Euler angles

Functions
void	euler_rotmat (const double euler[3], enum EulangSeq seq, const bool world, double *rotmat)
	Calculates the rotation matrix for a set of Euler angles.
void	euler_shiftmat (const double euler[3], enum EulangSeq seq, const bool world, const bool forward, double *shiftmat)
	Calculates the shifter matrix for a set of Euler angles.
void	euler_rotate_vectors (const int n, const double *v, const double euler[3], enum EulangSeq seq, const bool world, double *vrot)
	Rotates vectors with a set of Euler angles.
void	euler_shift_vectors (const int n, const double *v, const double euler[3], enum EulangSeq seq, const bool world, 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 three Euler angles, shifts vectors from A to B or B to A.
void	euler_shift_tensor2 (const double *A, const double euler[3], enum EulangSeq seq, const bool world, 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 three Euler angles, shifts second-order tensors from A to B or B to A.
void	euler_shift_tensor3 (const double *A, const double euler[3], enum EulangSeq seq, const bool world, 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 three Euler angles, shifts third-order tensors from A to B or B to A.
void	euler_to_quat (const double euler[3], enum EulangSeq seq, const bool world, double q[4])
	Convert Euler angles to a unit quaternion.
void	euler_to_aa (const double euler[3], enum EulangSeq seq, const bool world, double axis[3], double *angle)
	Convert Euler angles to an axis-angle representation.
void	euler_to_dcm (const double euler[3], enum EulangSeq seq, const bool world, double *dcm)
	Convert Euler angles to a direction cosine matrix.
void	euler_to_euler (const double euler[3], enum EulangSeq seq, const bool world, enum EulangSeq to_seq, const bool to_world, double to_euler[3])
	Converts Convert one set of Euler angles to another.

Detailed Description

Function Documentation

euler_rotate_vectors()

void euler_rotate_vectors	(	const int	n,
		const double *	v,
		const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		double *	vrot )

Rotates vectors with a set of Euler angles.

Parameters

[in]	n	Number of rows of v.
[in]	v	n x 3 array whose rows are the vectors to rotate.
[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[out]	vrot	n x 3 array whose rows are the rotated vectors.

euler_rotmat()

void euler_rotmat	(	const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		double *	rotmat )

Calculates the rotation matrix for a set of Euler angles.

Parameters

[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[out]	rotmat	3 x 3 rotation matrix.

euler_shift_tensor2()

void euler_shift_tensor2	(	const double *	A,
		const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		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 three Euler angles, shifts second-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 second-order tensor.
[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 shifted second-order tensor.

euler_shift_tensor3()

void euler_shift_tensor3	(	const double *	A,
		const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		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 three Euler angles, shifts third-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 x 3 third-order tensor.
[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[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.

euler_shift_vectors()

void euler_shift_vectors	(	const int	n,
		const double *	v,
		const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		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 three Euler angles, 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]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[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.

euler_shiftmat()

void euler_shiftmat	(	const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		const bool	forward,
		double *	shiftmat )

Calculates the shifter matrix for a set of Euler angles.

Parameters

[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	shiftmat	3 x 3 shifter matrix.

euler_to_aa()

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

Convert Euler angles to an axis-angle representation.

Parameters

[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[out]	axis	Unit vector along the axis of rotation.
[out]	angle	Angle of rotation in radian.

euler_to_dcm()

void euler_to_dcm	(	const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		double *	dcm )

Convert Euler angles to a direction cosine matrix.

Parameters

[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[out]	dcm	3 x 3 direction cosine matrix.

euler_to_euler()

void euler_to_euler	(	const double	euler[3],
		enum EulangSeq	seq,
		const bool	world,
		enum EulangSeq	to_seq,
		const bool	to_world,
		double	to_euler[3] )

Converts Convert one set of Euler angles to another.

Parameters

[in]	euler	Euler angles.
[in]	seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Sequence for Euler angles.
[in]	world	Whether the Euler angles are with respect to the world frame or not.
[in]	to_seq	ES_XYZ | ES_XZY | ES_YXZ | ES_YZX | ES_ZXY | ES_ZYX. Convert Euler angles with sequence seq to to_euler with sequence to_seq.
[in]	to_world	Whether the converted euler angles are with respect to the world frame or not.
[out]	to_euler	Converted Euler angles.

euler_to_quat()

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

Convert Euler angles to a unit quaternion.

Parameters

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