Quaternion

Functions
void	quat_rand (double q[4])
	Creates a unit quarternion with random orientation.
void	quat_identity (double q[4])
	Creates an identity quarternion.
void	quat_conjugated (double q[4])
	Performs in-place conjugation of a quaternion.
void	quat_inverted (double q[4])
	Performs in-place inversion of a quaternion.
void	quat_normalized (double q[4])
	Performs in-place normalization of a quaternion.
bool	quat_is_normalized (const double q[4])
	Returns true if a quaternion is normalized, i.e. if it is a unit quaternion.
void	quat_prod (const double p[4], const double q[4], double pq[4], bool normalize)
	Calculates the product of two unit quaternions.
double	quat_angle_between (const double p[4], const double q[4])
	Returns the angle between two unit quaternions.
void	quat_interpolate (const double q1[4], const double q2[4], const double t, double q[4])
	Interpolates between two unit quaternions.
void	quat_deriv_to_angvel_mat (const double q[4], double *mat)
	Returns the matrix mapping the derivative of a unit quaternion to angular velocity.
void	quat_deriv_to_angvel (const double q[4], const double qdot[4], double angvel[3])
	Calculates the angular velocity from a unit quaternion and its time derivative.
void	quat_deriv_from_angvel_mat (const double q[4], double *mat)
	Returns the matrix mapping the angular velocity to the time derivative of a unit quaternion.
void	quat_deriv_from_angvel (const double q[4], const double angvel[3], double qdot[4])
	Calculates the time derivative of a unit quaternion from angular velocity.
void	quat_rotmat (const double q[4], double *rotmat)
	Calculates the rotation matrix corresponding to a unit quaternion.
void	quat_shiftmat (const double q[4], const bool forward, double *shiftmat)
	Calculates the shifter matrix corresponding to a unit quaternion.
void	quat_rotate_vectors (const int n, const double *v, const double q[4], double *vrot)
	Rotates vectors by a unit quaternion.
void	quat_shift_vectors (const int n, const double *v, const double q[4], const bool forward, double *vshift)
	Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts vectors from A to B or B to A.
void	quat_shift_tensor2 (const double *A, const double q[4], const bool forward, double *Ashift)
	Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts second-order tensors from A to B or B to A.
void	quat_shift_tensor3 (const double *A, const double q[4], const bool forward, double *Ashift)
	Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts third-order tensors from A to B or B to A.
void	quat_to_aa (const double q[4], double axis[3], double *angle)
	Converts a unit quaternion to an axis-angle representation.
void	quat_to_dcm (const double q[4], double *dcm)
	Converts a unit quaternion to a direction cosine matrix.
void	quat_to_euler (const double q[4], enum EulangSeq seq, const bool world, double euler[3])
	Converts a unit quaternion to an Euler angle sequence.

Detailed Description

Function Documentation

quat_angle_between()

double quat_angle_between	(	const double	p[4],
		const double	q[4] )

Returns the angle between two unit quaternions.

Parameters

[in]	p	A quaternion.
[in]	q	Another quaternion.

Returns

Angle in radian.

quat_conjugated()

void quat_conjugated

(

double

q[4]

)

Performs in-place conjugation of a quaternion.

Parameters

[in,out]

q

in: A quaternion. out: The quaternion q conjugated.

quat_deriv_from_angvel()

void quat_deriv_from_angvel	(	const double	q[4],
		const double	angvel[3],
		double	qdot[4] )

Calculates the time derivative of a unit quaternion from angular velocity.

Parameters

[in]	q	A unit quaternion.
[in]	angvel	Angular velocity.
[out]	qdot	Time derivative of q.

quat_deriv_from_angvel_mat()

void quat_deriv_from_angvel_mat	(	const double	q[4],
		double *	mat )

Returns the matrix mapping the angular velocity to the time derivative of a unit quaternion.

Parameters

[in]	q	A unit quaternion.
[out]	mat	The 4 x 3 quaternion derivative matrix.

quat_deriv_to_angvel()

void quat_deriv_to_angvel	(	const double	q[4],
		const double	qdot[4],
		double	angvel[3] )

Calculates the angular velocity from a unit quaternion and its time derivative.

Parameters

[in]	q	A unit quaternion.
[in]	qdot	Time derivative of q.
[out]	angvel	Angular velocity.

quat_deriv_to_angvel_mat()

void quat_deriv_to_angvel_mat	(	const double	q[4],
		double *	mat )

Returns the matrix mapping the derivative of a unit quaternion to angular velocity.

Parameters

[in]	q	Derivative of a unit quaternion.
[out]	mat	The 3 x 4 angular velocity matrix.

quat_identity()

void quat_identity

(

double

q[4]

)

Creates an identity quarternion.

Parameters

[out]

q

Identity quaternion.

quat_interpolate()

void quat_interpolate	(	const double	q1[4],
		const double	q2[4],
		const double	t,
		double	q[4] )

Interpolates between two unit quaternions.

Parameters

[in]	q1	A unit quaternion.
[in]	q2	Another unit quaternion.
[in]	t	Interpolation factor, 0 <= t <= 1.
[out]	q	Interpolated unit quaternion.

quat_inverted()

void quat_inverted

(

double

q[4]

)

Performs in-place inversion of a quaternion.

Parameters

[in,out]

q

in: A quaternion. out: The quaternion q inverted.

quat_is_normalized()

bool quat_is_normalized

(

const double

q[4]

)

Returns true if a quaternion is normalized, i.e. if it is a unit quaternion.

Parameters

[in]

q

A quaternion.

Returns

true if q is normalized, false otherwise.

quat_normalized()

void quat_normalized

(

double

q[4]

)

Performs in-place normalization of a quaternion.

Parameters

[in,out]

q

in: A quaternion. out: The quaternion q normalized.

quat_prod()

void quat_prod	(	const double	p[4],
		const double	q[4],
		double	pq[4],
		bool	normalize )

Calculates the product of two unit quaternions.

Parameters

[in]	p	A quaternion.
[in]	q	Another quaternion.
[out]	pq	Product of p and q.
[in]	normalize	Whether to normalize the product.

quat_rand()

void quat_rand

(

double

q[4]

)

Creates a unit quarternion with random orientation.

Parameters

[out]

q

The unit quaternion.

quat_rotate_vectors()

void quat_rotate_vectors	(	const int	n,
		const double *	v,
		const double	q[4],
		double *	vrot )

Rotates vectors by a unit quaternion.

Parameters

[in]	n	Number of rows of v.
[in]	v	n x 3 array whose rows are the vectors to rotate.
[in]	q	A unit quaternion.
[out]	vrot	n x 3 array whose rows are the rotated vectors.

quat_rotmat()

void quat_rotmat	(	const double	q[4],
		double *	rotmat )

Calculates the rotation matrix corresponding to a unit quaternion.

Parameters

[in]	q	A unit quaternion.
[out]	rotmat	3 x 3 rotation matrix.

quat_shift_tensor2()

void quat_shift_tensor2	(	const double *	A,
		const double	q[4],
		const bool	forward,
		double *	Ashift )

Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts second-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 second-order tensor.
[in]	q	A unit quaternion.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 shifted second-order tensor.

quat_shift_tensor3()

void quat_shift_tensor3	(	const double *	A,
		const double	q[4],
		const bool	forward,
		double *	Ashift )

Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts third-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 x 3 third-order tensor.
[in]	q	A unit quaternion.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 x 3 shifted third-order tensor.

quat_shift_vectors()

void quat_shift_vectors	(	const int	n,
		const double *	v,
		const double	q[4],
		const bool	forward,
		double *	vshift )

Given two frames A and B such that the orientation of frame B with respect to frame A is given by a unit quaternion, shifts vectors from A to B or B to A.

Parameters

[in]	n	Number of rows of v.
[in]	v	n x 3 array whose rows are the vectors to shift.
[in]	q	A unit quaternion.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	vshift	n x 3 array whose rows are the rotated vectors.

quat_shiftmat()

void quat_shiftmat	(	const double	q[4],
		const bool	forward,
		double *	shiftmat )

Calculates the shifter matrix corresponding to a unit quaternion.

Parameters

[in]	q	A unit quaternion.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	shiftmat	3 x 3 shifter matrix.

quat_to_aa()

void quat_to_aa	(	const double	q[4],
		double	axis[3],
		double *	angle )

Converts a unit quaternion to an axis-angle representation.

Parameters

[in]	q	A unit quaternion.
[out]	axis	Unit vector along the axis of rotation.
[out]	angle	Angle in radian.

quat_to_dcm()

void quat_to_dcm	(	const double	q[4],
		double *	dcm )

Converts a unit quaternion to a direction cosine matrix.

Parameters

[in]	q	A unit quaternion.
[out]	dcm	3 x 3 direction cosine matrix.

quat_to_euler()

void quat_to_euler	(	const double	q[4],
		enum EulangSeq	seq,
		const bool	world,
		double	euler[3] )

Converts a unit quaternion to an Euler angle sequence.

Parameters

[in]	q	A unit quaternion.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Euler angle sequence.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[out]	euler	Euler angles.