CQuaternion.h

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//==============================================================================
/*
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    \author    <http://www.chai3d.org>
    \author    Phil Fong
    \version   3.2.0 $Rev: 1869 $
*/
//==============================================================================

//------------------------------------------------------------------------------
#ifndef CQuaternionH
#define CQuaternionH
//------------------------------------------------------------------------------
#include "math/CMatrix3d.h"
#include "math/CVector3d.h"
//------------------------------------------------------------------------------

//------------------------------------------------------------------------------
namespace chai3d {
//------------------------------------------------------------------------------

//==============================================================================
//==============================================================================

//==============================================================================
//==============================================================================
struct cQuaternion 
{
    //--------------------------------------------------------------------------
    // MEMBERS:
    //--------------------------------------------------------------------------

public:

    double w;

    double x;

    double y;

    double z;


    //--------------------------------------------------------------------------
    // CONSTRUCTOR & DESTRUCTOR:
    //--------------------------------------------------------------------------

public:

    cQuaternion() {}

    cQuaternion(double a_w, 
                double a_x, 
                double a_y, 
                double a_z) : w(a_w), x(a_x), y(a_y), z(a_z) {}

    cQuaternion(double const* in) : w(in[0]), x(in[1]), y(in[2]), z(in[3]) {}


    //--------------------------------------------------------------------------
    // OPERATORS:
    //--------------------------------------------------------------------------

public:

    inline operator double*() {return &w;}

    inline operator double const*() const { return &w;}

    inline cQuaternion& operator*= (cQuaternion const& a_quaternion)
    {
        double neww = w*a_quaternion.w - x*a_quaternion.x - y*a_quaternion.y - z*a_quaternion.z;
        double newx = w*a_quaternion.x + x*a_quaternion.w + y*a_quaternion.z - z*a_quaternion.y;
        double newy = w*a_quaternion.y - x*a_quaternion.z + y*a_quaternion.w + z*a_quaternion.x;
        double newz = w*a_quaternion.z + x*a_quaternion.y - y*a_quaternion.x + z*a_quaternion.w;
        w = neww;
        x = newx;
        y = newy;
        z = newz;

        return (*this);
    }

    inline cQuaternion& operator*= (double a_scale)
    {
        w *= a_scale;
        x *= a_scale;
        y *= a_scale;
        z *= a_scale;
        return (*this);
    }
    
    inline cQuaternion& operator+= (cQuaternion const& a_quaternion)
    {
        w+=a_quaternion.w;
        x+=a_quaternion.x;
        y+=a_quaternion.y;
        z+=a_quaternion.z;
        return (*this);
    }

    inline cQuaternion& operator-= (cQuaternion const& a_quaternion)
    {
        w-=a_quaternion.w;
        x-=a_quaternion.x;
        y-=a_quaternion.y;
        z-=a_quaternion.z;
        return (*this);
    }

   inline  bool operator==(cQuaternion const& a_quaternion) const
    {
        return ( (w==a_quaternion.w) &&
                 (x==a_quaternion.x) &&
                 (y==a_quaternion.y) &&
                 (z==a_quaternion.z) );
    }


    //--------------------------------------------------------------------------
    // PUBLIC METHODS:
    //--------------------------------------------------------------------------

public:

    inline void zero() { w=0.0; x=0.0; y=0.0; z=0.0; }

    inline void negate() { w=-w; x=-x; y=-y; z=-z; }
  
    inline double magsq() const { return (w*w) + (x*x) + (y*y) + (z*z); }

    inline double lengthsq() const { return magsq(); }

    inline double mag() const { return sqrt(magsq()); }

    inline double length() const { return mag(); }

    inline void normalize()
    {
        double m = mag();
        w /= m;
        x /= m;
        y /= m;
        z /= m;
    }


    //--------------------------------------------------------------------------
    //--------------------------------------------------------------------------
    inline void toRotMat(cMatrix3d& a_matrix) const
    {
        double x2 = 2.0*x*x;
        double y2 = 2.0*y*y;
        double z2 = 2.0*z*z;
        double xy = 2.0*x*y;
        double wz = 2.0*w*z;
        double xz = 2.0*x*z;
        double wy = 2.0*w*y;
        double yz = 2.0*y*z;
        double wx = 2.0*w*x;

        a_matrix(0,0) = 1.0 - y2 - z2;
        a_matrix(0,1) = xy - wz;
        a_matrix(0,2) = xz + wy;
        a_matrix(1,0) = xy + wz;
        a_matrix(1,1) = 1.0 - x2 - z2;
        a_matrix(1,2) = yz - wx;
        a_matrix(2,0) = xz - wy;
        a_matrix(2,1) = yz + wx;
        a_matrix(2,2) = 1.0 - x2 - y2;
    }


    //--------------------------------------------------------------------------
    //--------------------------------------------------------------------------
    inline void fromRotMat(cMatrix3d const& a_matrix)
    {
        double trace = 1.0 + a_matrix(0,0) + a_matrix(1,1) + a_matrix(2,2);

        if (trace > C_SMALL)
        {
            double s = 2.0*sqrt(trace);
            x = (a_matrix(2,1) - a_matrix(1,2))/s;
            y = (a_matrix(0,2) - a_matrix(2,0))/s;
            z = (a_matrix(1,0) - a_matrix(0,1))/s;
            w = 0.25*s;
        } 
        else if ((a_matrix(0,0) > a_matrix(1,1)) && (a_matrix(0,0) > a_matrix(2,2))) 
        {
            // column 1 has largest diagonal
            double s = 2.0*sqrt(1.0+a_matrix(0,0)-a_matrix(1,1)-a_matrix(2,2));
            x = 0.25*s;
            y = (a_matrix(1,0) + a_matrix(0,1))/s;
            z = (a_matrix(0,2) + a_matrix(2,0))/s;
            w = (a_matrix(2,1) - a_matrix(1,2))/s;
        } 
        else if (a_matrix(1,1) > a_matrix(2,2)) 
        {
            // column 2 has largest diagonal
            double s = 2.0*sqrt(1.0+a_matrix(1,1)-a_matrix(0,0)-a_matrix(2,2));
            x = (a_matrix(1,0) + a_matrix(0,1))/s;
            y = 0.25*s;
            z = (a_matrix(2,1) + a_matrix(1,2))/s;
            w = (a_matrix(0,2) - a_matrix(2,0))/s;
        } 
        else 
        {
            // column 3 has largest diagonal
            double s = 2.0*sqrt(1.0+a_matrix(2,2)-a_matrix(0,0)-a_matrix(1,1));
            x = (a_matrix(0,2) + a_matrix(2,0))/s;
            y = (a_matrix(2,1) + a_matrix(1,2))/s;
            z = 0.25*s;
            w = (a_matrix(1,0) - a_matrix(0,1))/s;
        }
    }


    //--------------------------------------------------------------------------
    //--------------------------------------------------------------------------
    inline void fromAxisAngle(cVector3d a_axis, double a_angleRad)
    {
        // note that the axis is passed by value so that we can normalize it
        // without affecting the original value.
        a_axis.normalize();
        double sina = sin(a_angleRad / 2.0);
        double cosa = cos(a_angleRad / 2.0);
        w = cosa;
        x = a_axis(0) * sina;
        y = a_axis(1) * sina;
        z = a_axis(2) * sina;
    }


    //--------------------------------------------------------------------------
    //---------------------------------------------------------------------------
    inline void toAxisAngle(cVector3d& a_axis, double& a_angleRad) const
    {
        double cosa = w / mag();
        a_angleRad = acos(cosa);
        a_axis(0) = x;
        a_axis(1) = y;
        a_axis(2) = z;
    }


    //--------------------------------------------------------------------------
    //---------------------------------------------------------------------------
    inline void conj()
    {
        x = -x;
        y = -y;
        z = -z;
    }


    //--------------------------------------------------------------------------
    //---------------------------------------------------------------------------
    inline void invert()
    {
        double m2 = magsq();
        w =  w/m2;
        x = -x/m2;
        y = -y/m2;
        z = -z/m2;
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline void mul(cQuaternion const& a_quaternion)
    {
        double neww = w*a_quaternion.w - x*a_quaternion.x - y*a_quaternion.y - z*a_quaternion.z;
        double newx = w*a_quaternion.x + x*a_quaternion.w + y*a_quaternion.z - z*a_quaternion.y;
        double newy = w*a_quaternion.y - x*a_quaternion.z + y*a_quaternion.w + z*a_quaternion.x;
        double newz = w*a_quaternion.z + x*a_quaternion.y - y*a_quaternion.x + z*a_quaternion.w;

        w = neww;
        x = newx;
        y = newy;
        z = newz;
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline void mul(double a_scale)
    {
        w *= a_scale;
        x *= a_scale;
        y *= a_scale;
        z *= a_scale;
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline double dot(cQuaternion const& a_quaternion) const
    {
        return (w*a_quaternion.w + x*a_quaternion.x + y*a_quaternion.y + z*a_quaternion.z);
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline void add(cQuaternion const& a_quaternion)
    {
        w+=a_quaternion.w;
        x+=a_quaternion.x;
        y+=a_quaternion.y;
        z+=a_quaternion.z;
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline void sub(cQuaternion const& a_quaternion)
    {
        w-=a_quaternion.w;
        x-=a_quaternion.x;
        y-=a_quaternion.y;
        z-=a_quaternion.z;
    }


    //---------------------------------------------------------------
    //---------------------------------------------------------------
    inline void slerp(double a_level, 
                      cQuaternion const& a_quaternion0, 
                      cQuaternion a_quaternion1)
    {
        // a_quaternion1 is passed by value so that we can scale it, etc.
        // compute angle between a_quaternion0 and a_quaternion1
        double costheta = a_quaternion0.dot(a_quaternion1);
        if ((costheta-1.0) < 1e-4 && (costheta-1.0) > -1e-4)
        {
            // quaternions are parallel
            // linearly interpolate and normalize
            *this = a_quaternion0;
            this->mul(1.0-a_level);
            a_quaternion1.mul(a_level);
            this->operator +=(a_quaternion1);
            this->normalize();
        }
        else
        {
            double ratio1, ratio2;
            if ((costheta+1.0) > -1e-4 && (costheta+1.0) < 1e-4) 
            {
                // a_quaternion0 and a_quaternion1 are 180 degrees apart
                // there is no unique path between them
                a_quaternion1.w = a_quaternion0.z;
                a_quaternion1.x = -a_quaternion0.y;
                a_quaternion1.y = a_quaternion0.x;
                a_quaternion1.z = -a_quaternion0.w;
                ratio1 = sin(C_PI*(0.5-a_level));
                ratio2 = sin(C_PI*a_level);
            } 
            else 
            {
                if (costheta < 0.0) 
                {
                    costheta = -costheta;
                    a_quaternion1.negate();
                }
                double theta = acos(costheta);
                double sintheta = sin(theta);

                ratio1 = sin(theta*(1.0-a_level))/sintheta;
                ratio2 = sin(theta*a_level)/sintheta;
            }
            *this = a_quaternion0;
            this->mul(ratio1);
            a_quaternion1.mul(ratio2);
            this->operator +=(a_quaternion1);
        }
    }


    //--------------------------------------------------------------------------
    //--------------------------------------------------------------------------
    inline std::string str(const unsigned int a_precision = 2) const
    {
        std::string result;
        result = ("("+
                  cStr(w, a_precision) + "| " +
                  cStr(x, a_precision) + ", " +
                  cStr(y, a_precision) + ", " +
                  cStr(z, a_precision) + 
                  ")");
        return (result);
    }
};


//==============================================================================
// OPERATORS:
//==============================================================================


inline cQuaternion operator*(const cQuaternion& a_quaternion, const double a_scale)
{
    cQuaternion result = a_quaternion;
    result.mul(a_scale);
    return (result);
}


inline cQuaternion operator*(const double a_scale, const cQuaternion& a_quaternion)
{
    cQuaternion result = a_quaternion;
    result.mul(a_scale);
    return (result);
}


inline cQuaternion operator*(const cQuaternion& a_quaternion0, const cQuaternion& a_quaternion1)
{
    cQuaternion result = a_quaternion0;
    result.mul(a_quaternion1);
    return (result);
}


inline cQuaternion operator+(const cQuaternion& a_quaternion0, const cQuaternion& a_quaternion1)
{
    cQuaternion result = a_quaternion0;
    result.add(a_quaternion1);
    return (result);
}


inline cQuaternion operator-(const cQuaternion& a_quaternion0, const cQuaternion& a_quaternion1)
{
    cQuaternion result = a_quaternion0;
    result.sub(a_quaternion1);
    return (result);
}


static inline std::ostream &operator << (std::ostream &a_os, cQuaternion const& a_quaternion)
{
    a_os << a_quaternion.str(3);
    return (a_os);
}


//------------------------------------------------------------------------------
} // namespace chai3d
//------------------------------------------------------------------------------

//------------------------------------------------------------------------------
#endif
//------------------------------------------------------------------------------