Unit Quaternions

Rotations using quaternions. More...

Classes
struct	fsb::Quaternion
	Unit quaternion. More...

Functions
Quaternion	fsb::quat_multiply (const Quaternion &q_a, const Quaternion &q_b)
	Multiply two quaternions.
Vec3	fsb::quat_rotate_vector (const Quaternion &q_in, const Vec3 &p_in)
	Rotate vector by quaternion.
Quaternion	fsb::quat_conjugate (const Quaternion &q_in)
	Conjugate of quaternion.
real_t	fsb::quat_norm (const Quaternion &q_in)
	2-norm of quaternion
void	fsb::quat_normalize (Quaternion &q_inout)
	Normalize quaternion.
Vec3	fsb::quat_log (const Quaternion &q_in)
	Logarithm of unit quaternion.
Quaternion	fsb::quat_exp (const Vec3 &v_in)
	Exponential of quaternion vector.
Quaternion	fsb::quat_boxplus (const Quaternion &quat, const Vec3 &phi_delta)
	Add body-fixed rotation vector to quaternion.
Vec3	fsb::quat_boxminus (const Quaternion &q_a, const Quaternion &q_b)
	Get body-fixed rotation vector from quaternion difference.
Quaternion	fsb::quat_circplus (const Quaternion &quat, const Vec3 &phi_delta)
	Add space frame rotation vector to quaternion.
Vec3	fsb::quat_circminus (const Quaternion &q_a, const Quaternion &q_b)
	Get space frame rotation vector from quaternion difference.
Quaternion	fsb::quat_identity ()
	Identity quaternion.
Quaternion	fsb::quat_rx (real_t rx)
	Rotation about x-axis.
Quaternion	fsb::quat_ry (real_t ry)
	Rotation about y-axis.
Quaternion	fsb::quat_rz (real_t rz)
	Rotation about z-axis.

Detailed Description

Rotations using quaternions.

Function Documentation

quat_boxminus()

Vec3 fsb::quat_boxminus	(	const Quaternion &	q_a,
		const Quaternion &	q_b
	)

Get body-fixed rotation vector from quaternion difference.

\( q_a \boxminus q_b = 2 \log(q_b^{-1} q_a) \)

Parameters

q_a	Orientation a
q_b	Orietnation b

Returns

Body-fixed rotation vector from b to a in radians

quat_boxplus()

Quaternion fsb::quat_boxplus	(	const Quaternion &	quat,
		const Vec3 &	phi_delta
	)

Add body-fixed rotation vector to quaternion.

\( q \boxplus \phi = q \exp\left(\tfrac{1}{2}\phi \right) \)

Parameters

quat	Quaternion to rotate
phi_delta	Rotation vector in radians

Returns

Rotated quaternion

quat_circminus()

Vec3 fsb::quat_circminus	(	const Quaternion &	q_a,
		const Quaternion &	q_b
	)

Get space frame rotation vector from quaternion difference.

\( q_a \ominus q_b = 2 \log(q_a q_b^{-1}) \)

Parameters

q_a	Orientation a
q_b	Orietnation b

Returns

Space frame rotation vector from b to a in radians

quat_circplus()

Quaternion fsb::quat_circplus	(	const Quaternion &	quat,
		const Vec3 &	phi_delta
	)

Add space frame rotation vector to quaternion.

\( q \oplus \phi = \exp\left(\tfrac{1}{2}\phi \right) q \)

Parameters

quat	Initial orientation
phi_delta	Axis-angle rotation vector

Returns

Final orientation

quat_conjugate()

Quaternion fsb::quat_conjugate

(

const Quaternion &

q_in

)

Conjugate of quaternion.

Returns conjugate: \( q^* = [q_w, -q_x, -q_y, -q_z] \)

Parameters

q_in	Quaternion

Returns

Conjugate of quaternion

quat_exp()

Quaternion fsb::quat_exp

(

const Vec3 &

v_in

)

Exponential of quaternion vector.

Parameters

v_in	Quaternion vector with assumed scalar component of zero

Returns

Unit quaternion

quat_identity()

Quaternion fsb::quat_identity

(

)

Identity quaternion.

\( q = [1, 0, 0, 0] \)

Returns

Identity quaternion

quat_log()

Vec3 fsb::quat_log

(

const Quaternion &

q_in

)

Logarithm of unit quaternion.

Parameters

q_in	Unit quaternion

Returns

Logarithm of unit quaternion

quat_multiply()

Quaternion fsb::quat_multiply	(	const Quaternion &	q_a,
		const Quaternion &	q_b
	)

Multiply two quaternions.

Returns quaternion multiplication:

\[ q = q_a q_b \]

Parameters

q_a	Quaterion a
q_b	Quaternion b

Returns

Quaternion product of a and b

quat_norm()

real_t fsb::quat_norm

(

const Quaternion &

q_in

)

2-norm of quaternion

\( \| q \| = \sqrt{q_w^2 + q_x^2 + q_y^2 + q_z^2} \)

Parameters

q_in	Quaternion

Returns

Norm of quaternion

quat_normalize()

void fsb::quat_normalize

(

Quaternion &

q_inout

)

Normalize quaternion.

Parameters

q_inout

Quaternion to normalize on input, normalized on output

quat_rotate_vector()

Vec3 fsb::quat_rotate_vector	(	const Quaternion &	q_in,
		const Vec3 &	p_in
	)

Rotate vector by quaternion.

Parameters

q_in	Quaternion
p_in	Point to rotate

Returns

Rotated point

quat_rx()

Quaternion fsb::quat_rx

(

real_t

rx

)

Rotation about x-axis.

Parameters

rx	Rotation angle in radians

Returns

Rotation unit quaternion

quat_ry()

Quaternion fsb::quat_ry

(

real_t

ry

)

Rotation about y-axis.

Parameters

ry	Rotation angle in radians

Returns

Rotation unit quaternion

quat_rz()

Quaternion fsb::quat_rz

(

real_t

rz

)

Rotation about z-axis.

Parameters

rz	Rotation angle in radians

Returns

Rotation unit quaternion