RBFInterpolationTemplates.C

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/*---------------------------------------------------------------------------*\
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License
    This file is part of foam-extend.
 
    foam-extend 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.
 
    foam-extend 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 foam-extend.  If not, see <http://www.gnu.org/licenses/>.
 
Description
    RBF interpolation templates
 
Author
    Frank Bos, TU Delft.  All rights reserved.
    Dubravko Matijasevic, FSB Zagreb.
 
\*---------------------------------------------------------------------------*/
 
#include "RBFInterpolation.H"
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Type>
Foam::tmp<Foam::Field<Type>> Foam::RBFInterpolation::interpolate
                          (
                              const Field<Type>& ctrlField
                          ) const
{
    // HJ and FB (05 Jan 2009)
    // Collect the values from ALL control points to all CPUs
    // Then, each CPU will do interpolation only on local dataPoints_
    if (ctrlField.size() != controlPoints_.size())
    {
        FatalErrorIn
        (
            "tmp<Field<Type> > RBFInterpolation::interpolate\n"
            "(\n"
            "    const Field<Type>& ctrlField\n"
            ") const"
        )   << "Incorrect size of source field.  Size = " << ctrlField.size()
            << " nControlPoints = " << controlPoints_.size()
            << abort(FatalError);
    }
 
    tmp<Field<Type>> tresult
                  (
                      new Field<Type>(dataPoints_.size(), pTraits<Type>::zero)
                  );
    Field<Type>& result = const_cast<Field<Type>&>(tresult());
    // FB 21-12-2008
    // 1) Calculate alpha and beta coefficients using the Inverse
    // 2) Calculate displacements of internal nodes using RBF values,
    //    alpha's and beta's
    // 3) Return displacements using tresult()
    const label nControlPoints = controlPoints_.size();
    const scalarSquareMatrix& mat = this->B();
    // Determine interpolation coefficients
    Field<Type> alpha(nControlPoints, pTraits<Type>::zero);
    Field<Type> beta(4, pTraits<Type>::zero);
 
    for (label row = 0; row < nControlPoints; row++)
    {
        for (label col = 0; col < nControlPoints; col++)
        {
            alpha[row] += mat[row][col] * ctrlField[col];
        }
    }
 
    if (polynomials_)
    {
        for
        (
            label row = nControlPoints;
            row < nControlPoints + 4;
            row++
        )
        {
            for (label col = 0; col < nControlPoints; col++)
            {
                beta[row - nControlPoints] += mat[row][col] * ctrlField[col];
            }
        }
    }
 
    // Evaluation
    scalar t;
    // Algorithmic improvement, Matteo Lombardi.  21/Mar/2011
    forAll (dataPoints_, flPoint)
    {
        // Cut-off function to justify neglecting outer boundary points
        t = (mag(dataPoints_[flPoint] - focalPoint_) - innerRadius_) /
            (outerRadius_ - innerRadius_);
 
        if (t >= 1)
        {
            // Increment is zero: w = 0
            result[flPoint] = 0 * result[flPoint];
        }
        else
        {
            // Full calculation of weights
            scalarField weights =
                RBF_->weights(controlPoints_, dataPoints_[flPoint]);
            forAll (controlPoints_, i)
            {
                result[flPoint] += weights[i] * alpha[i];
            }
 
            if (polynomials_)
            {
                result[flPoint] +=
                    beta[0]
                    + beta[1] * dataPoints_[flPoint].x()
                    + beta[2] * dataPoints_[flPoint].y()
                    + beta[3] * dataPoints_[flPoint].z();
            }
 
            scalar w;
 
            if (t <= 0)
            {
                w = 1.0;
            }
            else
            {
                w = 1 - sqr(t) * (3 - 2 * t);
            }
 
            result[flPoint] = w * result[flPoint];
        }
    }
    return tresult;
}
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //