septernion.H

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License
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Class
    Foam::septernion

Description
    Septernion class used to perform translations and rotations in 3D space.

    It is composed of a translation vector and rotation quaternion and as
    such has seven components hence the name "septernion" from the Latin to
    be consistent with quaternion rather than "hepternion" derived from the
    Greek.

SourceFiles
    septernionI.H
    septernion.C

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

#ifndef septernion_H
#define septernion_H

#include "vector.H"
#include "quaternion.H"
#include "spatialTransform.H"
#include "word.H"
#include "contiguous.H"

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

namespace Foam
{

// Forward declaration of friend functions and operators

class septernion;
Istream& operator>>(Istream& is, septernion&);
Ostream& operator<<(Ostream& os, const septernion& C);


/*---------------------------------------------------------------------------*\
                         Class septernion Declaration
\*---------------------------------------------------------------------------*/

class septernion
{
    // private data

        //- Translation vector
        vector t_;

        //- Rotation quaternion
        quaternion r_;


public:

    // Static Data Members

        static const char* const typeName;

        static const septernion zero;
        static const septernion I;


    // Constructors

        //- Construct null
        inline septernion();

        //- Construct given a translation vector and rotation quaternion
        inline septernion(const vector& t, const quaternion& r);

        //- Construct a pure translation septernion given a translation vector
        inline explicit septernion(const vector& t);

        //- Construct a pure rotation septernion given a rotation quaternion
        inline explicit septernion(const quaternion& r);

        //- Construct a general septernion from the given spatialTransform
        inline explicit septernion(const spatialTransform& st);

        //- Construct from Istream
        septernion(Istream&);


    // Member Functions

           // Access

               inline const vector& t() const;
               inline const quaternion& r() const;


           // Edit

               inline vector& t();
               inline quaternion& r();


           // Transform

               //- Transform the given coordinate point
               inline vector transformPoint(const vector& v) const;

               //- Inverse Transform the given coordinate point
               inline vector invTransformPoint(const vector& v) const;


    // Member Operators

        inline void operator*=(const septernion&);

        inline void operator=(const vector&);
        inline void operator+=(const vector&);
        inline void operator-=(const vector&);

        inline void operator=(const quaternion&);
        inline void operator*=(const quaternion&);
        inline void operator/=(const quaternion&);

        inline void operator*=(const scalar);
        inline void operator/=(const scalar);


    // IOstream Operators

        friend Istream& operator>>(Istream& is, septernion&);
        friend Ostream& operator<<(Ostream& os, const septernion& C);
};


// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //

//- Return the inverse of the given septernion
inline septernion inv(const septernion& tr);

//- Return a string representation of a septernion
word name(const septernion&);

//- Spherical linear interpolation of septernions. 0 for qa, 1 for qb
septernion slerp
(
    const septernion& qa,
    const septernion& qb,
    const scalar t
);

//- Simple weighted average
septernion average
(
    const UList<septernion>& ss,
    const UList<scalar> w
);

//- Data associated with septernion type are contiguous
template<>
inline bool contiguous<septernion>() {return true;}


// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //

inline bool operator==(const septernion& tr1, const septernion& tr2);
inline bool operator!=(const septernion& tr1, const septernion& tr2);
inline septernion operator+(const septernion& tr, const vector& t);
inline septernion operator+(const vector& t, const septernion& tr);
inline septernion operator-(const septernion& tr, const vector& t);
inline septernion operator*(const quaternion& r, const septernion& tr);
inline septernion operator*(const septernion& tr, const quaternion& r);
inline septernion operator/(const septernion& tr, const quaternion& r);
inline septernion operator*(const septernion& q1, const septernion& q2);
inline septernion operator/(const septernion& q1, const septernion& q2);
inline septernion operator*(const scalar s, const septernion& tr);
inline septernion operator*(const septernion& tr, const scalar s);
inline septernion operator/(const septernion& tr, const scalar s);


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

} // End namespace Foam

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

#include "septernionI.H"

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

#endif

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