quaternion.H

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/*---------------------------------------------------------------------------*\
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  \\      /  F ield         | OpenFOAM: The Open Source CFD Toolbox
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    \\  /    A nd           | www.openfoam.com
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-------------------------------------------------------------------------------
    Copyright (C) 2011-2016 OpenFOAM Foundation
    Copyright (C) 2019 OpenCFD Ltd.
-------------------------------------------------------------------------------
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/>.
 
Class
    Foam::quaternion
 
Description
    Quaternion class used to perform rotations in 3D space.
 
SourceFiles
    quaternionI.H
    quaternion.C
 
\*---------------------------------------------------------------------------*/
 
#ifndef quaternion_H
#define quaternion_H
 
#include "scalar.H"
#include "vector.H"
#include "tensor.H"
#include "word.H"
#include "Enum.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
namespace Foam
{
 
/*---------------------------------------------------------------------------*\
                           Class quaternion Declaration
\*---------------------------------------------------------------------------*/
 
class quaternion
{
    // Private Data
 
        //- Scalar part of the quaternion ( = cos(theta/2) for rotation)
        scalar w_;
 
        //- Vector part of the quaternion ( = axis of rotation)
        vector v_;
 
 
        //- Multiply vector v by quaternion as if v is a pure quaternion
        inline quaternion mulq0v(const vector& v) const;
 
        //- Conversion of two-axis rotation components into Euler-angles
        inline static vector twoAxes
        (
            const scalar t11,
            const scalar t12,
            const scalar c2,
            const scalar t31,
            const scalar t32
        );
 
        //- Conversion of three-axis rotation components into Euler-angles
        inline static vector threeAxes
        (
            const scalar t11,
            const scalar t12,
            const scalar s2,
            const scalar t31,
            const scalar t32
        );
 
 
public:
 
    // Public Types
 
        //- Component type
        typedef scalar cmptType;
 
        //- Magnitude type
        typedef scalar magType;
 
        //- Euler-angle rotation order
        enum eulerOrder : unsigned char
        {
            // Proper Euler angles
            XZX, XYX, YXY, YZY, ZYZ, ZXZ,
 
            // Tait-Bryan angles
            XZY, XYZ, YXZ, YZX, ZYX, ZXY
        };
 
        //- The names for Euler-angle rotation order
        static const Enum<eulerOrder> eulerOrderNames;
 
 
    // Member Constants
 
        //- Rank of quaternion is 1
        static constexpr direction rank = 1;
 
 
    // Static Data Members
 
        static constexpr const char* const typeName = "quaternion";
 
        static const quaternion zero;
        static const quaternion I;
 
 
    // Constructors
 
        //- Construct null
        inline quaternion();
 
        //- Construct zero initialized
        inline quaternion(const Foam::zero);
 
        //- Construct given scalar and vector parts
        inline quaternion(const scalar w, const vector& v);
 
        //- Construct rotation quaternion given direction d and angle theta
        inline quaternion(const vector& d, const scalar theta);
 
        //- Construct a rotation quaternion given direction d
        //- and cosine angle cosTheta and flag if d is normalized
        inline quaternion
        (
            const vector& d,
            const scalar cosTheta,
            const bool normalized
        );
 
        //- Construct a real quaternion from the given scalar part,
        //- the vector part = zero
        inline explicit quaternion(const scalar w);
 
        //- Construct a pure imaginary quaternion given the vector part,
        //- the scalar part = 0
        inline explicit quaternion(const vector& v);
 
        //- Return the unit quaternion (versor) from the given vector
        //- (w = sqrt(1 - |sqr(v)|))
        static inline quaternion unit(const vector& v);
 
        //- Construct from three Euler rotation angles
        inline quaternion(const eulerOrder order, const vector& angles);
 
        //- Construct from a rotation tensor
        inline explicit quaternion(const tensor& rotationTensor);
 
        //- Construct from Istream
        explicit quaternion(Istream& is);
 
 
    // Member Functions
 
    // Access
 
       //- Scalar part of the quaternion ( = cos(theta/2) for rotation)
       inline scalar w() const;
 
       //- Vector part of the quaternion ( = axis of rotation)
       inline const vector& v() const;
 
       //- The rotation tensor corresponding to the quaternion
       inline tensor R() const;
 
       //- Return the Euler rotation angles corresponding to the
       //- specified rotation order
       inline vector eulerAngles(const eulerOrder order) const;
 
       //- Return the quaternion normalized by its magnitude
       inline quaternion normalized() const;
 
 
   // Edit
 
       //- Scalar part of the quaternion ( = cos(theta/2) for rotation)
       inline scalar& w();
 
       //- Vector part of the quaternion ( = axis of rotation)
       inline vector& v();
 
       //- Normalize the quaternion by its magnitude
       inline void normalize();
 
 
   // Transform
 
       //- Rotate the given vector
       inline vector transform(const vector& v) const;
 
       //- Rotate the given vector anti-clockwise
       inline vector invTransform(const vector& v) const;
 
       //- Rotate the given quaternion (and normalize)
       inline quaternion transform(const quaternion& q) const;
 
       //- Rotate the given quaternion anti-clockwise (and normalize)
       inline quaternion invTransform(const quaternion& q) const;
 
 
    // Member Operators
 
        inline void operator=(const quaternion& q);
        inline void operator+=(const quaternion& q);
        inline void operator-=(const quaternion& q);
        inline void operator*=(const quaternion& q);
        inline void operator/=(const quaternion& q);
 
        //- Change scalar portion
        inline void operator=(const scalar s);
 
        //- Change vector portion
        inline void operator=(const vector& v);
 
        inline void operator*=(const scalar s);
        inline void operator/=(const scalar s);
};
 
 
// * * * * * * * * * * * * * * * * * Traits  * * * * * * * * * * * * * * * * //
 
//- Contiguous data for quaternion
template<> struct is_contiguous<quaternion> : std::true_type {};
 
//- Contiguous scalar data for quaternion
template<> struct is_contiguous_scalar<quaternion> : std::true_type {};
 
 
// * * * * * * * * * * * * * * * Global Functions  * * * * * * * * * * * * * //
 
inline scalar magSqr(const quaternion& q);
inline scalar mag(const quaternion& q);
 
//- Return the conjugate of the given quaternion
inline quaternion conjugate(const quaternion& q);
 
//- Return the normalized (unit) quaternion of the given quaternion
inline quaternion normalize(const quaternion& q);
 
//- Return the inverse of the given quaternion
inline quaternion inv(const quaternion& q);
 
//- Return a string representation of a quaternion
word name(const quaternion& q);
 
//- Spherical linear interpolation of quaternions
quaternion slerp
(
    const quaternion& qa,
    const quaternion& qb,
    const scalar t
);
 
//- Simple weighted average with sign change
quaternion average
(
    const UList<quaternion>& qs,
    const UList<scalar> w
);
 
//- Exponent of a quaternion
quaternion exp(const quaternion& q);
 
//- Power of a quaternion
quaternion pow(const quaternion& q, const label power);
 
//- Power of a quaternion
quaternion pow(const quaternion& q, const scalar power);
 
 
// * * * * * * * * * * * * * * * Global Operators  * * * * * * * * * * * * * //
 
Istream& operator>>(Istream& is, quaternion& q);
Ostream& operator<<(Ostream& os, const quaternion& q);
 
inline bool operator==(const quaternion& q1, const quaternion& q2);
inline bool operator!=(const quaternion& q1, const quaternion& q2);
inline quaternion operator+(const quaternion& q1, const quaternion& q2);
inline quaternion operator-(const quaternion& q);
inline quaternion operator-(const quaternion& q1, const quaternion& q2);
inline scalar operator&(const quaternion& q1, const quaternion& q2);
inline quaternion operator*(const quaternion& q1, const quaternion& q2);
inline quaternion operator/(const quaternion& q1, const quaternion& q2);
inline quaternion operator*(const scalar s, const quaternion& q);
inline quaternion operator*(const quaternion& q, const scalar s);
inline quaternion operator/(const quaternion& q, const scalar s);
 
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
} // End namespace Foam
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#include "quaternionI.H"
 
// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
 
#endif
 
// ************************************************************************* //