Functions
void	aa_fix (double axis[3], double *angle, const bool normalize)
	Modifies axis and angle to ensure a right handed rotation with angle $\in [0, \pi)$ $\in [0, \pi)$ .
void	aa_rand (double axis[3], double *angle)
	Generates a random orientation in axis-angle representation.
void	aa_rotmat (const double axis[3], const double angle, double *rotmat)
	Calculates the rotation matrix corresponding to an axis-angle representation.
void	aa_from_rotmat (const double rotmat, double axis[3], double angle)
	Extracts axis and angle from a rotation matrix.
void	aa_rotate_vectors (const int n, const double v, const double axis[3], const double angle, double vrot)
	Rotates vectors about axis by angle.
void	aa_shiftmat (const double axis[3], const double angle, const bool forward, double *shiftmat)
	Calculates the shifter matrix corresponding to an axis-angle representation.
void	aa_shift_vectors (const int n, const double v, const double axis[3], const double angle, 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 an axis-angle representation, shifts vectors from A to B or B to A.
void	aa_shift_tensor2 (const double A, const double axis[3], const double angle, 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 axis-angle representation, shifts second-order tensors from A to B or B to A.
void	aa_shift_tensor3 (const double A, const double axis[3], const double angle, 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 axis-angle representation, shifts third-order tensors from A to B or B to A.
void	aa_to_quat (const double axis[3], const double angle, double q[4])
	Converts an axis-angle representation to a unit quaternion.
void	aa_to_dcm (const double axis[3], const double angle, double *dcm)
	Converts an axis-angle representation to a direction cosine matrix.
void	aa_to_euler (const double axis[3], const double angle, enum EulangSeq seq, const bool world, double euler[3])
	Converts an axis-angle representation to an Euler angle sequence.

Detailed Description

Function Documentation

◆ aa_fix()

void aa_fix	(	double	axis[3],
		double *	angle,
		const bool	normalize )

Modifies axis and angle to ensure a right handed rotation with angle $\in [0, \pi)$ $\in [0, \pi)$ .

Parameters

[in,out]	axis	Axis of rotation. If this is not a unit vector, set normalize to true.
[in,out]	angle	Angle in radian.
[in]	normalize	Whether to normalize axis to a unit vector.

◆ aa_from_rotmat()

void aa_from_rotmat	(	const double *	rotmat,
		double	axis[3],
		double *	angle )

Extracts axis and angle from a rotation matrix.

Parameters

[in]	rotmat	3 x 3 rotation matrix.
[out]	axis	Unit vector along the axis.
[out]	angle	Angle in radian.

◆ aa_rand()

void aa_rand	(	double	axis[3],
		double *	angle )

Generates a random orientation in axis-angle representation.

The axis is a random vector drawn from a uniform distribution on the surface of a unit sphere. The current implementation in based on the algorithm from Allen & Tildesley p. 349.

Parameters

[out]	axis	Axis of rotation.
[out]	angle	Angle in radian.

◆ aa_rotate_vectors()

void aa_rotate_vectors	(	const int	n,
		const double *	v,
		const double	axis[3],
		const double	angle,
		double *	vrot )

Rotates vectors about axis by angle.

Parameters

[in]	n	Number of rows of v.
[in]	v	n x 3 array whose rows are the vectors to rotate.
[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[out]	vrot	n x 3 array whose rows are the rotated vectors.

◆ aa_rotmat()

void aa_rotmat	(	const double	axis[3],
		const double	angle,
		double *	rotmat )

Calculates the rotation matrix corresponding to an axis-angle representation.

Parameters

[in]	axis	Axis of rotation.
[in]	angle	Angle in radian. 0 <= angle < pi.
[out]	rotmat	3 x 3 rotation matrix.

◆ aa_shift_tensor2()

void aa_shift_tensor2	(	const double *	A,
		const double	axis[3],
		const double	angle,
		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 axis-angle representation, shifts second-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 second-order tensor.
[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 shifted second-order tensor.

◆ aa_shift_tensor3()

void aa_shift_tensor3	(	const double *	A,
		const double	axis[3],
		const double	angle,
		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 axis-angle representation, shifts third-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 x 3 third-order tensor.
[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 x 3 shifted second-order tensor.

◆ aa_shift_vectors()

void aa_shift_vectors	(	const int	n,
		const double *	v,
		const double	axis[3],
		const double	angle,
		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 an axis-angle representation, 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]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[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.

◆ aa_shiftmat()

void aa_shiftmat	(	const double	axis[3],
		const double	angle,
		const bool	forward,
		double *	shiftmat )

Calculates the shifter matrix corresponding to an axis-angle representation.

Parameters

[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	shiftmat	3 x 3 shifter matrix.

◆ aa_to_dcm()

void aa_to_dcm	(	const double	axis[3],
		const double	angle,
		double *	dcm )

Converts an axis-angle representation to a direction cosine matrix.

Parameters

[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[out]	dcm	3 x 3 direction cosine matrix.

◆ aa_to_euler()

void aa_to_euler	(	const double	axis[3],
		const double	angle,
		enum EulangSeq	seq,
		const bool	world,
		double	euler[3] )

Converts an axis-angle representation to an Euler angle sequence.

Parameters

[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[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.

◆ aa_to_quat()

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

Converts an axis-angle representation to a unit quaternion.

Parameters

[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian. 0 <= angle < pi.
[out]	q	A unit quaternion.

Functions

Detailed Description

Function Documentation

◆ aa_fix()

◆ aa_from_rotmat()

◆ aa_rand()

◆ aa_rotate_vectors()

◆ aa_rotmat()

◆ aa_shift_tensor2()

◆ aa_shift_tensor3()

◆ aa_shift_vectors()

◆ aa_shiftmat()

◆ aa_to_dcm()

◆ aa_to_euler()

◆ aa_to_quat()