Quaternion Class Reference

Detailed Description

A Quaternion representation.

#include <include/maliput/math/quaternion.h>

Public Member Functions
	MALIPUT_DEFAULT_COPY_AND_MOVE_AND_ASSIGN (Quaternion)
	Quaternion ()
	Constructs a Quaternion initialized to \( 1+0i+0j+0k \). More...
	Quaternion (double w, double x, double y, double z)
	Constructs a Quaternion and initializes it to \( w+xi+yj+zk \). More...
	Quaternion (double angle, const Vector3 &axis)
	Constructs a Quaternion expressed by angle rotation around axis vector. More...
	Quaternion (const Vector4 &coeffs)
	Constructs a Quaternion from a 4D vector matching all its components. More...
	Quaternion (const Matrix3 &rotation_matrix)
	Constructs a Quaternion from a 3D rotation matrix. More...
double	w () const
double	x () const
double	y () const
double	z () const
double &	w ()
double &	x ()
double &	y ()
double &	z ()
Vector3	vec () const
	}@ More...
Vector4	coeffs () const
Quaternion &	set_identity ()
	Sets the identity quaternion values as if it was initialized with \( [1, 0, 0, 0] \). More...
double	squared_norm () const
double	norm () const
void	normalize ()
	Normalizes (norm() == 1) this quaternion coefficients. More...
Quaternion	normalized () const
double	dot (const Quaternion &other) const
	Executes the dot product between this quaternion coefficients and other. More...
double	AngularDistance (const Quaternion &other) const
	Computes the angular distance between the rotation of this quaternion and other. More...
Matrix3	ToRotationMatrix () const
void	SetFromTwoVectors (const Vector3 &a, const Vector3 &b)
	Sets this quaternion with the coefficients that makes a transform into b. More...
Quaternion	operator* (const Quaternion &q) const
	Product operator overload. More...
Quaternion &	operator*= (const Quaternion &q)
	Product and assignment operator overload. More...
Vector3	operator* (const Vector3 &v) const
	Forwards the call to TransformVector(v). More...
bool	operator== (const Quaternion &other) const
	Operator equal to overload. More...
bool	operator!= (const Quaternion &other) const
	Operator not equal to overload. More...
Quaternion	Inverse () const
Quaternion	conjugate () const
Quaternion	Slerp (double t, const Quaternion &other) const
bool	IsApprox (const Quaternion &other, double precision) const
	Evaluates if this quaternion is almost equal to other up to precision tolerance. More...
Vector3	TransformVector (const Vector3 &v) const
	Applies this quaternion transformation to v 3D vector. More...

Static Public Member Functions
static Quaternion	Identity ()
static Quaternion	FromTwoVectors (const Vector3 &a, const Vector3 &b)

Static Public Attributes
static constexpr double	kTolerance {1e-15}

Constructor & Destructor Documentation

Quaternion() [1/5]

Quaternion

(

)

Constructs a Quaternion initialized to \( 1+0i+0j+0k \).

Quaternion() [2/5]

Quaternion	(	double	w,
		double	x,
		double	y,
		double	z
	)

Constructs a Quaternion and initializes it to \( w+xi+yj+zk \).

Parameters

w	The real \( w \) coefficient.
x	The internal \( x \) coefficient.
y	The internal \( y \) coefficient.
z	The internal \( z \)s coefficient.

Quaternion() [3/5]

Quaternion	(	double	angle,
		const Vector3 &	axis
	)

Constructs a Quaternion expressed by angle rotation around axis vector.

Parameters

angle	A scalar representing an angle in radians.
axis	A 3D vector representing the rotation angle.

Quaternion() [4/5]

Quaternion ( const Vector4 &  coeffs )

explicit

Constructs a Quaternion from a 4D vector matching all its components.

Parameters

coeffs

A 4D vector whose first element is \( w \), second element is \( x \), third element is \( y \) and fourth element is \( z \).

Quaternion() [5/5]

Quaternion ( const Matrix3 &  rotation_matrix )

explicit

Constructs a Quaternion from a 3D rotation matrix.

Parameters

rotation_matrix

A 3x3 matrix whose elements represent a rotation matrix.

See also

https://bitbucket.org/ignitionrobotics/ign-math/src/ac54456ab8c431a59fbecfa1cf4b7c2b6f96cb33/include/ignition/math/Quaternion.hh#lines-461:503

Member Function Documentation

AngularDistance()

double AngularDistance

(

const Quaternion &

other

)

const

Computes the angular distance between the rotation of this quaternion and other.

Parameters

other

A Quaternion.

Returns

The angle in radians between this rotation and other's rotation.

coeffs()

Vector4 coeffs

(

)

const

Returns

This quaternion coefficients: \( [w, x, y, z] \).

conjugate()

Quaternion conjugate

(

)

const

Returns

A Quaternion that results from conjugating this.

dot()

double dot

(

const Quaternion &

other

)

const

Executes the dot product between this quaternion coefficients and other.

Parameters

other

A Quaternion.

Returns

The dot product between this quaternion and other.

FromTwoVectors()

Quaternion FromTwoVectors ( const Vector3 &  a, const Vector3 &  b  )

static

Returns

A quaternion initialized from two vectors.

See also

https://bitbucket.org/ignitionrobotics/ign-math/src/ac54456ab8c431a59fbecfa1cf4b7c2b6f96cb33/include/ignition/math/Quaternion.hh#lines-505:582

Identity()

Quaternion Identity ( )

static

Returns

A quaternion initialized with \( [1, 0, 0, 0] \).

Inverse()

Quaternion Inverse

(

)

const

Returns

A Quaternion that results from computing the inverse rotation.

IsApprox()

bool IsApprox	(	const Quaternion &	other,
		double	precision
	)		const

Evaluates if this quaternion is almost equal to other up to precision tolerance.

this quaternion is approximately equal to other when the squared norm of the vector difference from both quaternion's coefficients is smaller than the minimum squared norm between this and other scaled with the squared precision.

Parameters

other	A Quaternion to compare with.
precision	The tolerance.

Returns

true When this quaternion is almost equal to other up to precision tolerance.

MALIPUT_DEFAULT_COPY_AND_MOVE_AND_ASSIGN()

MALIPUT_DEFAULT_COPY_AND_MOVE_AND_ASSIGN

(

Quaternion

)

norm()

double norm

(

)

const

Returns

The norm of this quaternion.

normalize()

void normalize

(

)

Normalizes (norm() == 1) this quaternion coefficients.

When the norm() < kTolerance, the result is equivalent to call set_identity().

normalized()

Quaternion normalized

(

)

const

Returns

*this quaternion with normalized coefficients.

operator!=()

bool operator!=

(

const Quaternion &

other

)

const

Operator not equal to overload.

Performs a coefficient wise comparison.

Parameters

other

A quaternion to compare to this quaternion.

Returns

true When this' and other's coefficients are not equal.

operator*() [1/2]

Quaternion operator*

(

const Quaternion &

q

)

const

Product operator overload.

Parameters

q	A Quaternion.

Returns

A quaternion that results from \( `this` * `q` \).

See also

https://bitbucket.org/ignitionrobotics/ign-math/src/ac54456ab8c431a59fbecfa1cf4b7c2b6f96cb33/include/ignition/math/Quaternion.hh#lines-638:648

operator*() [2/2]

Vector3 operator*

(

const Vector3 &

v

)

const

Forwards the call to TransformVector(v).

operator*=()

Quaternion & operator*=

(

const Quaternion &

q

)

Product and assignment operator overload.

Parameters

q	A Quaternion.

Returns

A mutable reference to *this initialized with \( `this` * `q` \).

See also

https://bitbucket.org/ignitionrobotics/ign-math/src/ac54456ab8c431a59fbecfa1cf4b7c2b6f96cb33/include/ignition/math/Quaternion.hh#lines-638:648

operator==()

bool operator==

(

const Quaternion &

other

)

const

Operator equal to overload.

Performs a coefficient wise comparison.

Parameters

other

A quaternion to compare to this quaternion.

Returns

true When this' and other's coefficients are equal.

set_identity()

Quaternion& set_identity

(

)

Sets the identity quaternion values as if it was initialized with \( [1, 0, 0, 0] \).

Returns

*this.

SetFromTwoVectors()

void SetFromTwoVectors	(	const Vector3 &	a,
		const Vector3 &	b
	)

Sets this quaternion with the coefficients that makes a transform into b.

Parameters

a	A 3D vector.
b	A 3D vector.

See also

https://bitbucket.org/ignitionrobotics/ign-math/src/ac54456ab8c431a59fbecfa1cf4b7c2b6f96cb33/include/ignition/math/Quaternion.hh#lines-505:582

Slerp()

Quaternion Slerp	(	double	t,
		const Quaternion &	other
	)		const

Returns

The spherical linear interpolation between the two quaternions *this and other at the parameter t.

Parameters

t	The interpolation parameter. It must be in [0; 1].
other	A quaternion.

squared_norm()

double squared_norm

(

)

const

Returns

The squared norm of this quaternion.

ToRotationMatrix()

Matrix3 ToRotationMatrix

(

)

const

Returns

A rotation Matrix3 equivalent to this normalized quaternion rotation.

TransformVector()

Vector3 TransformVector

(

const Vector3 &

v

)

const

Applies this quaternion transformation to v 3D vector.

Parameters

v	A 3D vector.

Returns

A transformed 3D vector.

vec()

Vector3 vec

(

)

const

}@

Returns

This quaternion vector: \( [x, y, z] \).

w() [1/2]

double& w

(

)

w() [2/2]

double w

(

)

const

x() [1/2]

double& x

(

)

x() [2/2]

double x

(

)

const

y() [1/2]

double& y

(

)

y() [2/2]

double y

(

)

const

z() [1/2]

double& z

(

)

z() [2/2]

double z

(

)

const

Member Data Documentation

kTolerance

constexpr double kTolerance {1e-15}

staticconstexpr

---

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

• quaternion.h
• quaternion.cc