OgreQuaternion.h

/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2014 Torus Knot Software Ltd

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*/
// This file is based on material originally from:
// Geometric Tools, LLC
// Copyright (c) 1998-2010
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt


#ifndef __Quaternion_H__
#define __Quaternion_H__

#include "Prerequisites.h"
#include "OgreMath.h"


    /** \addtogroup Core
    *  @{
    */
    /** \addtogroup Math
    *  @{
    */
    /** Implementation of a Quaternion, i.e. a rotation around an axis.
        For more information about Quaternions and the theory behind it, we recommend reading:
        http://www.ogre3d.org/tikiwiki/Quaternion+and+Rotation+Primer and
        http://www.cprogramming.com/tutorial/3d/quaternions.html and
        http://www.gamedev.net/page/resources/_/reference/programming/math-and-physics/quaternions/quaternion-powers-r1095
    */
    class  Quaternion
    {
    public:
        /// Default constructor, initializes to identity rotation (aka 0°)
        inline Quaternion ()
            : w(1), x(0), y(0), z(0)
        {
        }
        /// Construct from an explicit list of values
        inline Quaternion (
            Real fW,
            Real fX, Real fY, Real fZ)
            : w(fW), x(fX), y(fY), z(fZ)
        {
        }
        /// Construct a quaternion from a rotation matrix
        inline Quaternion(const Matrix3& rot)
        {
            this->FromRotationMatrix(rot);
        }
        /// Construct a quaternion from an angle/axis
        inline Quaternion(const Radian& rfAngle, const Vector3& rkAxis)
        {
            this->FromAngleAxis(rfAngle, rkAxis);
        }
        /// Construct a quaternion from 3 orthonormal local axes
        inline Quaternion(const Vector3& xaxis, const Vector3& yaxis, const Vector3& zaxis)
        {
            this->FromAxes(xaxis, yaxis, zaxis);
        }
        /// Construct a quaternion from 3 orthonormal local axes
        inline Quaternion(const Vector3* akAxis)
        {
            this->FromAxes(akAxis);
        }
        /// Construct a quaternion from 4 manual w/x/y/z values
        inline Quaternion(Real* valptr)
        {
            memcpy(&w, valptr, sizeof(Real)*4);
        }

        /** Exchange the contents of this quaternion with another. 
        */
        inline void swap(Quaternion& other)
        {
            std::swap(w, other.w);
            std::swap(x, other.x);
            std::swap(y, other.y);
            std::swap(z, other.z);
        }

        /// Array accessor operator
        inline Real operator [] ( const size_t i ) const
        {
            assert( i < 4 );

            return *(&w+i);
        }

        /// Array accessor operator
        inline Real& operator [] ( const size_t i )
        {
            assert( i < 4 );

            return *(&w+i);
        }

        /// Pointer accessor for direct copying
        inline Real* ptr()
        {
            return &w;
        }

        /// Pointer accessor for direct copying
        inline const Real* ptr() const
        {
            return &w;
        }

        void FromRotationMatrix (const Matrix3& kRot);
        void ToRotationMatrix (Matrix3& kRot) const;
        /** Setups the quaternion using the supplied vector, and "roll" around
            that vector by the specified radians.
        */
        void FromAngleAxis (const Radian& rfAngle, const Vector3& rkAxis);
        void ToAngleAxis (Radian& rfAngle, Vector3& rkAxis) const;
        inline void ToAngleAxis (Degree& dAngle, Vector3& rkAxis) const {
            Radian rAngle;
            ToAngleAxis ( rAngle, rkAxis );
            dAngle = rAngle;
        }
        /** Constructs the quaternion using 3 axes, the axes are assumed to be orthonormal
            @see FromAxes
        */
        void FromAxes (const Vector3* akAxis);
        void FromAxes (const Vector3& xAxis, const Vector3& yAxis, const Vector3& zAxis);
        /** Gets the 3 orthonormal axes defining the quaternion. @see FromAxes */
        void ToAxes (Vector3* akAxis) const;
        void ToAxes (Vector3& xAxis, Vector3& yAxis, Vector3& zAxis) const;

        /** Returns the X orthonormal axis defining the quaternion. Same as doing
            xAxis = Vector3::UNIT_X * this. Also called the local X-axis
        */
        Vector3 xAxis(void) const;

        /** Returns the Y orthonormal axis defining the quaternion. Same as doing
            yAxis = Vector3::UNIT_Y * this. Also called the local Y-axis
        */
        Vector3 yAxis(void) const;

        /** Returns the Z orthonormal axis defining the quaternion. Same as doing
            zAxis = Vector3::UNIT_Z * this. Also called the local Z-axis
        */
        Vector3 zAxis(void) const;

        inline Quaternion& operator= (const Quaternion& rkQ)
        {
            w = rkQ.w;
            x = rkQ.x;
            y = rkQ.y;
            z = rkQ.z;
            return *this;
        }
        Quaternion operator+ (const Quaternion& rkQ) const;
        Quaternion operator- (const Quaternion& rkQ) const;
        Quaternion operator* (const Quaternion& rkQ) const;
        Quaternion operator* (Real fScalar) const;
         friend Quaternion operator* (Real fScalar,
            const Quaternion& rkQ);
        Quaternion operator- () const;
        inline bool operator== (const Quaternion& rhs) const
        {
            return (rhs.x == x) && (rhs.y == y) &&
                (rhs.z == z) && (rhs.w == w);
        }
        inline bool operator!= (const Quaternion& rhs) const
        {
            return !operator==(rhs);
        }
        // functions of a quaternion
        /// Returns the dot product of the quaternion
        Real Dot (const Quaternion& rkQ) const;
        /* Returns the normal length of this quaternion.
            @note This does <b>not</b> alter any values.
        */
        Real Norm () const;
        /// Normalises this quaternion, and returns the previous length
        Real normalise(void); 
        Quaternion Inverse () const;  /// Apply to non-zero quaternion
        Quaternion UnitInverse () const;  /// Apply to unit-length quaternion
        Quaternion Exp () const;
        Quaternion Log () const;

        /// Rotation of a vector by a quaternion
        Vector3 operator* (const Vector3& rkVector) const;

        /** Calculate the local roll element of this quaternion.
        @param reprojectAxis By default the method returns the 'intuitive' result
            that is, if you projected the local X of the quaternion onto the XY plane,
            the angle between it and global X is returned. The co-domain of the returned
            value is from -180 to 180 degrees. If set to false though, the result is
            the rotation around Z axis that could be used to implement the quaternion
            using some non-intuitive order of rotations. This behavior is preserved for
            backward compatibility, to decompose quaternion into yaw, pitch and roll use
            q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead.
        */
        Radian getRoll(bool reprojectAxis = true) const;
        /** Calculate the local pitch element of this quaternion
        @param reprojectAxis By default the method returns the 'intuitive' result
            that is, if you projected the local Y of the quaternion onto the YZ plane,
            the angle between it and global Y is returned. The co-domain of the returned
            value is from -180 to 180 degrees. If set to false though, the result is
            the rotation around X axis that could be used to implement the quaternion
            using some non-intuitive order of rotations. This behavior is preserved for
            backward compatibility, to decompose quaternion into yaw, pitch and roll use
            q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead.
        */
        Radian getPitch(bool reprojectAxis = true) const;
        /** Calculate the local yaw element of this quaternion
        @param reprojectAxis By default the method returns the 'intuitive' result
            that is, if you projected the local Z of the quaternion onto the ZX plane,
            the angle between it and global Z is returned. The co-domain of the returned
            value is from -180 to 180 degrees. If set to false though, the result is
            the rotation around Y axis that could be used to implement the quaternion 
            using some non-intuitive order of rotations. This behavior is preserved for
            backward compatibility, to decompose quaternion into yaw, pitch and roll use
            q.ToRotationMatrix().ToEulerAnglesYXZ(yaw, pitch, roll) instead.
        */
        Radian getYaw(bool reprojectAxis = true) const;
        
        /** Equality with tolerance (tolerance is max angle difference)
        @remark Both equals() and orientationEquals() measure the exact same thing.
                One measures the difference by angle, the other by a different, non-linear metric.
        */
        bool equals(const Quaternion& rhs, const Radian& tolerance) const;
        
        /** Compare two quaternions which are assumed to be used as orientations.
        @remark Both equals() and orientationEquals() measure the exact same thing.
                One measures the difference by angle, the other by a different, non-linear metric.
        @return true if the two orientations are the same or very close, relative to the given tolerance.
            Slerp ( 0.75f, A, B ) != Slerp ( 0.25f, B, A );
            therefore be careful if your code relies in the order of the operands.
            This is specially important in IK animation.
        */
        inline bool orientationEquals( const Quaternion& other, Real tolerance = 1e-3 ) const
        {
            Real d = this->Dot(other);
            return 1 - d*d < tolerance;
        }
        
        /** Performs Spherical linear interpolation between two quaternions, and returns the result.
            Slerp ( 0.0f, A, B ) = A
            Slerp ( 1.0f, A, B ) = B
            @return Interpolated quaternion
            @remarks
            Slerp has the proprieties of performing the interpolation at constant
            velocity, and being torque-minimal (unless shortestPath=false).
            However, it's NOT commutative, which means
            Slerp ( 0.75f, A, B ) != Slerp ( 0.25f, B, A );
            therefore be careful if your code relies in the order of the operands.
            This is specially important in IK animation.
        */
        static Quaternion Slerp (Real fT, const Quaternion& rkP,
            const Quaternion& rkQ, bool shortestPath = false);

        /** @see Slerp. It adds extra "spins" (i.e. rotates several times) specified
            by parameter 'iExtraSpins' while interpolating before arriving to the
            final values
        */
        static Quaternion SlerpExtraSpins (Real fT,
            const Quaternion& rkP, const Quaternion& rkQ,
            int iExtraSpins);

        /// Setup for spherical quadratic interpolation
        static void Intermediate (const Quaternion& rkQ0,
            const Quaternion& rkQ1, const Quaternion& rkQ2,
            Quaternion& rka, Quaternion& rkB);

        /// Spherical quadratic interpolation
        static Quaternion Squad (Real fT, const Quaternion& rkP,
            const Quaternion& rkA, const Quaternion& rkB,
            const Quaternion& rkQ, bool shortestPath = false);

        /** Performs Normalised linear interpolation between two quaternions, and returns the result.
            nlerp ( 0.0f, A, B ) = A
            nlerp ( 1.0f, A, B ) = B
            @remarks
            Nlerp is faster than Slerp.
            Nlerp has the proprieties of being commutative (@see Slerp;
            commutativity is desired in certain places, like IK animation), and
            being torque-minimal (unless shortestPath=false). However, it's performing
            the interpolation at non-constant velocity; sometimes this is desired,
            sometimes it is not. Having a non-constant velocity can produce a more
            natural rotation feeling without the need of tweaking the weights; however
            if your scene relies on the timing of the rotation or assumes it will point
            at a specific angle at a specific weight value, Slerp is a better choice.
        */
        static Quaternion nlerp(Real fT, const Quaternion& rkP, 
            const Quaternion& rkQ, bool shortestPath = false);

        /// Cutoff for sine near zero
        static const Real msEpsilon;

        // special values
        static const Quaternion ZERO;
        static const Quaternion IDENTITY;

        Real w, x, y, z;

        /// Check whether this quaternion contains valid values
        inline bool isNaN() const
        {
            return Math::isNaN(x) || Math::isNaN(y) || Math::isNaN(z) || Math::isNaN(w);
        }

        /** Function for writing to a stream. Outputs "Quaternion(w, x, y, z)" with w,x,y,z
            being the member values of the quaternion.
        */
        inline  friend std::ostream& operator <<
            ( std::ostream& o, const Quaternion& q )
        {
            o << "Quaternion(" << q.w << ", " << q.x << ", " << q.y << ", " << q.z << ")";
            return o;
        }

    };
#endif