fei3dtetlin.C

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/*
 *
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 *              ##   ##  ##   ##  ####    ####    ##  #  ##
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 *            ##   ##  ##   ##  ##      ##      ##     ##
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 *
 *
 *             OOFEM : Object Oriented Finite Element Code
 *
 *               Copyright (C) 1993 - 2025   Borek Patzak
 *
 *
 *
 *       Czech Technical University, Faculty of Civil Engineering,
 *   Department of Structural Mechanics, 166 29 Prague, Czech Republic
 *
 *  This library is free software; you can redistribute it and/or
 *  modify it under the terms of the GNU Lesser General Public
 *  License as published by the Free Software Foundation; either
 *  version 2.1 of the License, or (at your option) any later version.
 *
 *  This program 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
 *  Lesser General Public License for more details.
 *
 *  You should have received a copy of the GNU Lesser General Public
 *  License along with this library; if not, write to the Free Software
 *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
 */
 
#include "fei3dtetlin.h"
#include "mathfem.h"
#include "floatmatrix.h"
#include "floatarray.h"
#include "floatarrayf.h"
#include "floatmatrixf.h"
#include "gaussintegrationrule.h"
 
namespace oofem {
 
FloatArrayF<4>
FEI3dTetLin :: evalN(const FloatArrayF<3> &lcoords)
{
    return {
        lcoords[0],
        lcoords[1],
        lcoords[2],
        1.0 - lcoords[0] - lcoords[1] - lcoords[2]
    };
}
 
void
FEI3dTetLin :: evalN(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
#if 0
    answer = evalN(lcoords);
#else
    answer.resize(4);
 
    answer.at(1) = lcoords.at(1);
    answer.at(2) = lcoords.at(2);
    answer.at(3) = lcoords.at(3);
    answer.at(4) = 1. - lcoords.at(1) - lcoords.at(2) - lcoords.at(3);
#endif
}
 
std::pair<double, FloatMatrixF<3,4>>
FEI3dTetLin :: evaldNdx(const FEICellGeometry &cellgeo)
{
    //auto [x1, y1, z1] = cellgeo.giveVertexCoordinates(1);
    //auto [x2, y2, z2] = cellgeo.giveVertexCoordinates(2);
    //auto [x3, y3, z3] = cellgeo.giveVertexCoordinates(3);
    //auto [x4, y4, z4] = cellgeo.giveVertexCoordinates(4);
 
    double x1 = cellgeo.giveVertexCoordinates(1).at(1);
    double x2 = cellgeo.giveVertexCoordinates(2).at(1);
    double x3 = cellgeo.giveVertexCoordinates(3).at(1);
    double x4 = cellgeo.giveVertexCoordinates(4).at(1);
 
    double y1 = cellgeo.giveVertexCoordinates(1).at(2);
    double y2 = cellgeo.giveVertexCoordinates(2).at(2);
    double y3 = cellgeo.giveVertexCoordinates(3).at(2);
    double y4 = cellgeo.giveVertexCoordinates(4).at(2);
 
    double z1 = cellgeo.giveVertexCoordinates(1).at(3);
    double z2 = cellgeo.giveVertexCoordinates(2).at(3);
    double z3 = cellgeo.giveVertexCoordinates(3).at(3);
    double z4 = cellgeo.giveVertexCoordinates(4).at(3);
 
    double detJ = ( ( x4 - x1 ) * ( y2 - y1 ) * ( z3 - z1 ) - ( x4 - x1 ) * ( y3 - y1 ) * ( z2 - z1 ) +
            ( x3 - x1 ) * ( y4 - y1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( y4 - y1 ) * ( z3 - z1 ) +
            ( x2 - x1 ) * ( y3 - y1 ) * ( z4 - z1 ) - ( x3 - x1 ) * ( y2 - y1 ) * ( z4 - z1 ) );
 
    FloatMatrixF<3,4> ans = {
        -( ( y3 - y2 ) * ( z4 - z2 ) - ( y4 - y2 ) * ( z3 - z2 ) ),
        -( ( x4 - x2 ) * ( z3 - z2 ) - ( x3 - x2 ) * ( z4 - z2 ) ),
        -( ( x3 - x2 ) * ( y4 - y2 ) - ( x4 - x2 ) * ( y3 - y2 ) ),
        ( y4 - y3 ) * ( z1 - z3 ) - ( y1 - y3 ) * ( z4 - z3 ),
        ( x1 - x3 ) * ( z4 - z3 ) - ( x4 - x3 ) * ( z1 - z3 ),
        ( x4 - x3 ) * ( y1 - y3 ) - ( x1 - x3 ) * ( y4 - y3 ),
        -( ( y1 - y4 ) * ( z2 - z4 ) - ( y2 - y4 ) * ( z1 - z4 ) ),
        -( ( x2 - x4 ) * ( z1 - z4 ) - ( x1 - x4 ) * ( z2 - z4 ) ),
        -( ( x1 - x4 ) * ( y2 - y4 ) - ( x2 - x4 ) * ( y1 - y4 ) ),
        ( y2 - y1 ) * ( z3 - z1 ) - ( y3 - y1 ) * ( z2 - z1 ),
        ( x3 - x1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( z3 - z1 ),
        ( x2 - x1 ) * ( y3 - y1 ) - ( x3 - x1 ) * ( y2 - y1 ),
    };
    return {detJ, ans * (1. / detJ)};
}
 
double
FEI3dTetLin :: evaldNdx(FloatMatrix &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
#if 0
    auto tmp = evaldNdx(lcoords, cellgeo);
    answer = tmp.second;
    return tmp.first;
#else
    double x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4, detJ;
    answer.resize(4, 3);
 
    x1 = cellgeo.giveVertexCoordinates(1).at(1);
    x2 = cellgeo.giveVertexCoordinates(2).at(1);
    x3 = cellgeo.giveVertexCoordinates(3).at(1);
    x4 = cellgeo.giveVertexCoordinates(4).at(1);
 
    y1 = cellgeo.giveVertexCoordinates(1).at(2);
    y2 = cellgeo.giveVertexCoordinates(2).at(2);
    y3 = cellgeo.giveVertexCoordinates(3).at(2);
    y4 = cellgeo.giveVertexCoordinates(4).at(2);
 
    z1 = cellgeo.giveVertexCoordinates(1).at(3);
    z2 = cellgeo.giveVertexCoordinates(2).at(3);
    z3 = cellgeo.giveVertexCoordinates(3).at(3);
    z4 = cellgeo.giveVertexCoordinates(4).at(3);
 
    detJ = ( ( x4 - x1 ) * ( y2 - y1 ) * ( z3 - z1 ) - ( x4 - x1 ) * ( y3 - y1 ) * ( z2 - z1 ) +
            ( x3 - x1 ) * ( y4 - y1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( y4 - y1 ) * ( z3 - z1 ) +
            ( x2 - x1 ) * ( y3 - y1 ) * ( z4 - z1 ) - ( x3 - x1 ) * ( y2 - y1 ) * ( z4 - z1 ) );
 
    if ( detJ <= 0.0 ) {
        OOFEM_ERROR("negative volume");
    }
 
    answer.at(1, 1) = -( ( y3 - y2 ) * ( z4 - z2 ) - ( y4 - y2 ) * ( z3 - z2 ) );
    answer.at(2, 1) = ( y4 - y3 ) * ( z1 - z3 ) - ( y1 - y3 ) * ( z4 - z3 );
    answer.at(3, 1) = -( ( y1 - y4 ) * ( z2 - z4 ) - ( y2 - y4 ) * ( z1 - z4 ) );
    answer.at(4, 1) = ( y2 - y1 ) * ( z3 - z1 ) - ( y3 - y1 ) * ( z2 - z1 );
 
    answer.at(1, 2) = -( ( x4 - x2 ) * ( z3 - z2 ) - ( x3 - x2 ) * ( z4 - z2 ) );
    answer.at(2, 2) = ( x1 - x3 ) * ( z4 - z3 ) - ( x4 - x3 ) * ( z1 - z3 );
    answer.at(3, 2) = -( ( x2 - x4 ) * ( z1 - z4 ) - ( x1 - x4 ) * ( z2 - z4 ) );
    answer.at(4, 2) = ( x3 - x1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( z3 - z1 );
 
    answer.at(1, 3) = -( ( x3 - x2 ) * ( y4 - y2 ) - ( x4 - x2 ) * ( y3 - y2 ) );
    answer.at(2, 3) = ( x4 - x3 ) * ( y1 - y3 ) - ( x1 - x3 ) * ( y4 - y3 );
    answer.at(3, 3) = -( ( x1 - x4 ) * ( y2 - y4 ) - ( x2 - x4 ) * ( y1 - y4 ) );
    answer.at(4, 3) = ( x2 - x1 ) * ( y3 - y1 ) - ( x3 - x1 ) * ( y2 - y1 );
 
    answer.times(1. / detJ);
 
    return detJ;
#endif
}
 
void
FEI3dTetLin :: local2global(FloatArray &answer, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray n;
    this->evalN(n, lcoords, cellgeo);
 
    answer.clear();
    for ( int i = 1; i <= 4; i++ ) {
        answer.add( n.at(i), cellgeo.giveVertexCoordinates(i) );
    }
}
 
#define POINT_TOL 1.e-3
 
int
FEI3dTetLin :: global2local(FloatArray &answer, const FloatArray &coords, const FEICellGeometry &cellgeo) const
{
    double x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4, xp, yp, zp, volume;
    answer.resize(4);
 
    x1 = cellgeo.giveVertexCoordinates(1).at(1);
    x2 = cellgeo.giveVertexCoordinates(2).at(1);
    x3 = cellgeo.giveVertexCoordinates(3).at(1);
    x4 = cellgeo.giveVertexCoordinates(4).at(1);
 
    y1 = cellgeo.giveVertexCoordinates(1).at(2);
    y2 = cellgeo.giveVertexCoordinates(2).at(2);
    y3 = cellgeo.giveVertexCoordinates(3).at(2);
    y4 = cellgeo.giveVertexCoordinates(4).at(2);
 
    z1 = cellgeo.giveVertexCoordinates(1).at(3);
    z2 = cellgeo.giveVertexCoordinates(2).at(3);
    z3 = cellgeo.giveVertexCoordinates(3).at(3);
    z4 = cellgeo.giveVertexCoordinates(4).at(3);
 
    xp = coords.at(1);
    yp = coords.at(2);
    zp = coords.at(3);
 
    volume = ( ( x4 - x1 ) * ( y2 - y1 ) * ( z3 - z1 ) - ( x4 - x1 ) * ( y3 - y1 ) * ( z2 - z1 ) +
              ( x3 - x1 ) * ( y4 - y1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( y4 - y1 ) * ( z3 - z1 ) +
              ( x2 - x1 ) * ( y3 - y1 ) * ( z4 - z1 ) - ( x3 - x1 ) * ( y2 - y1 ) * ( z4 - z1 ) ) / 6.;
 
    answer.resize(4);
 
    answer.at(1) = ( ( x3 - x2 ) * ( yp - y2 ) * ( z4 - z2 ) - ( xp - x2 ) * ( y3 - y2 ) * ( z4 - z2 ) +
                    ( x4 - x2 ) * ( y3 - y2 ) * ( zp - z2 ) - ( x4 - x2 ) * ( yp - y2 ) * ( z3 - z2 ) +
                    ( xp - x2 ) * ( y4 - y2 ) * ( z3 - z2 ) - ( x3 - x2 ) * ( y4 - y2 ) * ( zp - z2 ) ) / 6. / volume;
 
    answer.at(2) = ( ( x4 - x1 ) * ( yp - y1 ) * ( z3 - z1 ) - ( xp - x1 ) * ( y4 - y1 ) * ( z3 - z1 ) +
                    ( x3 - x1 ) * ( y4 - y1 ) * ( zp - z1 ) - ( x3 - x1 ) * ( yp - y1 ) * ( z4 - z1 ) +
                    ( xp - x1 ) * ( y3 - y1 ) * ( z4 - z1 ) - ( x4 - x1 ) * ( y3 - y1 ) * ( zp - z1 ) ) / 6. / volume;
 
    answer.at(3) = ( ( x2 - x1 ) * ( yp - y1 ) * ( z4 - z1 ) - ( xp - x1 ) * ( y2 - y1 ) * ( z4 - z1 ) +
                    ( x4 - x1 ) * ( y2 - y1 ) * ( zp - z1 ) - ( x4 - x1 ) * ( yp - y1 ) * ( z2 - z1 ) +
                    ( xp - x1 ) * ( y4 - y1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( y4 - y1 ) * ( zp - z1 ) ) / 6. / volume;
 
    // test if inside + clamping
    bool inside = true;
    for ( int i = 1; i <= 3; i++ ) {
        if ( answer.at(i) < ( 0. - POINT_TOL ) ) {
            answer.at(i) = 0.;
            inside = false;
        } else if ( answer.at(i) > ( 1. + POINT_TOL ) ) {
            answer.at(i) = 1.;
            inside = false;
        }
    }
 
    answer.at(4) = 1.0 - answer.at(1) - answer.at(2) - answer.at(3);
 
    return inside;
}
 
 
double
FEI3dTetLin :: giveTransformationJacobian(const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double detJ, x1, x2, x3, x4, y1, y2, y3, y4, z1, z2, z3, z4;
 
    x1 = cellgeo.giveVertexCoordinates(1).at(1);
    x2 = cellgeo.giveVertexCoordinates(2).at(1);
    x3 = cellgeo.giveVertexCoordinates(3).at(1);
    x4 = cellgeo.giveVertexCoordinates(4).at(1);
 
    y1 = cellgeo.giveVertexCoordinates(1).at(2);
    y2 = cellgeo.giveVertexCoordinates(2).at(2);
    y3 = cellgeo.giveVertexCoordinates(3).at(2);
    y4 = cellgeo.giveVertexCoordinates(4).at(2);
 
    z1 = cellgeo.giveVertexCoordinates(1).at(3);
    z2 = cellgeo.giveVertexCoordinates(2).at(3);
    z3 = cellgeo.giveVertexCoordinates(3).at(3);
    z4 = cellgeo.giveVertexCoordinates(4).at(3);
 
    detJ = ( ( x4 - x1 ) * ( y2 - y1 ) * ( z3 - z1 ) - ( x4 - x1 ) * ( y3 - y1 ) * ( z2 - z1 ) +
            ( x3 - x1 ) * ( y4 - y1 ) * ( z2 - z1 ) - ( x2 - x1 ) * ( y4 - y1 ) * ( z3 - z1 ) +
            ( x2 - x1 ) * ( y3 - y1 ) * ( z4 - z1 ) - ( x3 - x1 ) * ( y2 - y1 ) * ( z4 - z1 ) );
 
    return detJ;
}
 
 
void
FEI3dTetLin :: edgeEvalN(FloatArray &answer, int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    double ksi = lcoords.at(1);
    answer.resize(2);
 
    answer.at(1) = ( 1. - ksi ) * 0.5;
    answer.at(2) = ( 1. + ksi ) * 0.5;
}
 
void
FEI3dTetLin :: edgeEvaldNdx(FloatMatrix &answer, int iedge,
                            const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    const auto &edgeNodes = this->computeLocalEdgeMapping(iedge);
    double l = this->edgeComputeLength(edgeNodes, cellgeo);
    double coeff = 1.0 / l / l;
 
    double x1 = cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(1);
    double y1 = cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(2);
    double z1 = cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(3);
    double x2 = cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(1);
    double y2 = cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(2);
    double z2 = cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(3);
 
    answer.resize(2, 3);
    answer.at(1, 1) = ( x1 - x2 ) * coeff;
    answer.at(1, 2) = ( y1 - y2 ) * coeff;
    answer.at(1, 3) = ( z1 - z2 ) * coeff;
 
    answer.at(2, 1) = ( x2 - x1 ) * coeff;
    answer.at(2, 2) = ( y2 - y1 ) * coeff;
    answer.at(2, 3) = ( z2 - z1 ) * coeff;
}
 
void
FEI3dTetLin :: edgeLocal2global(FloatArray &answer, int iedge,
                                const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    FloatArray n;
    const auto &edgeNodes = this->computeLocalEdgeMapping(iedge);
    this->edgeEvalN(n, iedge, lcoords, cellgeo);
 
    answer.resize(3);
    answer.at(1) = n.at(1) * cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(1) +
                   n.at(2) * cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(1);
    answer.at(2) = n.at(1) * cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(2) +
                   n.at(2) * cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(2);
    answer.at(3) = n.at(1) * cellgeo.giveVertexCoordinates( edgeNodes.at(1) ).at(3) +
                   n.at(2) * cellgeo.giveVertexCoordinates( edgeNodes.at(2) ).at(3);
}
 
 
double
FEI3dTetLin :: edgeGiveTransformationJacobian(int iedge, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    const auto &edgeNodes = this->computeLocalEdgeMapping(iedge);
    return 0.5 * this->edgeComputeLength(edgeNodes, cellgeo);
}
 
 
IntArray
FEI3dTetLin :: computeLocalEdgeMapping(int iedge) const
{
    if ( iedge == 1 ) { // edge between nodes 1 2
        return {1, 2};
    } else if ( iedge == 2 ) { // edge between nodes 2 3
        return {2, 3};
    } else if ( iedge == 3 ) { // edge between nodes 3 1
        return {3, 1};
    } else if ( iedge == 4 ) { // edge between nodes 1 4
        return {1, 4};
    } else if ( iedge == 5 ) { // edge between nodes 2 4
        return {2, 4};
    } else if ( iedge == 6 ) { // edge between nodes 3 4
        return {3, 4};
    } else {
        throw std::range_error("invalid edge number");
    }
}
 
double
FEI3dTetLin :: edgeComputeLength(const IntArray &edgeNodes, const FEICellGeometry &cellgeo) const
{
    return distance(cellgeo.giveVertexCoordinates( edgeNodes.at(2) ), cellgeo.giveVertexCoordinates( edgeNodes.at(1) ));
}
 
void
FEI3dTetLin :: surfaceEvalN(FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    answer.resize(3);
 
    answer.at(1) = lcoords.at(1);
    answer.at(2) = lcoords.at(2);
    answer.at(3) = 1. - lcoords.at(1) - lcoords.at(2);
}
 
void
FEI3dTetLin :: surfaceLocal2global(FloatArray &answer, int iedge,
                                   const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    const auto &nodes = computeLocalSurfaceMapping(iedge);
 
    double l1 = lcoords.at(1);
    double l2 = lcoords.at(2);
    double l3 = 1.0 - l1 - l2;
 
    answer.resize(3);
    answer.at(1) = l1 * cellgeo.giveVertexCoordinates( nodes.at(1) ).at(1) +
                   l2 * cellgeo.giveVertexCoordinates( nodes.at(2) ).at(1) +
                   l3 * cellgeo.giveVertexCoordinates( nodes.at(3) ).at(1);
    answer.at(2) = l1 * cellgeo.giveVertexCoordinates( nodes.at(1) ).at(2) +
                   l2 * cellgeo.giveVertexCoordinates( nodes.at(2) ).at(2) +
                   l3 * cellgeo.giveVertexCoordinates( nodes.at(3) ).at(2);
    answer.at(3) = l1 * cellgeo.giveVertexCoordinates( nodes.at(1) ).at(3) +
                   l2 * cellgeo.giveVertexCoordinates( nodes.at(2) ).at(3) +
                   l3 * cellgeo.giveVertexCoordinates( nodes.at(3) ).at(3);
}
 
void
FEI3dTetLin :: surfaceEvaldNdx(FloatMatrix &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    // Note, this must be in correct order, not just the correct nodes, therefore we must use snodes;
    const auto &snodes = this->computeLocalSurfaceMapping(isurf);
 
    FloatArray lcoords_tet(4);
    lcoords_tet.at(snodes.at(1)) = lcoords.at(1);
    lcoords_tet.at(snodes.at(2)) = lcoords.at(2);
    lcoords_tet.at(snodes.at(3)) = 1. - lcoords.at(1) - lcoords.at(2);
 
    FloatMatrix fullB;
    this->evaldNdx(fullB, lcoords_tet, cellgeo);
    answer.resize(snodes.giveSize(), 3);
    for ( int i = 1; i <= snodes.giveSize(); ++i ) {
        for ( int j = 1; j <= 3; ++j ) {
            answer.at(i, j) = fullB.at(snodes.at(i), j);
        }
    }
}
 
double
FEI3dTetLin :: surfaceEvalNormal(FloatArray &answer, int isurf, const FloatArray &lcoords, const FEICellGeometry &cellgeo) const
{
    const auto &snodes = this->computeLocalSurfaceMapping(isurf);
 
    FloatArray a, b;
    a.beDifferenceOf( cellgeo.giveVertexCoordinates( snodes.at(2) ), cellgeo.giveVertexCoordinates( snodes.at(1) ) );
    b.beDifferenceOf( cellgeo.giveVertexCoordinates( snodes.at(3) ), cellgeo.giveVertexCoordinates( snodes.at(1) ) );
    answer.beVectorProductOf(a, b);
 
    return answer.normalize_giveNorm();
}
 
double
FEI3dTetLin :: surfaceGiveTransformationJacobian(int isurf, const FloatArray &lcoords,
                                                 const FEICellGeometry &cellgeo) const
{
    FloatArray c;
    return this->surfaceEvalNormal(c, isurf, lcoords, cellgeo);
}
 
IntArray
FEI3dTetLin :: computeLocalSurfaceMapping(int isurf) const
{
    int aNode = 0, bNode = 0, cNode = 0;
 
    if ( isurf == 1 ) { // surface 1 - nodes 1 3 2
        aNode = 1;
        bNode = 3;
        cNode = 2;
    } else if ( isurf == 2 ) { // surface 2 - nodes 1 2 4
        aNode = 1;
        bNode = 2;
        cNode = 4;
    } else if ( isurf == 3 ) { // surface 3  - nodes 2 3 4
        aNode = 2;
        bNode = 3;
        cNode = 4;
    } else if ( isurf == 4 ) { // surface 4 - nodes 1 4 3
        aNode = 1;
        bNode = 4;
        cNode = 3;
    } else {
        OOFEM_ERROR("wrong surface number (%d)", isurf);
    }
 
    return {aNode, bNode, cNode};
}
 
double
FEI3dTetLin :: evalNXIntegral(int iEdge, const FEICellGeometry &cellgeo) const
{
    auto fNodes = this->computeLocalSurfaceMapping(iEdge);
 
    const FloatArray &c1 = cellgeo.giveVertexCoordinates( fNodes.at(1) );
    const FloatArray &c2 = cellgeo.giveVertexCoordinates( fNodes.at(2) );
    const FloatArray &c3 = cellgeo.giveVertexCoordinates( fNodes.at(3) );
 
    return ( ( c2.at(1) * c3.at(2) - c3.at(1) * c2.at(2) ) * c1.at(3) +
            ( c3.at(1) * c1.at(2) - c1.at(1) * c3.at(2) ) * c2.at(3) +
            ( c1.at(1) * c2.at(2) - c2.at(1) * c1.at(2) ) * c3.at(3) ) * 0.5;
}
 
std::unique_ptr<IntegrationRule>
FEI3dTetLin :: giveIntegrationRule(int order, Element_Geometry_Type egt) const
{
    auto iRule = std::make_unique<GaussIntegrationRule>(1, nullptr);
    int points = iRule->getRequiredNumberOfIntegrationPoints(_Tetrahedra, order + 0);
    iRule->SetUpPointsOnTetrahedra(points, _Unknown);
    return std::move(iRule);
}
 
std::unique_ptr<IntegrationRule>
FEI3dTetLin :: giveBoundaryIntegrationRule(int order, int boundary, Element_Geometry_Type egt) const
{
    auto iRule = std::make_unique<GaussIntegrationRule>(1, nullptr);
    int points = iRule->getRequiredNumberOfIntegrationPoints(_Triangle, order + 0);
    iRule->SetUpPointsOnTriangle(points, _Unknown);
    return std::move(iRule);
}
} // end namespace oofem