tetrahedronI.H

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/*---------------------------------------------------------------------------*\
  =========                 |
  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
   \\    /   O peration     |
    \\  /    A nd           | Copyright (C) 2011-2015 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 "triangle.H"
#include "IOstreams.H"
#include "tetPoints.H"
#include "plane.H"
 
// * * * * * * * * * * * * * * * * Constructors  * * * * * * * * * * * * * * //
 
template<class Point, class PointRef>
inline Foam::tetrahedron<Point, PointRef>::tetrahedron
(
    const Point& a,
    const Point& b,
    const Point& c,
    const Point& d
)
:
    a_(a),
    b_(b),
    c_(c),
    d_(d)
{}
 
 
template<class Point, class PointRef>
inline Foam::tetrahedron<Point, PointRef>::tetrahedron
(
    const UList<Point>& points,
    const FixedList<label, 4>& indices
)
:
    a_(points[indices[0]]),
    b_(points[indices[1]]),
    c_(points[indices[2]]),
    d_(points[indices[3]])
{}
 
 
template<class Point, class PointRef>
inline Foam::tetrahedron<Point, PointRef>::tetrahedron(Istream& is)
{
    is  >> *this;
}
 
 
// * * * * * * * * * * * * * * * Member Functions  * * * * * * * * * * * * * //
 
template<class Point, class PointRef>
inline const Point& Foam::tetrahedron<Point, PointRef>::a() const
{
    return a_;
}
 
 
template<class Point, class PointRef>
inline const Point& Foam::tetrahedron<Point, PointRef>::b() const
{
    return b_;
}
 
 
template<class Point, class PointRef>
inline const Point& Foam::tetrahedron<Point, PointRef>::c() const
{
    return c_;
}
 
 
template<class Point, class PointRef>
inline const Point& Foam::tetrahedron<Point, PointRef>::d() const
{
    return d_;
}
 
 
template<class Point, class PointRef>
inline Foam::triPointRef Foam::tetrahedron<Point, PointRef>::tri
(
    const label faceI
) const
{
    // Warning. Ordering of faces needs to be the same for a tetrahedron
    // class, a tetrahedron cell shape model and a tetCell
 
    if (faceI == 0)
    {
        return triPointRef(b_, c_, d_);
    }
    else if (faceI == 1)
    {
        return triPointRef(a_, d_, c_);
    }
    else if (faceI == 2)
    {
        return triPointRef(a_, b_, d_);
    }
    else if (faceI == 3)
    {
        return triPointRef(a_, c_, b_);
    }
    else
    {
        FatalErrorInFunction
            << "index out of range 0 -> 3. faceI = " << faceI
            << abort(FatalError);
        return triPointRef(b_, c_, d_);
    }
}
 
 
template<class Point, class PointRef>
inline Foam::vector Foam::tetrahedron<Point, PointRef>::Sa() const
{
    return triangle<Point, PointRef>(b_, c_, d_).normal();
}
 
 
template<class Point, class PointRef>
inline Foam::vector Foam::tetrahedron<Point, PointRef>::Sb() const
{
    return triangle<Point, PointRef>(a_, d_, c_).normal();
}
 
 
template<class Point, class PointRef>
inline Foam::vector Foam::tetrahedron<Point, PointRef>::Sc() const
{
    return triangle<Point, PointRef>(a_, b_, d_).normal();
}
 
 
template<class Point, class PointRef>
inline Foam::vector Foam::tetrahedron<Point, PointRef>::Sd() const
{
    return triangle<Point, PointRef>(a_, c_, b_).normal();
}
 
 
template<class Point, class PointRef>
inline Point Foam::tetrahedron<Point, PointRef>::centre() const
{
    return 0.25*(a_ + b_ + c_ + d_);
}
 
 
template<class Point, class PointRef>
inline Foam::scalar Foam::tetrahedron<Point, PointRef>::mag() const
{
    return (1.0/6.0)*(((b_ - a_) ^ (c_ - a_)) & (d_ - a_));
}
 
 
template<class Point, class PointRef>
inline Point Foam::tetrahedron<Point, PointRef>::circumCentre() const
{
    vector a = b_ - a_;
    vector b = c_ - a_;
    vector c = d_ - a_;
 
    scalar lambda = magSqr(c) - (a & c);
    scalar mu = magSqr(b) - (a & b);
 
    vector ba = b ^ a;
    vector ca = c ^ a;
 
    vector num = lambda*ba - mu*ca;
    scalar denom = (c & ba);
 
    if (Foam::mag(denom) < ROOTVSMALL)
    {
        // Degenerate tetrahedron, returning centre instead of circumCentre.
 
        return centre();
    }
 
    return a_ + 0.5*(a + num/denom);
}
 
 
template<class Point, class PointRef>
inline Foam::scalar Foam::tetrahedron<Point, PointRef>::circumRadius() const
{
    vector a = b_ - a_;
    vector b = c_ - a_;
    vector c = d_ - a_;
 
    scalar lambda = magSqr(c) - (a & c);
    scalar mu = magSqr(b) - (a & b);
 
    vector ba = b ^ a;
    vector ca = c ^ a;
 
    vector num = lambda*ba - mu*ca;
    scalar denom = (c & ba);
 
    if (Foam::mag(denom) < ROOTVSMALL)
    {
        // Degenerate tetrahedron, returning GREAT for circumRadius.
        return GREAT;
    }
 
    return Foam::mag(0.5*(a + num/denom));
}
 
 
template<class Point, class PointRef>
inline Foam::scalar Foam::tetrahedron<Point, PointRef>::quality() const
{
    return
        mag()
       /(
            8.0/(9.0*sqrt(3.0))
           *pow3(min(circumRadius(), GREAT))
          + ROOTVSMALL
        );
}
 
 
template<class Point, class PointRef>
inline Point Foam::tetrahedron<Point, PointRef>::randomPoint
(
    Random& rndGen
) const
{
    // Adapted from
    // http://vcg.isti.cnr.it/activities/geometryegraphics/pointintetraedro.html
 
    scalar s = rndGen.scalar01();
    scalar t = rndGen.scalar01();
    scalar u = rndGen.scalar01();
 
    if (s + t > 1.0)
    {
        s = 1.0 - s;
        t = 1.0 - t;
    }
 
    if (t + u > 1.0)
    {
        scalar tmp = u;
        u = 1.0 - s - t;
        t = 1.0 - tmp;
    }
    else if (s + t + u > 1.0)
    {
        scalar tmp = u;
        u = s + t + u - 1.0;
        s = 1.0 - t - tmp;
    }
 
    return (1 - s - t - u)*a_ + s*b_ + t*c_ + u*d_;
}
 
 
template<class Point, class PointRef>
inline Point Foam::tetrahedron<Point, PointRef>::randomPoint
(
    cachedRandom& rndGen
) const
{
    // Adapted from
    // http://vcg.isti.cnr.it/activities/geometryegraphics/pointintetraedro.html
 
    scalar s = rndGen.sample01<scalar>();
    scalar t = rndGen.sample01<scalar>();
    scalar u = rndGen.sample01<scalar>();
 
    if (s + t > 1.0)
    {
        s = 1.0 - s;
        t = 1.0 - t;
    }
 
    if (t + u > 1.0)
    {
        scalar tmp = u;
        u = 1.0 - s - t;
        t = 1.0 - tmp;
    }
    else if (s + t + u > 1.0)
    {
        scalar tmp = u;
        u = s + t + u - 1.0;
        s = 1.0 - t - tmp;
    }
 
    return (1 - s - t - u)*a_ + s*b_ + t*c_ + u*d_;
}
 
 
template<class Point, class PointRef>
Foam::scalar Foam::tetrahedron<Point, PointRef>::barycentric
(
    const point& pt,
    List<scalar>& bary
) const
{
    // From:
    // http://en.wikipedia.org/wiki/Barycentric_coordinate_system_(mathematics)
 
    vector e0(a_ - d_);
    vector e1(b_ - d_);
    vector e2(c_ - d_);
 
    tensor t
    (
        e0.x(), e1.x(), e2.x(),
        e0.y(), e1.y(), e2.y(),
        e0.z(), e1.z(), e2.z()
    );
 
    scalar detT = det(t);
 
    if (Foam::mag(detT) < SMALL)
    {
        // Degenerate tetrahedron, returning 1/4 barycentric coordinates.
 
        bary = List<scalar>(4, 0.25);
 
        return detT;
    }
 
    vector res = inv(t, detT) & (pt - d_);
 
    bary.setSize(4);
 
    bary[0] = res.x();
    bary[1] = res.y();
    bary[2] = res.z();
    bary[3] = (1.0 - res.x() - res.y() - res.z());
 
    return detT;
}
 
 
template<class Point, class PointRef>
inline Foam::pointHit Foam::tetrahedron<Point, PointRef>::nearestPoint
(
    const point& p
) const
{
    // Adapted from:
    // Real-time collision detection, Christer Ericson, 2005, p142-144
 
    // Assuming initially that the point is inside all of the
    // halfspaces, so closest to itself.
 
    point closestPt = p;
 
    scalar minOutsideDistance = VGREAT;
 
    bool inside = true;
 
    if (((p - b_) & Sa()) >= 0)
    {
        // p is outside halfspace plane of tri
        pointHit info = triangle<Point, PointRef>(b_, c_, d_).nearestPoint(p);
 
        inside = false;
 
        if (info.distance() < minOutsideDistance)
        {
            closestPt = info.rawPoint();
 
            minOutsideDistance = info.distance();
        }
    }
 
    if (((p - a_) & Sb()) >= 0)
    {
        // p is outside halfspace plane of tri
        pointHit info = triangle<Point, PointRef>(a_, d_, c_).nearestPoint(p);
 
        inside = false;
 
        if (info.distance() < minOutsideDistance)
        {
            closestPt = info.rawPoint();
 
            minOutsideDistance = info.distance();
        }
    }
 
    if (((p - a_) & Sc()) >= 0)
    {
        // p is outside halfspace plane of tri
        pointHit info = triangle<Point, PointRef>(a_, b_, d_).nearestPoint(p);
 
        inside = false;
 
        if (info.distance() < minOutsideDistance)
        {
            closestPt = info.rawPoint();
 
            minOutsideDistance = info.distance();
        }
    }
 
    if (((p - a_) & Sd()) >= 0)
    {
        // p is outside halfspace plane of tri
        pointHit info = triangle<Point, PointRef>(a_, c_, b_).nearestPoint(p);
 
        inside = false;
 
        if (info.distance() < minOutsideDistance)
        {
            closestPt = info.rawPoint();
 
            minOutsideDistance = info.distance();
        }
    }
 
    // If the point is inside, then the distance to the closest point
    // is zero
    if (inside)
    {
        minOutsideDistance = 0;
    }
 
    return pointHit
    (
        inside,
        closestPt,
        minOutsideDistance,
        !inside
    );
}
 
 
template<class Point, class PointRef>
bool Foam::tetrahedron<Point, PointRef>::inside(const point& pt) const
{
    // For robustness, assuming that the point is in the tet unless
    // "definitively" shown otherwise by obtaining a positive dot
    // product greater than a tolerance of SMALL.
 
    // The tet is defined: tet(Cc, tetBasePt, pA, pB) where the normal
    // vectors and base points for the half-space planes are:
    // area[0] = Sa();
    // area[1] = Sb();
    // area[2] = Sc();
    // area[3] = Sd();
    // planeBase[0] = tetBasePt = b_
    // planeBase[1] = ptA       = c_
    // planeBase[2] = tetBasePt = b_
    // planeBase[3] = tetBasePt = b_
 
    vector n = vector::zero;
 
    {
        // 0, a
        const point& basePt = b_;
 
        n = Sa();
        n /= (Foam::mag(n) + VSMALL);
 
        if (((pt - basePt) & n) > SMALL)
        {
            return false;
        }
    }
 
    {
        // 1, b
        const point& basePt = c_;
 
        n = Sb();
        n /= (Foam::mag(n) + VSMALL);
 
        if (((pt - basePt) & n) > SMALL)
        {
            return false;
        }
    }
 
    {
        // 2, c
        const point& basePt = b_;
 
        n = Sc();
        n /= (Foam::mag(n) + VSMALL);
 
        if (((pt - basePt) & n) > SMALL)
        {
            return false;
        }
    }
 
    {
        // 3, d
        const point& basePt = b_;
 
        n = Sd();
        n /= (Foam::mag(n) + VSMALL);
 
        if (((pt - basePt) & n) > SMALL)
        {
            return false;
        }
    }
 
    return true;
}
 
 
template<class Point, class PointRef>
inline void Foam::tetrahedron<Point, PointRef>::dummyOp::operator()
(
    const tetPoints&
)
{}
 
 
template<class Point, class PointRef>
inline Foam::tetrahedron<Point, PointRef>::sumVolOp::sumVolOp()
:
    vol_(0.0)
{}
 
 
template<class Point, class PointRef>
inline void Foam::tetrahedron<Point, PointRef>::sumVolOp::operator()
(
    const tetPoints& tet
)
{
    vol_ += tet.tet().mag();
}
 
 
template<class Point, class PointRef>
inline Foam::tetrahedron<Point, PointRef>::storeOp::storeOp
(
    tetIntersectionList& tets,
    label& nTets
)
:
    tets_(tets),
    nTets_(nTets)
{}
 
 
template<class Point, class PointRef>
inline void Foam::tetrahedron<Point, PointRef>::storeOp::operator()
(
    const tetPoints& tet
)
{
    tets_[nTets_++] = tet;
}
 
 
template<class Point, class PointRef>
inline Foam::point Foam::tetrahedron<Point, PointRef>::planeIntersection
(
    const FixedList<scalar, 4>& d,
    const tetPoints& t,
    const label negI,
    const label posI
)
{
    return
        (d[posI]*t[negI] - d[negI]*t[posI])
      / (-d[negI]+d[posI]);
}
 
 
template<class Point, class PointRef>
template<class TetOp>
inline void Foam::tetrahedron<Point, PointRef>::decomposePrism
(
    const FixedList<point, 6>& points,
    TetOp& op
)
{
    op(tetPoints(points[1], points[3], points[2], points[0]));
    op(tetPoints(points[1], points[2], points[3], points[4]));
    op(tetPoints(points[4], points[2], points[3], points[5]));
}
 
 
template<class Point, class PointRef>
template<class AboveTetOp, class BelowTetOp>
inline void Foam::tetrahedron<Point, PointRef>::
tetSliceWithPlane
(
    const plane& pl,
    const tetPoints& tet,
    AboveTetOp& aboveOp,
    BelowTetOp& belowOp
)
{
    // Distance to plane
    FixedList<scalar, 4> d;
    label nPos = 0;
    forAll(tet, i)
    {
        d[i] = ((tet[i]-pl.refPoint()) & pl.normal());
        if (d[i] > 0)
        {
            nPos++;
        }
    }
 
    if (nPos == 4)
    {
        aboveOp(tet);
    }
    else if (nPos == 3)
    {
        // Sliced into below tet and above prism. Prism gets split into
        // two tets.
 
        // Find the below tet
        label i0 = -1;
        forAll(d, i)
        {
            if (d[i] <= 0)
            {
                i0 = i;
                break;
            }
        }
 
        label i1 = d.fcIndex(i0);
        label i2 = d.fcIndex(i1);
        label i3 = d.fcIndex(i2);
 
        point p01 = planeIntersection(d, tet, i0, i1);
        point p02 = planeIntersection(d, tet, i0, i2);
        point p03 = planeIntersection(d, tet, i0, i3);
 
        // i0 = tetCell vertex 0: p01,p02,p03 outwards pointing triad
        //          ,,         1 :     ,,     inwards pointing triad
        //          ,,         2 :     ,,     outwards pointing triad
        //          ,,         3 :     ,,     inwards pointing triad
 
        //Pout<< "Split 3pos tet " << tet << " d:" << d << " into" << nl;
 
        if (i0 == 0 || i0 == 2)
        {
            tetPoints t(tet[i0], p01, p02, p03);
            //Pout<< "    belowtet:" << t << " around i0:" << i0 << endl;
            //checkTet(t, "nPos 3, belowTet i0==0 or 2");
            belowOp(t);
 
            // Prism
            FixedList<point, 6> p;
            p[0] = tet[i1];
            p[1] = tet[i3];
            p[2] = tet[i2];
            p[3] = p01;
            p[4] = p03;
            p[5] = p02;
            //Pout<< "    aboveprism:" << p << endl;
            decomposePrism(p, aboveOp);
        }
        else
        {
            tetPoints t(p01, p02, p03, tet[i0]);
            //Pout<< "    belowtet:" << t << " around i0:" << i0 << endl;
            //checkTet(t, "nPos 3, belowTet i0==1 or 3");
            belowOp(t);
 
            // Prism
            FixedList<point, 6> p;
            p[0] = tet[i3];
            p[1] = tet[i1];
            p[2] = tet[i2];
            p[3] = p03;
            p[4] = p01;
            p[5] = p02;
            //Pout<< "    aboveprism:" << p << endl;
            decomposePrism(p, aboveOp);
        }
    }
    else if (nPos == 2)
    {
        // Tet cut into two prisms. Determine the positive one.
        label pos0 = -1;
        label pos1 = -1;
        forAll(d, i)
        {
            if (d[i] > 0)
            {
                if (pos0 == -1)
                {
                    pos0 = i;
                }
                else
                {
                    pos1 = i;
                }
            }
        }
 
        //Pout<< "Split 2pos tet " << tet << " d:" << d
        //    << " around pos0:" << pos0 << " pos1:" << pos1
        //    << " neg0:" << neg0 << " neg1:" << neg1 << " into" << nl;
 
        const edge posEdge(pos0, pos1);
 
        if (posEdge == edge(0, 1))
        {
            point p02 = planeIntersection(d, tet, 0, 2);
            point p03 = planeIntersection(d, tet, 0, 3);
            point p12 = planeIntersection(d, tet, 1, 2);
            point p13 = planeIntersection(d, tet, 1, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[0];
                p[1] = p02;
                p[2] = p03;
                p[3] = tet[1];
                p[4] = p12;
                p[5] = p13;
                //Pout<< "    01 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[2];
                p[1] = p02;
                p[2] = p12;
                p[3] = tet[3];
                p[4] = p03;
                p[5] = p13;
                //Pout<< "    01 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else if (posEdge == edge(1, 2))
        {
            point p01 = planeIntersection(d, tet, 0, 1);
            point p13 = planeIntersection(d, tet, 1, 3);
            point p02 = planeIntersection(d, tet, 0, 2);
            point p23 = planeIntersection(d, tet, 2, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[1];
                p[1] = p01;
                p[2] = p13;
                p[3] = tet[2];
                p[4] = p02;
                p[5] = p23;
                //Pout<< "    12 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[3];
                p[1] = p23;
                p[2] = p13;
                p[3] = tet[0];
                p[4] = p02;
                p[5] = p01;
                //Pout<< "    12 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else if (posEdge == edge(2, 0))
        {
            point p01 = planeIntersection(d, tet, 0, 1);
            point p03 = planeIntersection(d, tet, 0, 3);
            point p12 = planeIntersection(d, tet, 1, 2);
            point p23 = planeIntersection(d, tet, 2, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[2];
                p[1] = p12;
                p[2] = p23;
                p[3] = tet[0];
                p[4] = p01;
                p[5] = p03;
                //Pout<< "    20 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[1];
                p[1] = p12;
                p[2] = p01;
                p[3] = tet[3];
                p[4] = p23;
                p[5] = p03;
                //Pout<< "    20 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else if (posEdge == edge(0, 3))
        {
            point p01 = planeIntersection(d, tet, 0, 1);
            point p02 = planeIntersection(d, tet, 0, 2);
            point p13 = planeIntersection(d, tet, 1, 3);
            point p23 = planeIntersection(d, tet, 2, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[3];
                p[1] = p23;
                p[2] = p13;
                p[3] = tet[0];
                p[4] = p02;
                p[5] = p01;
                //Pout<< "    03 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[2];
                p[1] = p23;
                p[2] = p02;
                p[3] = tet[1];
                p[4] = p13;
                p[5] = p01;
                //Pout<< "    03 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else if (posEdge == edge(1, 3))
        {
            point p01 = planeIntersection(d, tet, 0, 1);
            point p12 = planeIntersection(d, tet, 1, 2);
            point p03 = planeIntersection(d, tet, 0, 3);
            point p23 = planeIntersection(d, tet, 2, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[1];
                p[1] = p12;
                p[2] = p01;
                p[3] = tet[3];
                p[4] = p23;
                p[5] = p03;
                //Pout<< "    13 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[2];
                p[1] = p12;
                p[2] = p23;
                p[3] = tet[0];
                p[4] = p01;
                p[5] = p03;
                //Pout<< "    13 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else if (posEdge == edge(2, 3))
        {
            point p02 = planeIntersection(d, tet, 0, 2);
            point p12 = planeIntersection(d, tet, 1, 2);
            point p03 = planeIntersection(d, tet, 0, 3);
            point p13 = planeIntersection(d, tet, 1, 3);
            // Split the resulting prism
            {
                FixedList<point, 6> p;
                p[0] = tet[2];
                p[1] = p02;
                p[2] = p12;
                p[3] = tet[3];
                p[4] = p03;
                p[5] = p13;
                //Pout<< "    23 aboveprism:" << p << endl;
                decomposePrism(p, aboveOp);
            }
            {
                FixedList<point, 6> p;
                p[0] = tet[0];
                p[1] = p02;
                p[2] = p03;
                p[3] = tet[1];
                p[4] = p12;
                p[5] = p13;
                //Pout<< "    23 belowprism:" << p << endl;
                decomposePrism(p, belowOp);
            }
        }
        else
        {
            FatalErrorInFunction
                << "Missed edge:" << posEdge
                << abort(FatalError);
        }
    }
    else if (nPos == 1)
    {
        // Find the positive tet
        label i0 = -1;
        forAll(d, i)
        {
            if (d[i] > 0)
            {
                i0 = i;
                break;
            }
        }
 
        label i1 = d.fcIndex(i0);
        label i2 = d.fcIndex(i1);
        label i3 = d.fcIndex(i2);
 
        point p01 = planeIntersection(d, tet, i0, i1);
        point p02 = planeIntersection(d, tet, i0, i2);
        point p03 = planeIntersection(d, tet, i0, i3);
 
        //Pout<< "Split 1pos tet " << tet << " d:" << d << " into" << nl;
 
        if (i0 == 0 || i0 == 2)
        {
            tetPoints t(tet[i0], p01, p02, p03);
            //Pout<< "    abovetet:" << t << " around i0:" << i0 << endl;
            //checkTet(t, "nPos 1, aboveTets i0==0 or 2");
            aboveOp(t);
 
            // Prism
            FixedList<point, 6> p;
            p[0] = tet[i1];
            p[1] = tet[i3];
            p[2] = tet[i2];
            p[3] = p01;
            p[4] = p03;
            p[5] = p02;
            //Pout<< "    belowprism:" << p << endl;
            decomposePrism(p, belowOp);
        }
        else
        {
            tetPoints t(p01, p02, p03, tet[i0]);
            //Pout<< "    abovetet:" << t << " around i0:" << i0 << endl;
            //checkTet(t, "nPos 1, aboveTets i0==1 or 3");
            aboveOp(t);
 
            // Prism
            FixedList<point, 6> p;
            p[0] = tet[i3];
            p[1] = tet[i1];
            p[2] = tet[i2];
            p[3] = p03;
            p[4] = p01;
            p[5] = p02;
            //Pout<< "    belowprism:" << p << endl;
            decomposePrism(p, belowOp);
        }
    }
    else    // nPos == 0
    {
        belowOp(tet);
    }
}
 
 
template<class Point, class PointRef>
template<class AboveTetOp, class BelowTetOp>
inline void Foam::tetrahedron<Point, PointRef>::sliceWithPlane
(
    const plane& pl,
    AboveTetOp& aboveOp,
    BelowTetOp& belowOp
) const
{
    tetSliceWithPlane(pl, tetPoints(a_, b_, c_, d_), aboveOp, belowOp);
}
 
 
// * * * * * * * * * * * * * * * Ostream Operator  * * * * * * * * * * * * * //
 
template<class Point, class PointRef>
inline Foam::Istream& Foam::operator>>
(
    Istream& is,
    tetrahedron<Point, PointRef>& t
)
{
    is.readBegin("tetrahedron");
    is  >> t.a_ >> t.b_ >> t.c_ >> t.d_;
    is.readEnd("tetrahedron");
 
    is.check("Istream& operator>>(Istream&, tetrahedron&)");
 
    return is;
}
 
 
template<class Point, class PointRef>
inline Foam::Ostream& Foam::operator<<
(
    Ostream& os,
    const tetrahedron<Point, PointRef>& t
)
{
    os  << nl
        << token::BEGIN_LIST
        << t.a_ << token::SPACE
        << t.b_ << token::SPACE
        << t.c_ << token::SPACE
        << t.d_
        << token::END_LIST;
 
    return os;
}
 
 
// ************************************************************************* //