source: downloads/ogre_src_v1-9-0/OgreMain/include/OgreQuaternion.h @ 148

/*
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This source file is part of OGRE
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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 "OgrePrerequisites.h"
#include "OgreMath.h"

namespace Ogre {

        /** \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
                http://www.cprogramming.com/tutorial/3d/quaternions.html
                http://www.gamedev.net/page/resources/_/reference/programming/math-and-physics/
                quaternions/quaternion-powers-r1095
    */
    class _OgreExport 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;
        _OgreExport 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 Y of the quaternion onto the X and
                        Y axes, the angle between them is returned. If set to false though, the
                        result is the actual yaw that will be used to implement the quaternion,
                        which is the shortest possible path to get to the same orientation and 
             may involve less axial rotation.  The co-domain of the returned value is 
             from -180 to 180 degrees.
                */
                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 Z of the quaternion onto the X and
                        Y axes, the angle between them is returned. If set to true though, the
                        result is the actual yaw that will be used to implement the quaternion,
                        which is the shortest possible path to get to the same orientation and 
            may involve less axial rotation.  The co-domain of the returned value is 
            from -180 to 180 degrees.
                */
                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 Y of the quaternion onto the X and
                        Z axes, the angle between them is returned. If set to true though, the
                        result is the actual yaw that will be used to implement the quaternion,
                        which is the shortest possible path to get to the same orientation and 
                        may involve less axial rotation. The co-domain of the returned value is 
            from -180 to 180 degrees.
                */
                Radian getYaw(bool reprojectAxis = true) const;         
                /// Equality with tolerance (tolerance is max angle difference)
                bool equals(const Quaternion& rhs, const Radian& tolerance) const;
                
            /** 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 _OgreExport friend std::ostream& operator <<
            ( std::ostream& o, const Quaternion& q )
        {
            o << "Quaternion(" << q.w << ", " << q.x << ", " << q.y << ", " << q.z << ")";
            return o;
        }

    };
        /** @} */
        /** @} */

}




#endif