
Info << "Tolerance " << tol << endl;
# endif
bool finished;
do
{
finished = true;
lastFunc = evaluateMetric();
iterI = 0;
do
{
# ifdef DEBUGSmooth
Info << "Iteration " << iterI << endl;
Info << "Initial metric value " << lastFunc << endl;
# endif
//- store previous value
const point pOrig = p_;
//- evaluate gradients
evaluateGradients(gradF, gradGradF);
//- calculate displacement
const scalar determinant = det(gradGradF);
if( determinant > SMALL )
{
disp = (inv(gradGradF, determinant) & gradF);
for(direction i=0;i<vector::nComponents;++i)
{
const scalar& val = disp[i];
if( (val != val) || ((val - val) != (val - val)) )
{
disp = vector::zero;
break;
}
}
p_ -= disp;
func = evaluateMetric();
# ifdef DEBUGSmooth
Info << "Second grad " << gradGradF << endl;
Info << "inv(gradGradF, determinant) " << inv(gradGradF, determinant) << endl;
Info << "Gradient " << gradF << endl;
Info << "Determinant " << determinant << endl;
Info << "Displacement " << disp << endl;
Info << "New metric value " << func << endl;
# endif
scalar relax(0.8);
label nLoops(0);
while( func > lastFunc )
{
p_ = pOrig - relax * disp;
relax *= 0.5;
func = evaluateMetric();
if( func < lastFunc )
continue;
//- it seems that this direction is wrong
if( ++nLoops == 5 )
{
p_ = pOrig;
disp = vector::zero;
func = 0.0;
}
}
lastFunc = func;
}
else
{
disp = vector::zero;
}
} while( (magSqr(disp) > tol) && (++iterI < 10) );
if( (lastFunc < VSMALL) && (evaluateMetricNoBeta() > VSMALL) )
{
beta_ /= 2.0;
finished = false;
}
} while( !finished && (++outerIter < 5) );
# ifdef DEBUGSmooth
Info << "Last value " << lastFunc << endl;
Info << "Beta " << beta_ << endl;
Info << "Metric with no beta " << evaluateMetricNoBeta() << endl;
forAll(normals_, nI)
{
const scalar fx = normals_[nI] & (p_ - centres_[nI]);
Info << "Tet " << nI << " has distance " << fx << " func "
<< Foam::sqr(mag(fx) - fx) << endl;
}
//::exit(1);
# endif
}
scalar volumeOptimizer::optimiseSteepestDescent(const scalar tol)
{
label iter(0);
point& p = points_[pointI_];
# ifdef DEBUGSmooth
Info << nl << "Smoothing point " << pointI_
<< " with coordinates " << p << endl;
scalar Vmina(VGREAT);
forAll(tets_, tetI)
Vmina = Foam::min(Vmina, tets_[tetI].mag(points_));
Info << "Vmin before " << Vmina << endl;
# endif
vector gradF;
vector disp(vector::zero);
tensor gradGradF;
point pOrig;
scalar funcBefore, funcAfter(evaluateFunc());
bool finished;
do
{
finished = false;
pOrig = p;
funcBefore = funcAfter;
evaluateGradientsExact(gradF, gradGradF);
const scalar determinant = Foam::det(gradGradF);
if( determinant > SMALL )
{
disp = (inv(gradGradF, determinant) & gradF);
p -= disp;
funcAfter = evaluateFunc();
# ifdef DEBUGSmooth
Info << nl << "gradF " << gradF << endl;
Info << "gradGradF " << gradGradF << endl;
Info << "det(gradGradF) " << determinant << endl;
Info << "disp " << disp << endl;
Info << "Func before " << funcBefore << endl;
Info << "Func after " << funcAfter << endl;
# endif
scalar relax(0.8);
label nLoops(0);
while( funcAfter > funcBefore )
{
p = pOrig - relax * disp;
relax *= 0.5;
funcAfter = evaluateFunc();
if( funcAfter < funcBefore )
continue;
if( ++nLoops == 5 )
{
//- it seems that this direction is wrong, stop the loop
p = pOrig;
disp = vector::zero;
finished = true;
funcAfter = funcBefore;
}
}
if( mag(funcBefore - funcAfter) / funcBefore < tol )
finished = true;
}
else
{
//- move in random direction
//- this is usually needed to move the point off the zero volume
disp = vector::zero;
forAll(tets_, tetI)
{
const partTet& tet = tets_[tetI];
const scalar Vtri = tet.mag(points_);
if( Vtri < SMALL )
{
triangle<point, point> tri
(
points_[tet.a()],
points_[tet.b()],
points_[tet.c()]
);
vector n = tri.normal();
const scalar d = mag(n);
if( d > VSMALL )
disp += 0.01 * (n / d);
}
}
p += disp;
funcAfter = evaluateFunc();
}
} while( (++iter < 100) && !finished );
# ifdef DEBUGSmooth
scalar Vmin(VGREAT);
forAll(tets_, tetI)
Vmin = Foam::min(Vmin, tets_[tetI].mag(points_));
Info << nl << "New coordinates for point "
<< pointI_ << " are " << p << endl;
Info << "Num iterations " << iter << " gradient " << gradF << endl;
Info << "Vmin " << Vmin << endl;
# endif
return funcAfter;
}
