Quaternion class for rotation representation. More...

#include <Quaternion.hpp>

Public Member Functions
	Quaternion ()
	Default constructor: Identity quaternion (1, 0, 0, 0).
	Quaternion (Scalar w, Scalar x, Scalar y, Scalar z)
	Component constructor.
	Quaternion (const Vec4< Scalar > &v)
	Construct from Vec4 [w, x, y, z].
Quaternion	operator* (const Quaternion &other) const
	Hamilton product.
Quaternion	operator* (const Scalar &s) const
	Scalar multiplication.
Quaternion	operator+ (const Quaternion &other) const
	Quaternion addition.
Quaternion	conjugate () const
	Conjugate (w, -x, -y, -z).
Quaternion	inverse () const
	Inverse (conjugate / norm_sq).
Scalar	squared_norm () const
	Squared norm (w^2 + x^2 + y^2 + z^2).
Scalar	norm () const
	Quaternion norm.
Quaternion	normalized () const
	Return unit quaternion.
Vec3< Scalar >	rotate (const Vec3< Scalar > &v) const
	Rotate a 3D vector: v_rot = q * v * q_conj.
Mat3< Scalar >	to_rotation_matrix () const
	Convert to 3x3 rotation matrix.
Vec4< Scalar >	coeffs () const
	Export as vector [w, x, y, z].
Vec3< Scalar >	to_euler () const
	Extract Euler angles (Roll-Pitch-Yaw / XYZ).

Static Public Member Functions
static Quaternion	from_euler (Scalar roll, Scalar pitch, Scalar yaw)
	Create from Euler Angles (Yaw-Pitch-Roll / Z-Y-X sequence).
static Quaternion	from_axis_angle (const Vec3< Scalar > &axis, Scalar angle)
	Create from axis-angle representation.
static Quaternion	from_rotation_vector (const Vec3< Scalar > &rot_vec)
	Create from rotation vector (axis * angle).
static Quaternion	from_rotation_matrix (const Mat3< Scalar > &mat)
	Create from 3x3 rotation matrix.

Public Attributes
Scalar	w
Scalar	x
Scalar	y
Scalar	z

Detailed Description

template<typename Scalar>
class janus::Quaternion< Scalar >

Quaternion class for rotation representation.

Stores quaternion in (w, x, y, z) convention where w is the scalar part. All operations support both numeric and symbolic types.

Template Parameters

Scalar Scalar type (NumericScalar or SymbolicScalar)

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

template<typename Scalar>

janus::Quaternion< Scalar >::Quaternion ( )

inline

Default constructor: Identity quaternion (1, 0, 0, 0).

◆ Quaternion() [2/3]

template<typename Scalar>

janus::Quaternion< Scalar >::Quaternion	(	Scalar	w,
		Scalar	x,
		Scalar	y,
		Scalar	z )

inline

Component constructor.

◆ Quaternion() [3/3]

template<typename Scalar>

janus::Quaternion< Scalar >::Quaternion ( const Vec4< Scalar > & v )

inlineexplicit

Construct from Vec4 [w, x, y, z].

Member Function Documentation

◆ coeffs()

template<typename Scalar>

Vec4< Scalar > janus::Quaternion< Scalar >::coeffs ( ) const

inline

Export as vector [w, x, y, z].

Returns: 4-element coefficient vector

◆ conjugate()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::conjugate ( ) const

inline

Conjugate (w, -x, -y, -z).

Returns: Conjugate quaternion

◆ from_axis_angle()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::from_axis_angle	(	const Vec3< Scalar > &	axis,
		Scalar	angle )

inlinestatic

Create from axis-angle representation.

Parameters

axis	Rotation axis (will be normalized)
angle	Rotation angle (radians)

Returns: Quaternion

◆ from_euler()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::from_euler	(	Scalar	roll,
		Scalar	pitch,
		Scalar	yaw )

inlinestatic

Create from Euler Angles (Yaw-Pitch-Roll / Z-Y-X sequence).

Parameters

roll	Roll angle (radians)
pitch	Pitch angle (radians)
yaw	Yaw angle (radians)

Returns: Quaternion

See also: rotation_matrix_from_euler_angles

◆ from_rotation_matrix()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::from_rotation_matrix ( const Mat3< Scalar > & mat )

inlinestatic

Create from 3x3 rotation matrix.

Parameters

mat	Rotation matrix

Returns: Quaternion

◆ from_rotation_vector()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::from_rotation_vector ( const Vec3< Scalar > & rot_vec )

inlinestatic

Create from rotation vector (axis * angle).

Parameters

rot_vec Rotation vector

Returns: Quaternion

◆ inverse()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::inverse ( ) const

inline

Inverse (conjugate / norm_sq).

Returns: Inverse quaternion

◆ norm()

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::norm ( ) const

inline

Quaternion norm.

Returns: Euclidean norm

◆ normalized()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::normalized ( ) const

inline

Return unit quaternion.

Returns: Normalized copy

◆ operator*() [1/2]

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::operator* ( const Quaternion< Scalar > & other ) const

inline

Hamilton product.

Parameters

other Right-hand quaternion

Returns: Product quaternion

◆ operator*() [2/2]

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::operator* ( const Scalar & s ) const

inline

Scalar multiplication.

Parameters

s	Scalar factor

Returns: Scaled quaternion

◆ operator+()

template<typename Scalar>

Quaternion janus::Quaternion< Scalar >::operator+ ( const Quaternion< Scalar > & other ) const

inline

Quaternion addition.

Parameters

other Right-hand quaternion

Returns: Sum quaternion

◆ rotate()

template<typename Scalar>

Vec3< Scalar > janus::Quaternion< Scalar >::rotate ( const Vec3< Scalar > & v ) const

inline

Rotate a 3D vector: v_rot = q * v * q_conj.

Parameters

v	Input vector

Returns: Rotated vector

◆ squared_norm()

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::squared_norm ( ) const

inline

Squared norm (w^2 + x^2 + y^2 + z^2).

Returns: Squared norm

◆ to_euler()

template<typename Scalar>

Vec3< Scalar > janus::Quaternion< Scalar >::to_euler ( ) const

inline

Extract Euler angles (Roll-Pitch-Yaw / XYZ).

Returns: Vec3 of (roll, pitch, yaw)

◆ to_rotation_matrix()

template<typename Scalar>

Mat3< Scalar > janus::Quaternion< Scalar >::to_rotation_matrix ( ) const

inline

Convert to 3x3 rotation matrix.

Returns: Rotation matrix

Member Data Documentation

◆ w

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::w

◆ x

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::x

◆ y

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::y

◆ z

template<typename Scalar>

Scalar janus::Quaternion< Scalar >::z

The documentation for this class was generated from the following file:

include/janus/math/Quaternion.hpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

◆ Quaternion() [2/3]

◆ Quaternion() [3/3]

Member Function Documentation

◆ coeffs()

◆ conjugate()

◆ from_axis_angle()

◆ from_euler()

◆ from_rotation_matrix()

◆ from_rotation_vector()

◆ inverse()

◆ norm()

◆ normalized()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator+()

◆ rotate()

◆ squared_norm()

◆ to_euler()

◆ to_rotation_matrix()

Member Data Documentation

◆ w

◆ x

◆ y

◆ z