spatialTransform.H

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    Copyright (C) 2016 OpenFOAM Foundation
-------------------------------------------------------------------------------
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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    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::spatialTransform
 
Description
    Compact representation of the Plücker spatial transformation tensor
    in terms of the rotation tensor \c E and translation vector \c r .
 
    See Chapter 2 and Appendix A in reference:
    \verbatim
        Featherstone, R. (2008).
        Rigid body dynamics algorithms.
        Springer.
    \endverbatim
 
SourceFiles
    spatialTransformI.H
 
\*---------------------------------------------------------------------------*/
 
#ifndef spatialTransform_H
#define spatialTransform_H
 
#include "tensor.H"
#include "spatialVector.H"
#include "spatialTensor.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
// Forward Declarations
class spatialTransform;
Istream& operator>>(Istream&, spatialTransform&);
Ostream& operator<<(Ostream&, const spatialTransform&);
 
 
/*---------------------------------------------------------------------------*\
                         Class spatialTransform Declaration
\*---------------------------------------------------------------------------*/
 
class spatialTransform
{
    // Private data
 
        //- Rotation tensor
        tensor E_;
 
        //- Translation vector
        vector r_;
 
 
    // Private member functions
 
        //- Return E . *r
        inline tensor Erx() const;
 
 
public:
 
        //- Wrapper-class to provide transpose functions and operators
        class transpose
        {
            const spatialTransform& X_;
 
        public:
 
            //- Construct from a spatialTransform
            inline transpose(const spatialTransform& X);
 
            //- Return the transpose transformation tensor ^A{X^*}_B
            //  X^T
            inline operator spatialTensor() const;
 
            //- Transpose transform dual f: ^A{X^*}_B & f
            //  X^T . f = (E^T . fl + r ^ E^T . fw, E^T . fl)
            inline spatialVector operator&(const spatialVector& f) const;
        };
 
 
        //- Wrapper-class to provide dual functions and operators
        class dual
        {
            const spatialTransform& X_;
 
        public:
 
            //- Construct from a spatialTransform
            inline dual(const spatialTransform& X);
 
            //- Return dual transformation tensor ^B{X^*}_A
            inline operator spatialTensor() const;
 
            //- Transform dual f: ^B{X^*}_A & f
            //  X^* . f = (E . fw - r ^ fl, E . fl)
            inline spatialVector operator&(const spatialVector& f) const;
        };
 
 
    // Constructors
 
        //- Construct null
        inline spatialTransform();
 
        //- Construct from components
        inline spatialTransform(const tensor& E, const vector& r);
 
        //- Construct from Istream
        inline spatialTransform(Istream&);
 
 
    // Member Functions
 
        //- Return the rotation tensor
        inline const tensor& E() const;
 
        //- Return non-const access to the rotation tensor
        inline tensor& E();
 
        //- Return the translation vector
        inline const vector& r() const;
 
        //- Return non-const access to the translation vector
        inline vector& r();
 
        //- Return the transpose transformation tensor ^A{X^*}_B
        //  X^T
        inline transpose T() const;
 
        //- Return the inverse transformation tensor: X^-1
        //  X^-1 = (E^T, −E.r)
        inline spatialTransform inv() const;
 
 
    // Member Operators
 
        //- Return the dual transformation tensor ^B{X^*}_A
        inline dual operator*() const;
 
        //- Return transformation tensor ^BX_A
        //  X
        inline operator spatialTensor() const;
 
        //- Inner-product multiply with a transformation tensor
        inline void operator&=(const spatialTransform& X);
 
        //- Return the inner-product of two transformation tensors
        inline spatialTransform operator&(const spatialTransform& X) const;
 
        //- Transform v: ^BX_A . v
        //  X.v = (E . vw, E . (vl - r^vw))
        inline spatialVector operator&(const spatialVector& v) const;
 
        //- Transform position p
        //  X:p = E . (pl - r)
        inline vector transformPoint(const vector& p) const;
 
        //- Transform position p
        //  X:p = (E . pw, E . (vl - r))
        inline spatialVector operator&&(const spatialVector& v) const;
 
 
    // IOstream Operators
 
        friend Istream& operator>>(Istream&, spatialTransform&);
        friend Ostream& operator<<(Ostream&, const spatialTransform&);
};
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#include "spatialTransformI.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //