Quaternion.h

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/*
Copyright (c) 2003-2006 Gino van den Bergen / Erwin Coumans  http://continuousphysics.com/Bullet/

This software is provided 'as-is', without any express or implied warranty.
In no event will the authors be held liable for any damages arising from the use of this software.
Permission is granted to anyone to use this software for any purpose, 
including commercial applications, and to alter it and redistribute it freely, 
subject to the following restrictions:

1. The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation would be appreciated but is not required.
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3. This notice may not be removed or altered from any source distribution.
*/



#ifndef TF2_QUATERNION_H_
#define TF2_QUATERNION_H_


#include "Vector3.h"
#include "QuadWord.h"

namespace tf2
{

class Quaternion : public QuadWord {
public:
        Quaternion() {}

        //              template <typename tf2Scalar>
        //              explicit Quaternion(const tf2Scalar *v) : Tuple4<tf2Scalar>(v) {}
        Quaternion(const tf2Scalar& x, const tf2Scalar& y, const tf2Scalar& z, const tf2Scalar& w) 
                : QuadWord(x, y, z, w) 
        {}
        Quaternion(const Vector3& axis, const tf2Scalar& angle) 
        { 
                setRotation(axis, angle); 
        }
  Quaternion(const tf2Scalar& yaw, const tf2Scalar& pitch, const tf2Scalar& roll) __attribute__((deprecated))
        { 
#ifndef TF2_EULER_DEFAULT_ZYX
                setEuler(yaw, pitch, roll); 
#else
                setRPY(roll, pitch, yaw);
#endif 
        }
        void setRotation(const Vector3& axis, const tf2Scalar& angle)
        {
                tf2Scalar d = axis.length();
                tf2Assert(d != tf2Scalar(0.0));
                tf2Scalar s = tf2Sin(angle * tf2Scalar(0.5)) / d;
                setValue(axis.x() * s, axis.y() * s, axis.z() * s, 
                        tf2Cos(angle * tf2Scalar(0.5)));
        }
        void setEuler(const tf2Scalar& yaw, const tf2Scalar& pitch, const tf2Scalar& roll)
        {
                tf2Scalar halfYaw = tf2Scalar(yaw) * tf2Scalar(0.5);  
                tf2Scalar halfPitch = tf2Scalar(pitch) * tf2Scalar(0.5);  
                tf2Scalar halfRoll = tf2Scalar(roll) * tf2Scalar(0.5);  
                tf2Scalar cosYaw = tf2Cos(halfYaw);
                tf2Scalar sinYaw = tf2Sin(halfYaw);
                tf2Scalar cosPitch = tf2Cos(halfPitch);
                tf2Scalar sinPitch = tf2Sin(halfPitch);
                tf2Scalar cosRoll = tf2Cos(halfRoll);
                tf2Scalar sinRoll = tf2Sin(halfRoll);
                setValue(cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw,
                        cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw,
                        sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw,
                        cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw);
        }
  void setRPY(const tf2Scalar& roll, const tf2Scalar& pitch, const tf2Scalar& yaw)
        {
                tf2Scalar halfYaw = tf2Scalar(yaw) * tf2Scalar(0.5);  
                tf2Scalar halfPitch = tf2Scalar(pitch) * tf2Scalar(0.5);  
                tf2Scalar halfRoll = tf2Scalar(roll) * tf2Scalar(0.5);  
                tf2Scalar cosYaw = tf2Cos(halfYaw);
                tf2Scalar sinYaw = tf2Sin(halfYaw);
                tf2Scalar cosPitch = tf2Cos(halfPitch);
                tf2Scalar sinPitch = tf2Sin(halfPitch);
                tf2Scalar cosRoll = tf2Cos(halfRoll);
                tf2Scalar sinRoll = tf2Sin(halfRoll);
                setValue(sinRoll * cosPitch * cosYaw - cosRoll * sinPitch * sinYaw, //x
                         cosRoll * sinPitch * cosYaw + sinRoll * cosPitch * sinYaw, //y
                         cosRoll * cosPitch * sinYaw - sinRoll * sinPitch * cosYaw, //z
                         cosRoll * cosPitch * cosYaw + sinRoll * sinPitch * sinYaw); //formerly yzx
        }
  void setEulerZYX(const tf2Scalar& yaw, const tf2Scalar& pitch, const tf2Scalar& roll) __attribute__((deprecated))
        {
          setRPY(roll, pitch, yaw);
        }
        TF2SIMD_FORCE_INLINE    Quaternion& operator+=(const Quaternion& q)
        {
                m_floats[0] += q.x(); m_floats[1] += q.y(); m_floats[2] += q.z(); m_floats[3] += q.m_floats[3];
                return *this;
        }

        Quaternion& operator-=(const Quaternion& q) 
        {
                m_floats[0] -= q.x(); m_floats[1] -= q.y(); m_floats[2] -= q.z(); m_floats[3] -= q.m_floats[3];
                return *this;
        }

        Quaternion& operator*=(const tf2Scalar& s)
        {
                m_floats[0] *= s; m_floats[1] *= s; m_floats[2] *= s; m_floats[3] *= s;
                return *this;
        }

        Quaternion& operator*=(const Quaternion& q)
        {
                setValue(m_floats[3] * q.x() + m_floats[0] * q.m_floats[3] + m_floats[1] * q.z() - m_floats[2] * q.y(),
                        m_floats[3] * q.y() + m_floats[1] * q.m_floats[3] + m_floats[2] * q.x() - m_floats[0] * q.z(),
                        m_floats[3] * q.z() + m_floats[2] * q.m_floats[3] + m_floats[0] * q.y() - m_floats[1] * q.x(),
                        m_floats[3] * q.m_floats[3] - m_floats[0] * q.x() - m_floats[1] * q.y() - m_floats[2] * q.z());
                return *this;
        }
        tf2Scalar dot(const Quaternion& q) const
        {
                return m_floats[0] * q.x() + m_floats[1] * q.y() + m_floats[2] * q.z() + m_floats[3] * q.m_floats[3];
        }

        tf2Scalar length2() const
        {
                return dot(*this);
        }

        tf2Scalar length() const
        {
                return tf2Sqrt(length2());
        }

        Quaternion& normalize() 
        {
                return *this /= length();
        }

        TF2SIMD_FORCE_INLINE Quaternion
        operator*(const tf2Scalar& s) const
        {
                return Quaternion(x() * s, y() * s, z() * s, m_floats[3] * s);
        }


        Quaternion operator/(const tf2Scalar& s) const
        {
                tf2Assert(s != tf2Scalar(0.0));
                return *this * (tf2Scalar(1.0) / s);
        }

        Quaternion& operator/=(const tf2Scalar& s) 
        {
                tf2Assert(s != tf2Scalar(0.0));
                return *this *= tf2Scalar(1.0) / s;
        }

        Quaternion normalized() const 
        {
                return *this / length();
        } 
        tf2Scalar angle(const Quaternion& q) const 
        {
                tf2Scalar s = tf2Sqrt(length2() * q.length2());
                tf2Assert(s != tf2Scalar(0.0));
                return tf2Acos(dot(q) / s);
        }
        tf2Scalar angleShortestPath(const Quaternion& q) const 
        {
                tf2Scalar s = tf2Sqrt(length2() * q.length2());
                tf2Assert(s != tf2Scalar(0.0));
                if (dot(q) < 0) // Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
                        return tf2Acos(dot(-q) / s) * tf2Scalar(2.0);
                else 
                        return tf2Acos(dot(q) / s) * tf2Scalar(2.0);
        }
        tf2Scalar getAngle() const 
        {
                tf2Scalar s = tf2Scalar(2.) * tf2Acos(m_floats[3]);
                return s;
        }

        tf2Scalar getAngleShortestPath() const 
        {
        tf2Scalar s;
                if (m_floats[3] >= 0)
                        s = tf2Scalar(2.) * tf2Acos(m_floats[3]);
                else
                        s = tf2Scalar(2.) * tf2Acos(-m_floats[3]);

                return s;
        }

        Vector3 getAxis() const
        {
                tf2Scalar s_squared = tf2Scalar(1.) - tf2Pow(m_floats[3], tf2Scalar(2.));
                if (s_squared < tf2Scalar(10.) * TF2SIMD_EPSILON) //Check for divide by zero
                        return Vector3(1.0, 0.0, 0.0);  // Arbitrary
                tf2Scalar s = tf2Sqrt(s_squared);
                return Vector3(m_floats[0] / s, m_floats[1] / s, m_floats[2] / s);
        }

        Quaternion inverse() const
        {
                return Quaternion(-m_floats[0], -m_floats[1], -m_floats[2], m_floats[3]);
        }

        TF2SIMD_FORCE_INLINE Quaternion
        operator+(const Quaternion& q2) const
        {
                const Quaternion& q1 = *this;
                return Quaternion(q1.x() + q2.x(), q1.y() + q2.y(), q1.z() + q2.z(), q1.m_floats[3] + q2.m_floats[3]);
        }

        TF2SIMD_FORCE_INLINE Quaternion
        operator-(const Quaternion& q2) const
        {
                const Quaternion& q1 = *this;
                return Quaternion(q1.x() - q2.x(), q1.y() - q2.y(), q1.z() - q2.z(), q1.m_floats[3] - q2.m_floats[3]);
        }

        TF2SIMD_FORCE_INLINE Quaternion operator-() const
        {
                const Quaternion& q2 = *this;
                return Quaternion( - q2.x(), - q2.y(),  - q2.z(),  - q2.m_floats[3]);
        }
        TF2SIMD_FORCE_INLINE Quaternion farthest( const Quaternion& qd) const 
        {
                Quaternion diff,sum;
                diff = *this - qd;
                sum = *this + qd;
                if( diff.dot(diff) > sum.dot(sum) )
                        return qd;
                return (-qd);
        }

        TF2SIMD_FORCE_INLINE Quaternion nearest( const Quaternion& qd) const 
        {
                Quaternion diff,sum;
                diff = *this - qd;
                sum = *this + qd;
                if( diff.dot(diff) < sum.dot(sum) )
                        return qd;
                return (-qd);
        }


        Quaternion slerp(const Quaternion& q, const tf2Scalar& t) const
        {
          tf2Scalar theta = angleShortestPath(q) / tf2Scalar(2.0);
                if (theta != tf2Scalar(0.0))
                {
                        tf2Scalar d = tf2Scalar(1.0) / tf2Sin(theta);
                        tf2Scalar s0 = tf2Sin((tf2Scalar(1.0) - t) * theta);
                        tf2Scalar s1 = tf2Sin(t * theta);   
                        if (dot(q) < 0) // Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
                          return Quaternion((m_floats[0] * s0 + -q.x() * s1) * d,
                                              (m_floats[1] * s0 + -q.y() * s1) * d,
                                              (m_floats[2] * s0 + -q.z() * s1) * d,
                                              (m_floats[3] * s0 + -q.m_floats[3] * s1) * d);
                        else
                          return Quaternion((m_floats[0] * s0 + q.x() * s1) * d,
                                              (m_floats[1] * s0 + q.y() * s1) * d,
                                              (m_floats[2] * s0 + q.z() * s1) * d,
                                              (m_floats[3] * s0 + q.m_floats[3] * s1) * d);
                        
                }
                else
                {
                        return *this;
                }
        }

        static const Quaternion&        getIdentity()
        {
                static const Quaternion identityQuat(tf2Scalar(0.),tf2Scalar(0.),tf2Scalar(0.),tf2Scalar(1.));
                return identityQuat;
        }

        TF2SIMD_FORCE_INLINE const tf2Scalar& getW() const { return m_floats[3]; }

        
};


TF2SIMD_FORCE_INLINE Quaternion
operator-(const Quaternion& q)
{
        return Quaternion(-q.x(), -q.y(), -q.z(), -q.w());
}



TF2SIMD_FORCE_INLINE Quaternion
operator*(const Quaternion& q1, const Quaternion& q2) {
        return Quaternion(q1.w() * q2.x() + q1.x() * q2.w() + q1.y() * q2.z() - q1.z() * q2.y(),
                q1.w() * q2.y() + q1.y() * q2.w() + q1.z() * q2.x() - q1.x() * q2.z(),
                q1.w() * q2.z() + q1.z() * q2.w() + q1.x() * q2.y() - q1.y() * q2.x(),
                q1.w() * q2.w() - q1.x() * q2.x() - q1.y() * q2.y() - q1.z() * q2.z()); 
}

TF2SIMD_FORCE_INLINE Quaternion
operator*(const Quaternion& q, const Vector3& w)
{
        return Quaternion( q.w() * w.x() + q.y() * w.z() - q.z() * w.y(),
                q.w() * w.y() + q.z() * w.x() - q.x() * w.z(),
                q.w() * w.z() + q.x() * w.y() - q.y() * w.x(),
                -q.x() * w.x() - q.y() * w.y() - q.z() * w.z()); 
}

TF2SIMD_FORCE_INLINE Quaternion
operator*(const Vector3& w, const Quaternion& q)
{
        return Quaternion( w.x() * q.w() + w.y() * q.z() - w.z() * q.y(),
                w.y() * q.w() + w.z() * q.x() - w.x() * q.z(),
                w.z() * q.w() + w.x() * q.y() - w.y() * q.x(),
                -w.x() * q.x() - w.y() * q.y() - w.z() * q.z()); 
}

TF2SIMD_FORCE_INLINE tf2Scalar 
dot(const Quaternion& q1, const Quaternion& q2) 
{ 
        return q1.dot(q2); 
}


TF2SIMD_FORCE_INLINE tf2Scalar
length(const Quaternion& q) 
{ 
        return q.length(); 
}

TF2SIMD_FORCE_INLINE tf2Scalar
angle(const Quaternion& q1, const Quaternion& q2) 
{ 
        return q1.angle(q2); 
}

TF2SIMD_FORCE_INLINE tf2Scalar
angleShortestPath(const Quaternion& q1, const Quaternion& q2) 
{ 
        return q1.angleShortestPath(q2); 
}

TF2SIMD_FORCE_INLINE Quaternion
inverse(const Quaternion& q) 
{
        return q.inverse();
}

TF2SIMD_FORCE_INLINE Quaternion
slerp(const Quaternion& q1, const Quaternion& q2, const tf2Scalar& t) 
{
        return q1.slerp(q2, t);
}

TF2SIMD_FORCE_INLINE Vector3 
quatRotate(const Quaternion& rotation, const Vector3& v) 
{
        Quaternion q = rotation * v;
        q *= rotation.inverse();
        return Vector3(q.getX(),q.getY(),q.getZ());
}

TF2SIMD_FORCE_INLINE Quaternion 
shortestArcQuat(const Vector3& v0, const Vector3& v1) // Game Programming Gems 2.10. make sure v0,v1 are normalized
{
        Vector3 c = v0.cross(v1);
        tf2Scalar  d = v0.dot(v1);

        if (d < -1.0 + TF2SIMD_EPSILON)
        {
                Vector3 n,unused;
                tf2PlaneSpace1(v0,n,unused);
                return Quaternion(n.x(),n.y(),n.z(),0.0f); // just pick any vector that is orthogonal to v0
        }

        tf2Scalar  s = tf2Sqrt((1.0f + d) * 2.0f);
        tf2Scalar rs = 1.0f / s;

        return Quaternion(c.getX()*rs,c.getY()*rs,c.getZ()*rs,s * 0.5f);
}

TF2SIMD_FORCE_INLINE Quaternion 
shortestArcQuatNormalize2(Vector3& v0,Vector3& v1)
{
        v0.normalize();
        v1.normalize();
        return shortestArcQuat(v0,v1);
}

}
#endif