Rotation matrices and conversions

Conversions and operations for rotations in SO(3) More...

Functions
Mat3	fsb::skew_symmetric (const Vec3 &vec)
	Skew-symmetric matrix from vector.
Vec3	fsb::quat_to_ezyx (const Quaternion &quat)
	Convert unit quaternion to intrinsic ZYX Euler-angles.
Quaternion	fsb::ezyx_to_quat (const Vec3 &ezyx)
	Convert intrinsic ZYX Euler-angles to unit quaternion.
Mat3	fsb::quat_to_rot (const Quaternion &quat)
	Convert unit quaternion to rotation matrix.
Quaternion	fsb::rot_to_quat (const Mat3 &rot)
	Convert rotation matrix to unit quaternion.
Vec3	fsb::quat_to_rotvec (const Quaternion &quat)
	Convert unit quaternion to rotation vector.
Quaternion	fsb::rotvec_to_quat (const Vec3 &rotvec)
	Convert rotation vector to unit quaternion.
Mat3	fsb::rot_identity ()
	Identity rotation matrix.
Mat3	fsb::rot_rx (real_t rx)
	Rotation matrix about x-axis.
Mat3	fsb::rot_ry (real_t ry)
	Rotation matrix about y-axis.
Mat3	fsb::rot_rz (real_t rz)
	Rotation matrix about z-axis.
Vec3	fsb::rotate_mat3 (const Mat3 &rot, const Vec3 &vec)
	Matrix multiplication with rotation matrix.
Vec3	fsb::rotate_mat3_transpose (const Mat3 &rot, const Vec3 &vec)
	Transposed matrix multiplication with rotation matrix.

Detailed Description

Conversions and operations for rotations in SO(3)

Function Documentation

ezyx_to_quat()

Quaternion fsb::ezyx_to_quat

(

const Vec3 &

ezyx

)

Convert intrinsic ZYX Euler-angles to unit quaternion.

Parameters

ezyx	Euler angles in radians

Returns

Quaternion

quat_to_ezyx()

Vec3 fsb::quat_to_ezyx

(

const Quaternion &

quat

)

Convert unit quaternion to intrinsic ZYX Euler-angles.

Parameters

quat	Quaternion

Returns

Euler angles in radians

quat_to_rot()

Mat3 fsb::quat_to_rot

(

const Quaternion &

quat

)

Convert unit quaternion to rotation matrix.

Parameters

quat	Quaternion

Returns

Rotation matrix

quat_to_rotvec()

Vec3 fsb::quat_to_rotvec

(

const Quaternion &

quat

)

Convert unit quaternion to rotation vector.

Parameters

quat	Quaternion

Returns

Rotation vector

rot_identity()

Mat3 fsb::rot_identity

(

)

Identity rotation matrix.

\( \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \)

Returns

Identity rotation matrix

rot_rx()

Mat3 fsb::rot_rx

(

real_t

rx

)

Rotation matrix about x-axis.

Parameters

rx	Rotation angle in radians

Returns

Rotation matrix

rot_ry()

Mat3 fsb::rot_ry

(

real_t

ry

)

Rotation matrix about y-axis.

Parameters

ry	Rotation angle in radians

Returns

Rotation matrix

rot_rz()

Mat3 fsb::rot_rz

(

real_t

rz

)

Rotation matrix about z-axis.

Parameters

rz	Rotation angle in radians

Returns

Rotation matrix

rot_to_quat()

Quaternion fsb::rot_to_quat

(

const Mat3 &

rot

)

Convert rotation matrix to unit quaternion.

Parameters

rot	Rotation matrix

Returns

Quaternion

rotate_mat3()

Vec3 fsb::rotate_mat3	(	const Mat3 &	rot,
		const Vec3 &	vec
	)

Matrix multiplication with rotation matrix.

Parameters

rot	Rotation matrix
vec	Vector

Returns

Rotated vector

rotate_mat3_transpose()

Vec3 fsb::rotate_mat3_transpose	(	const Mat3 &	rot,
		const Vec3 &	vec
	)

Transposed matrix multiplication with rotation matrix.

Parameters

rot	Rotation matrix
vec	Vector

Returns

Rotated vector with transpose of rotation matrix

rotvec_to_quat()

Quaternion fsb::rotvec_to_quat

(

const Vec3 &

rotvec

)

Convert rotation vector to unit quaternion.

Parameters

rotvec

Rotation vector

Returns

Quaternion

skew_symmetric()

Mat3 fsb::skew_symmetric

(

const Vec3 &

vec

)

Skew-symmetric matrix from vector.

\( [v]^{\times} = \begin{bmatrix} 0 & -v_z & v_y \\ v_z & 0 & -v_x \\ -v_y & v_x & 0 \end{bmatrix} \)

Parameters

vec

Vector

Returns

Skew-symmetric matrix