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========= |
\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
\\ / O peration | Website: https://openfoam.org
\\ / A nd | Copyright (C) 2025 OpenFOAM Foundation
\\/ M anipulation |
-------------------------------------------------------------------------------
License
This file is part of OpenFOAM.
OpenFOAM is free software: you can redistribute it and/or modify it
under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
for more details.
You should have received a copy of the GNU General Public License
along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
\*---------------------------------------------------------------------------*/
#include "Spline.H"
// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
template<class Derived>
Foam::Spline<Derived>::Spline
(
const pointField& knots,
const scalar tol,
const label nIter
)
:
knots_(knots),
tol_(tol),
nIter_(nIter)
{}
template<class Derived>
Foam::Spline<Derived>::Spline(const pointField& knots)
:
knots_(knots),
tol_(rootSmall),
nIter_(16)
{}
// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
template<class Derived>
Foam::point Foam::Spline<Derived>::position(const scalar lambda) const
{
const Derived& derived = static_cast<const Derived&>(*this);
// Quick return if the parameter is out of range
if (lambda <= 0) return start();
if (lambda >= 1) return end();
// Evaluate the positions for the given local parameters
auto evaluatePoint = [&derived](const scalar& lambda)
{
const scalar l = lambda*derived.nSegments();
const label segmenti = floor(l);
const scalar segmentLambda = l - segmenti;
return derived.position(segmenti, segmentLambda);
};
// Algorithm for iteratively improving adherence to the desired grading
scalar lambdaStar = lambda;
scalar error = vGreat;
for (label iter = 0; error > tol_ && iter < nIter_; ++ iter)
{
// Evaluate the position at the current local parameter
const point p = evaluatePoint(lambdaStar);
// Calculate the actual local parameter based on cumulative distance
const scalar dist0 = mag(p - start());
const scalar dist1 = mag(p - end());
const scalar lambdaDist = dist0/(dist0 + dist1);
// Update the error
error = mag(lambda - lambdaDist);
// Interpolate a new parameter to try and space the cumulative distance
// as required by the original parameter
const scalar lambdaStar0 = lambda < lambdaDist ? 0 : lambdaStar;
const scalar lambdaStar1 = lambda < lambdaDist ? lambdaStar : 1;
const scalar lambdaDist0 = lambda < lambdaDist ? 0 : lambdaDist;
const scalar lambdaDist1 = lambda < lambdaDist ? lambdaDist : 1;
const scalar x =
(lambda - lambdaDist0)/max(lambdaDist1 - lambdaDist0, vSmall);
lambdaStar = (1 - x)*lambdaStar0 + x*lambdaStar1;
}
// Evaluate the position at the final local parameter and return
return evaluatePoint(lambdaStar);
}
template<class Derived>
Foam::tmp<Foam::pointField> Foam::Spline<Derived>::position
(
const scalarList& lambdasArg
) const
{
const Derived& derived = static_cast<const Derived&>(*this);
const label n = lambdasArg.size();
// Clip the parameters to the bounds
const scalarField lambdas
(
min(max(scalarField(lambdasArg), scalar(0)), scalar(1))
);
// Workspace
tmp<scalarField> tlambdasStar(new scalarField(lambdas));
tmp<scalarField> tlambdasStarNew(new scalarField(n));
scalarField lambdasDist(n);
// Allocate the result
tmp<pointField> tpoints(new pointField(n));
pointField& points = tpoints.ref();
// Evaluate the positions for the given local parameters
auto evaluatePoints = [&derived,&points](const scalarField& lambdas)
{
forAll(lambdas, i)
{
const scalar l = lambdas[i]*derived.nSegments();
const label segmenti = floor(l);
const scalar segmentLambda = l - segmenti;
points[i] = derived.position(segmenti, segmentLambda);
}
};
// Algorithm for iteratively improving adherence to the desired grading
scalar error = vGreat;
for (label iter = 0; error > tol_ && iter < nIter_; ++ iter)
{
scalarField& lambdasStar = tlambdasStar.ref();
scalarField& lambdasStarNew = tlambdasStarNew.ref();
// Evaluate the positions at the current local parameters
evaluatePoints(lambdasStar);
// Calculate the actual local parameters based on cumulative distance
scalarField lambdasDist(n);
lambdasDist.first() = mag(points.first() - start());
for (label i = 1; i < n; ++ i)
{
lambdasDist[i] =
lambdasDist[i - 1] + mag(points[i] - points[i - 1]);
}
lambdasDist /= lambdasDist.last() + mag(end() - points.last());
// Update the error
error = -vGreat;
forAll(lambdas, i)
{
error = max(error, mag(lambdas[i] - lambdasDist[i]));
}
// Interpolate new parameters to try and space the cumulative distance
// as required by the original parameters
label iNew = 0;
for (label i = 0; i <= n; ++ i)
{
const scalar lambdaStar0 = i == 0 ? 0 : lambdasStar[i - 1];
const scalar lambdaStar1 = i < n ? lambdasStar[i] : 1;
const scalar lambdaDist0 = i == 0 ? 0 : lambdasDist[i - 1];
const scalar lambdaDist1 = i < n ? lambdasDist[i] : 1;
while (iNew < n && lambdas[iNew] <= lambdaDist1)
{
const scalar x =
(lambdas[iNew] - lambdaDist0)
/max(lambdaDist1 - lambdaDist0, vSmall);
lambdasStarNew[iNew] = (1 - x)*lambdaStar0 + x*lambdaStar1;
iNew ++;
}
}
// Set the old parameters to the new ones and iterate
Swap(tlambdasStar, tlambdasStarNew);
}
// Evaluate the positions at the final local parameters
evaluatePoints(tlambdasStar());
return tpoints;
}
// ************************************************************************* //
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