Direction cosine matrix

Functions
bool	mat_is_dcm (const double *mat)
	Checks is a 3 x 3 array is a direction cosine matrix.
void	dcm_from_axes (const double *A, const double *B, double *dcm)
	Returns the direction cosine matrix of axes(i.e. frame) B with respect to axes(i.e. frame) A.
void	dcm_rotmat (const double *dcm, double *rotmat)
	Returns the rotation matrix corresponding to a direction cosine matrix.
void	dcm_shiftmat (const double *dcm, const bool forward, double *shiftmat)
	Returns the shifter matrix corresponding to a direction cosine matrix.
void	dcm_rotate_vectors (const int n, const double *v, const double *dcm, double *vrot)
	Rotates vectors by a direction cosine matrix.
void	dcm_shift_vectors (const int n, const double *v, const double *dcm, 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 direction cosine matrix, shifts vectors from A to B or B to A.
void	dcm_shift_tensor2 (const double *A, const double *dcm, 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 direction cosine matrix, shifts second-order tensors from A to B or B to A.
void	dcm_shift_tensor3 (const double *A, const double *dcm, 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 direction cosine matrix, shifts third-order tensors from A to B or B to A.
void	dcm_to_quat (const double *dcm, double q[4])
	Converts a direction cosine matrix to a unit quaternion.
void	dcm_to_aa (const double *dcm, double axis[3], double *angle)
	Converts a direction cosine matrix to an axis-angle representation.
void	dcm_to_euler (const double *dcm, enum EulangSeq seq, const bool world, double euler[3])
	Converts a direction cosine matrix to Euler angles.

Detailed Description

Function Documentation

dcm_from_axes()

void dcm_from_axes	(	const double *	A,
		const double *	B,
		double *	dcm )

Returns the direction cosine matrix of axes(i.e. frame) B with respect to axes(i.e. frame) A.

Parameters

[in]	A	3 x 3 array. The rows of A represent the orthonormal basis vectors of frame A.
[in]	B	3 x 3 array. The rows of B represent the orthonormal basis vectors of frame B.
[out]	dcm	3 x 3 direction cosine matrix.

dcm_rotate_vectors()

void dcm_rotate_vectors	(	const int	n,
		const double *	v,
		const double *	dcm,
		double *	vrot )

Rotates vectors by a direction cosine matrix.

Parameters

[in]	n	Number of rows of v.
[in]	v	n x 3 array whose rows are the vectors to rotate.
[in]	dcm	3 x 3 direction cosine matrix.
[out]	vrot	n x 3 array whose rows are the rotated vectors.

dcm_rotmat()

void dcm_rotmat	(	const double *	dcm,
		double *	rotmat )

Returns the rotation matrix corresponding to a direction cosine matrix.

Parameters

[in]	dcm	3 x 3 direction cosine matrix.
[out]	rotmat	3 x 3 rotation matrix.

dcm_shift_tensor2()

void dcm_shift_tensor2	(	const double *	A,
		const double *	dcm,
		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 direction cosine matrix, shifts second-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 second-order tensor.
[in]	dcm	3 x 3 direction cosine matrix.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	Ashift	3 x 3 shifted second-order tensor.

dcm_shift_tensor3()

void dcm_shift_tensor3	(	const double *	A,
		const double *	dcm,
		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 direction cosine matrix, shifts third-order tensors from A to B or B to A.

Parameters

[in]	A	3 x 3 x 3 third-order tensor.
[in]	dcm	3 x 3 direction cosine matrix.
[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.

dcm_shift_vectors()

void dcm_shift_vectors	(	const int	n,
		const double *	v,
		const double *	dcm,
		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 direction cosine matrix, 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]	dcm	3 x 3 direction cosine matrix.
[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.

dcm_shiftmat()

void dcm_shiftmat	(	const double *	dcm,
		const bool	forward,
		double *	shiftmat )

Returns the shifter matrix corresponding to a direction cosine matrix.

Parameters

[in]	dcm	3 x 3 direction cosine matrix.
[in]	forward	Whether to shift forward, i.e., along the orientation or shift reverse.
[out]	shiftmat	3 x 3 shifter matrix.

dcm_to_aa()

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

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

Parameters

[in]	dcm	3 x 3 direction cosine matrix.
[in]	axis	Unit vector along the axis.
[in]	angle	Angle in radian.

dcm_to_euler()

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

Converts a direction cosine matrix to Euler angles.

Parameters

[in]	dcm	3 x 3 direction cosine matrix.
[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.

dcm_to_quat()

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

Converts a direction cosine matrix to a unit quaternion.

Parameters

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

mat_is_dcm()

bool mat_is_dcm

(

const double *

mat

)

Checks is a 3 x 3 array is a direction cosine matrix.

Parameters

[in]

mat

3 x 3 array.

Returns

true if a (3,3) matrix is a direction cosine matrix.