libtf-dev 1.11.9-3 / usr / include / tf / LinearMath / Quaternion.h

/*
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.
2. Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
3. This notice may not be removed or altered from any source distribution.
*/



#ifndef TF_QUATERNION_H_
#define TF_QUATERNION_H_


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

namespace tf
{

/**@brief The Quaternion implements quaternion to perform linear algebra rotations in combination with Matrix3x3, Vector3 and Transform. */
class Quaternion : public QuadWord {
public:
  /**@brief No initialization constructor */
	Quaternion() {}


	//		template <typename tfScalar>
	//		explicit Quaternion(const tfScalar *v) : Tuple4<tfScalar>(v) {}
  /**@brief Constructor from scalars */
	Quaternion(const tfScalar& x, const tfScalar& y, const tfScalar& z, const tfScalar& w) 
		: QuadWord(x, y, z, w) 
	{}
  /**@brief Axis angle Constructor
   * @param axis The axis which the rotation is around
   * @param angle The magnitude of the rotation around the angle (Radians) */
	Quaternion(const Vector3& axis, const tfScalar& angle) 
	{ 
		setRotation(axis, angle); 
	}
  /**@brief Constructor from Euler angles
   * @param yaw Angle around Y unless TF_EULER_DEFAULT_ZYX defined then Z
   * @param pitch Angle around X unless TF_EULER_DEFAULT_ZYX defined then Y
   * @param roll Angle around Z unless TF_EULER_DEFAULT_ZYX defined then X */
  Quaternion(const tfScalar& yaw, const tfScalar& pitch, const tfScalar& roll) __attribute__((deprecated))
	{ 
#ifndef TF_EULER_DEFAULT_ZYX
		setEuler(yaw, pitch, roll); 
#else
		setRPY(roll, pitch, yaw);
#endif 
	}
  /**@brief Set the rotation using axis angle notation 
   * @param axis The axis around which to rotate
   * @param angle The magnitude of the rotation in Radians */
	void setRotation(const Vector3& axis, const tfScalar& angle)
	{
		tfScalar d = axis.length();
		tfAssert(d != tfScalar(0.0));
		tfScalar s = tfSin(angle * tfScalar(0.5)) / d;
		setValue(axis.x() * s, axis.y() * s, axis.z() * s, 
			tfCos(angle * tfScalar(0.5)));
	}
  /**@brief Set the quaternion using Euler angles
   * @param yaw Angle around Y
   * @param pitch Angle around X
   * @param roll Angle around Z */
	void setEuler(const tfScalar& yaw, const tfScalar& pitch, const tfScalar& roll)
	{
		tfScalar halfYaw = tfScalar(yaw) * tfScalar(0.5);  
		tfScalar halfPitch = tfScalar(pitch) * tfScalar(0.5);  
		tfScalar halfRoll = tfScalar(roll) * tfScalar(0.5);  
		tfScalar cosYaw = tfCos(halfYaw);
		tfScalar sinYaw = tfSin(halfYaw);
		tfScalar cosPitch = tfCos(halfPitch);
		tfScalar sinPitch = tfSin(halfPitch);
		tfScalar cosRoll = tfCos(halfRoll);
		tfScalar sinRoll = tfSin(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);
	}
  /**@brief Set the quaternion using fixed axis RPY
   * @param roll Angle around X 
   * @param pitch Angle around Y
   * @param yaw Angle around Z*/
  void setRPY(const tfScalar& roll, const tfScalar& pitch, const tfScalar& yaw)
	{
		tfScalar halfYaw = tfScalar(yaw) * tfScalar(0.5);  
		tfScalar halfPitch = tfScalar(pitch) * tfScalar(0.5);  
		tfScalar halfRoll = tfScalar(roll) * tfScalar(0.5);  
		tfScalar cosYaw = tfCos(halfYaw);
		tfScalar sinYaw = tfSin(halfYaw);
		tfScalar cosPitch = tfCos(halfPitch);
		tfScalar sinPitch = tfSin(halfPitch);
		tfScalar cosRoll = tfCos(halfRoll);
		tfScalar sinRoll = tfSin(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
	}
  /**@brief Set the quaternion using euler angles 
   * @param yaw Angle around Z
   * @param pitch Angle around Y
   * @param roll Angle around X */
  void setEulerZYX(const tfScalar& yaw, const tfScalar& pitch, const tfScalar& roll) __attribute__((deprecated))
	{
          setRPY(roll, pitch, yaw);
	}
  /**@brief Add two quaternions
   * @param q The quaternion to add to this one */
	TFSIMD_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;
	}

  /**@brief Sutfract out a quaternion
   * @param q The quaternion to sutfract from this one */
	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;
	}

  /**@brief Scale this quaternion
   * @param s The scalar to scale by */
	Quaternion& operator*=(const tfScalar& s)
	{
		m_floats[0] *= s; m_floats[1] *= s; m_floats[2] *= s; m_floats[3] *= s;
		return *this;
	}

  /**@brief Multiply this quaternion by q on the right
   * @param q The other quaternion 
   * Equivilant to this = this * q */
	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;
	}
  /**@brief Return the dot product between this quaternion and another
   * @param q The other quaternion */
	tfScalar 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];
	}

  /**@brief Return the length squared of the quaternion */
	tfScalar length2() const
	{
		return dot(*this);
	}

  /**@brief Return the length of the quaternion */
	tfScalar length() const
	{
		return tfSqrt(length2());
	}

  /**@brief Normalize the quaternion 
   * Such that x^2 + y^2 + z^2 +w^2 = 1 */
	Quaternion& normalize() 
	{
		return *this /= length();
	}

  /**@brief Return a scaled version of this quaternion
   * @param s The scale factor */
	TFSIMD_FORCE_INLINE Quaternion
	operator*(const tfScalar& s) const
	{
		return Quaternion(x() * s, y() * s, z() * s, m_floats[3] * s);
	}


  /**@brief Return an inversely scaled versionof this quaternion
   * @param s The inverse scale factor */
	Quaternion operator/(const tfScalar& s) const
	{
		tfAssert(s != tfScalar(0.0));
		return *this * (tfScalar(1.0) / s);
	}

  /**@brief Inversely scale this quaternion
   * @param s The scale factor */
	Quaternion& operator/=(const tfScalar& s) 
	{
		tfAssert(s != tfScalar(0.0));
		return *this *= tfScalar(1.0) / s;
	}

  /**@brief Return a normalized version of this quaternion */
	Quaternion normalized() const 
	{
		return *this / length();
	} 
  /**@brief Return the ***half*** angle between this quaternion and the other 
   * @param q The other quaternion */
	tfScalar angle(const Quaternion& q) const 
	{
		tfScalar s = tfSqrt(length2() * q.length2());
		tfAssert(s != tfScalar(0.0));
		return tfAcos(dot(q) / s);
	}
	/**@brief Return the angle between this quaternion and the other along the shortest path
	* @param q The other quaternion */
	tfScalar angleShortestPath(const Quaternion& q) const 
	{
		tfScalar s = tfSqrt(length2() * q.length2());
		tfAssert(s != tfScalar(0.0));
		if (dot(q) < 0) // Take care of long angle case see http://en.wikipedia.org/wiki/Slerp
			return tfAcos(dot(-q) / s) * tfScalar(2.0);
		else 
			return tfAcos(dot(q) / s) * tfScalar(2.0);
	}
  	/**@brief Return the angle [0, 2Pi] of rotation represented by this quaternion */
	tfScalar getAngle() const 
	{
		tfScalar s = tfScalar(2.) * tfAcos(m_floats[3]);
		return s;
	}

	/**@brief Return the angle [0, Pi] of rotation represented by this quaternion along the shortest path*/
	tfScalar getAngleShortestPath() const 
	{
		tfScalar s;
		if (m_floats[3] < 0)
		    s = tfScalar(2.) * tfAcos(-m_floats[3]);
		else
		    s = tfScalar(2.) * tfAcos(m_floats[3]);
		return s;
	}

	/**@brief Return the axis of the rotation represented by this quaternion */
	Vector3 getAxis() const
	{
		tfScalar s_squared = tfScalar(1.) - tfPow(m_floats[3], tfScalar(2.));
		if (s_squared < tfScalar(10.) * TFSIMD_EPSILON) //Check for divide by zero
			return Vector3(1.0, 0.0, 0.0);  // Arbitrary
		tfScalar s = tfSqrt(s_squared);
		return Vector3(m_floats[0] / s, m_floats[1] / s, m_floats[2] / s);
	}

	/**@brief Return the inverse of this quaternion */
	Quaternion inverse() const
	{
		return Quaternion(-m_floats[0], -m_floats[1], -m_floats[2], m_floats[3]);
	}

  /**@brief Return the sum of this quaternion and the other 
   * @param q2 The other quaternion */
	TFSIMD_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]);
	}

  /**@brief Return the difference between this quaternion and the other 
   * @param q2 The other quaternion */
	TFSIMD_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]);
	}

  /**@brief Return the negative of this quaternion 
   * This simply negates each element */
	TFSIMD_FORCE_INLINE Quaternion operator-() const
	{
		const Quaternion& q2 = *this;
		return Quaternion( - q2.x(), - q2.y(),  - q2.z(),  - q2.m_floats[3]);
	}
  /**@todo document this and it's use */
	TFSIMD_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);
	}

	/**@todo document this and it's use */
	TFSIMD_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);
	}


  /**@brief Return the quaternion which is the result of Spherical Linear Interpolation between this and the other quaternion
   * @param q The other quaternion to interpolate with 
   * @param t The ratio between this and q to interpolate.  If t = 0 the result is this, if t=1 the result is q.
   * Slerp interpolates assuming constant velocity.  */
	Quaternion slerp(const Quaternion& q, const tfScalar& t) const
	{
          tfScalar theta = angleShortestPath(q) / tfScalar(2.0);
		if (theta != tfScalar(0.0))
		{
			tfScalar d = tfScalar(1.0) / tfSin(theta);
			tfScalar s0 = tfSin((tfScalar(1.0) - t) * theta);
			tfScalar s1 = tfSin(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(tfScalar(0.),tfScalar(0.),tfScalar(0.),tfScalar(1.));
		return identityQuat;
	}

	TFSIMD_FORCE_INLINE const tfScalar& getW() const { return m_floats[3]; }

	
};


/**@brief Return the negative of a quaternion */
TFSIMD_FORCE_INLINE Quaternion
operator-(const Quaternion& q)
{
	return Quaternion(-q.x(), -q.y(), -q.z(), -q.w());
}



/**@brief Return the product of two quaternions */
TFSIMD_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()); 
}

TFSIMD_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()); 
}

TFSIMD_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()); 
}

/**@brief Calculate the dot product between two quaternions */
TFSIMD_FORCE_INLINE tfScalar 
dot(const Quaternion& q1, const Quaternion& q2) 
{ 
	return q1.dot(q2); 
}


/**@brief Return the length of a quaternion */
TFSIMD_FORCE_INLINE tfScalar
length(const Quaternion& q) 
{ 
	return q.length(); 
}

/**@brief Return the ***half*** angle between two quaternions*/
TFSIMD_FORCE_INLINE tfScalar
angle(const Quaternion& q1, const Quaternion& q2) 
{ 
	return q1.angle(q2); 
}

/**@brief Return the shortest angle between two quaternions*/
TFSIMD_FORCE_INLINE tfScalar
angleShortestPath(const Quaternion& q1, const Quaternion& q2) 
{ 
	return q1.angleShortestPath(q2); 
}

/**@brief Return the inverse of a quaternion*/
TFSIMD_FORCE_INLINE Quaternion
inverse(const Quaternion& q) 
{
	return q.inverse();
}

/**@brief Return the result of spherical linear interpolation betwen two quaternions 
 * @param q1 The first quaternion
 * @param q2 The second quaternion 
 * @param t The ration between q1 and q2.  t = 0 return q1, t=1 returns q2 
 * Slerp assumes constant velocity between positions. */
TFSIMD_FORCE_INLINE Quaternion
slerp(const Quaternion& q1, const Quaternion& q2, const tfScalar& t) 
{
	return q1.slerp(q2, t);
}

TFSIMD_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());
}

TFSIMD_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);
	tfScalar  d = v0.dot(v1);

	if (d < -1.0 + TFSIMD_EPSILON)
	{
		Vector3 n,unused;
		tfPlaneSpace1(v0,n,unused);
		return Quaternion(n.x(),n.y(),n.z(),0.0f); // just pick any vector that is orthogonal to v0
	}

	tfScalar  s = tfSqrt((1.0f + d) * 2.0f);
	tfScalar rs = 1.0f / s;

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

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

}
#endif