vectorTools.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.

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    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/>.

Class
    Foam::vectorTools

Description
    Functions for analysing the relationships between vectors

\*---------------------------------------------------------------------------*/

#ifndef vectorTools_H
#define vectorTools_H

#include "vector.H"
#include "unitConversion.H"

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

namespace Foam
{

/*---------------------------------------------------------------------------*\
                      Namespace vectorTools Declaration
\*---------------------------------------------------------------------------*/

//- Collection of functions for testing relationships between two vectors.
namespace vectorTools
{
    //- Test if a and b are parallel: a^b = 0
    //  Uses the cross product, so the tolerance is proportional to
    //  the sine of the angle between a and b in radians
    template<typename T>
    bool areParallel
    (
        const Vector<T>& a,
        const Vector<T>& b,
        const T& tolerance = SMALL
    )
    {
        return (mag(a ^ b) < tolerance) ? true : false;
//        return ( mag( mag(a & b)/(mag(a)*mag(b)) - 1.0 ) < tolerance )
//               ? true
//               : false;
    }

    //- Test if a and b are orthogonal: a.b = 0
    //  Uses the dot product, so the tolerance is proportional to
    //  the cosine of the angle between a and b in radians
    template<typename T>
    bool areOrthogonal
    (
        const Vector<T>& a,
        const Vector<T>& b,
        const T& tolerance = SMALL
    )
    {
        return (mag(a & b) < tolerance) ? true : false;
    }

    //- Test if angle between a and b is acute: a.b > 0
    template<typename T>
    bool areAcute
    (
        const Vector<T>& a,
        const Vector<T>& b
    )
    {
        return ((a & b) > 0) ? true : false;
    }

    //- Test if angle between a and b is obtuse: a.b < 0
    template<typename T>
    bool areObtuse
    (
        const Vector<T>& a,
        const Vector<T>& b
    )
    {
        return ((a & b) < 0) ? true : false;
    }

    //- Calculate angle between a and b in radians
    template<typename T>
    T cosPhi
    (
        const Vector<T>& a,
        const Vector<T>& b,
        const T& tolerance = SMALL
    )
    {
        scalar cosPhi = (a & b)/(mag(a)*mag(b) + tolerance);

        // Enforce bounding between -1 and 1
        return min(max(cosPhi, -1), 1);
    }

    //- Calculate angle between a and b in radians
    template<typename T>
    T radAngleBetween
    (
        const Vector<T>& a,
        const Vector<T>& b,
        const T& tolerance = SMALL
    )
    {
        scalar cosPhi = (a & b)/(mag(a)*mag(b) + tolerance);

        // Enforce bounding between -1 and 1
        return acos( min(max(cosPhi, -1), 1) );
    }

    //- Calculate angle between a and b in degrees
    template<typename T>
    T degAngleBetween
    (
        const Vector<T>& a,
        const Vector<T>& b,
        const T& tolerance = SMALL
    )
    {
        return radToDeg(radAngleBetween(a, b, tolerance));
    }

} // End namespace vectorTools


// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

} // End namespace Foam

// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //

#endif

// ************************************************************************* //