#include <Quaternion.h>

Inheritance diagram for biorbd::utils::Quaternion:

Public Member Functions
	Quaternion (double kStabilizer=1)
	Construct Quaternion. More...

	Quaternion (const biorbd::utils::Quaternion &other)
	Construct Quaternion from another quaternion. More...

	Quaternion (const RigidBodyDynamics::Math::Vector4d &vec4, double kStabilizer=1)
	Construct Quaternion. More...

	Quaternion (const biorbd::utils::Scalar &w, const biorbd::utils::Scalar &x, const biorbd::utils::Scalar &y, const biorbd::utils::Scalar &z, double kStabilizer=1)
	Construct Quaternion. More...

	Quaternion (const biorbd::utils::Scalar &w, const biorbd::utils::Vector3d &vec3, double kStabilizer=1)
	Construct Quaternion. More...

biorbd::utils::Scalar	w () const
	Return the real part (w) the Quaternion. More...

biorbd::utils::Scalar	x () const
	Return the X-Component of the imaginary part of the Quaternion. More...

biorbd::utils::Scalar	y () const
	Return the Y-Component of the imaginary part of the Quaternion. More...

biorbd::utils::Scalar	z () const
	Return the Z-Component of the imaginary part of the Quaternion. More...

void	setKStab (double newKStab)
	Set the k stabilizer. More...

double	kStab () const
	Return the k stabilizer. More...

biorbd::utils::Quaternion	operator* (const biorbd::utils::Quaternion &other) const
	Quaternion multiplication. More...

biorbd::utils::Quaternion	operator* (const biorbd::utils::Scalar &scalar) const
	Multiply the quaternion with a scalar. More...

biorbd::utils::Quaternion	operator* (float scalar) const
	Multiply the quaternion with a scalar. More...

biorbd::utils::Quaternion	operator+ (const biorbd::utils::Quaternion &other) const
	Add the quaternion to another. More...

biorbd::utils::Quaternion	operator- (const biorbd::utils::Quaternion &other) const
	Subtract the quaternion to another. More...

biorbd::utils::Rotation	toMatrix (bool skipAsserts=false) const
	Convert the quaternion to a RotoTrans. More...

biorbd::utils::Quaternion	slerp (double alpha, const Quaternion &quat) const
	Interpolation of the quaternion between to position. More...

biorbd::utils::Quaternion	conjugate () const
	Return the conjugate of the quaternion. More...

biorbd::utils::Quaternion	timeStep (const biorbd::utils::Vector3d &omega, double dt)
	Integrate the quaternion from its velocity. More...

biorbd::utils::Vector3d	rotate (const biorbd::utils::Vector3d &vec) const
	Return a rotated vector from the quaternion. More...

biorbd::utils::Quaternion	omegaToQDot (const biorbd::utils::Vector3d &omega) const
	Converts a 3d angular velocity vector. More...

biorbd::utils::Vector3d	eulerDotToOmega (const biorbd::utils::Vector3d &eulerDot, const biorbd::utils::Vector3d &euler, const biorbd::utils::String &seq)
	Converts a 3d angular velocity vector. More...

void	derivate (const biorbd::utils::Vector &w)
	Return the time derivative of the quaterion. More...

void	normalize ()
	Force the normalization of the quaternion. More...

Static Public Member Functions
static biorbd::utils::Quaternion	fromGLRotate (const biorbd::utils::Scalar &angle, const biorbd::utils::Scalar &x, const biorbd::utils::Scalar &y, const biorbd::utils::Scalar &z, double kStab=1)
	Construct Quaternion from a GL. More...

static biorbd::utils::Quaternion	fromAxisAngle (const biorbd::utils::Scalar &angle, const biorbd::utils::Vector3d &axis, double kStab=1)
	Construct Quaternion from an axis angle. More...

static biorbd::utils::Quaternion	fromMatrix (const biorbd::utils::RotoTrans &rt, double kStab=1)
	Construct Quaternion from a RotoTrans matrix. More...

static biorbd::utils::Quaternion	fromMatrix (const biorbd::utils::Rotation &mat, double kStab=1)
	Construct Quaternion from a Rotation matrix. More...

static biorbd::utils::Quaternion	fromZYXAngles (const biorbd::utils::Vector3d &zyx_angles, double kStab=1)
	Construct Quaternion from Euler angles (sequece ZYX) More...

static biorbd::utils::Quaternion	fromYXZAngles (const biorbd::utils::Vector3d &yxz_angles, double kStab=1)
	Construct Quaternion from Euler angles (sequece YXZ) More...

static biorbd::utils::Quaternion	fromXYZAngles (const biorbd::utils::Vector3d &xyz_angles, double kStab=1)
	Construct Quaternion from Euler angles (sequece XYZ) More...

Protected Attributes
double	m_Kstab
	Stabilization factor for the derivation.

Detailed Description

Description of a quaternion in the format (w, x, y, z)

The definition for conversions are taken from https://www.euclideanspace.com/maths/geometry/rotations/conversions/index.htm

Definition at line 26 of file Quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

biorbd::utils::Quaternion::Quaternion ( double kStabilizer = 1 )

Construct Quaternion.

Parameters

kStabilizer The value of the kstabilizer

Definition at line 10 of file Quaternion.cpp.

◆ Quaternion() [2/5]

biorbd::utils::Quaternion::Quaternion ( const biorbd::utils::Quaternion & other )

Construct Quaternion from another quaternion.

Parameters

other Other quaternion

Definition at line 17 of file Quaternion.cpp.

◆ Quaternion() [3/5]

biorbd::utils::Quaternion::Quaternion	(	const RigidBodyDynamics::Math::Vector4d &	vec4,
		double	kStabilizer = `1`
	)

Construct Quaternion.

Parameters

vec4	The vector describing the quaternion
kStabilizer	The value of the kstabilizer

Definition at line 24 of file Quaternion.cpp.

◆ Quaternion() [4/5]

biorbd::utils::Quaternion::Quaternion	(	const biorbd::utils::Scalar &	w,
		const biorbd::utils::Scalar &	x,
		const biorbd::utils::Scalar &	y,
		const biorbd::utils::Scalar &	z,
		double	kStabilizer = `1`
	)

Construct Quaternion.

Parameters

w	The W-Component of quaternion
x	The X-Component of quaternion
y	The Y-Component of quaternion
z	The Z-Component of quaternion
kStabilizer	The value of the kstabilizer

Definition at line 33 of file Quaternion.cpp.

◆ Quaternion() [5/5]

biorbd::utils::Quaternion::Quaternion	(	const biorbd::utils::Scalar &	w,
		const biorbd::utils::Vector3d &	vec3,
		double	kStabilizer = `1`
	)

Construct Quaternion.

Parameters

w	The W-Component of quaternion
vec3	The vector describing the imaginary part
kStabilizer	The value of the kstabilizer

Definition at line 44 of file Quaternion.cpp.

Member Function Documentation

◆ conjugate()

biorbd::utils::Quaternion biorbd::utils::Quaternion::conjugate ( ) const

Return the conjugate of the quaternion.

Returns: The conjugate of the quaternion

Definition at line 260 of file Quaternion.cpp.

◆ derivate()

void biorbd::utils::Quaternion::derivate ( const biorbd::utils::Vector & w )

Return the time derivative of the quaterion.

Parameters

w	The vector of time derivative (output)

Definition at line 317 of file Quaternion.cpp.

◆ eulerDotToOmega()

biorbd::utils::Vector3d biorbd::utils::Quaternion::eulerDotToOmega	(	const biorbd::utils::Vector3d &	eulerDot,
		const biorbd::utils::Vector3d &	euler,
		const biorbd::utils::String &	seq
	)

Converts a 3d angular velocity vector.

Parameters

eulerDot	the Euler angle rates
euler	the Euler angles
seq	the Euler angles sequence

Converts a 3d angular velocity vector expressed in terms of euler angles rate into the 3d angular velocity vector expressed in the fixed parent frame. See https://davidbrown3.github.io/2017-07-25/EulerAngles/ for correct equations.

Definition at line 298 of file Quaternion.cpp.

◆ fromAxisAngle()

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromAxisAngle	(	const biorbd::utils::Scalar &	angle,
		const biorbd::utils::Vector3d &	axis,
		double	kStab = `1`
	)

static

Construct Quaternion from an axis angle.

Parameters

angle	The angle in radians
axis	The 3d vector of the axis
kStab	The value of the kstabilizer

Definition at line 142 of file Quaternion.cpp.

◆ fromGLRotate()

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromGLRotate	(	const biorbd::utils::Scalar &	angle,
		const biorbd::utils::Scalar &	x,
		const biorbd::utils::Scalar &	y,
		const biorbd::utils::Scalar &	z,
		double	kStab = `1`
	)

static

Construct Quaternion from a GL.

Parameters

angle	The angle in radians
x	The X-Component of quaternion
y	The Y-Component of quaternion
z	The Z-Component of quaternion
kStab	The value of the kstabilizer

Definition at line 130 of file Quaternion.cpp.

◆ fromMatrix() [1/2]

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromMatrix	(	const biorbd::utils::Rotation &	mat,
		double	kStab = `1`
	)

static

Construct Quaternion from a Rotation matrix.

Parameters

mat	The rotation matrix
kStab	The value of the kstabilizer

Definition at line 161 of file Quaternion.cpp.

◆ fromMatrix() [2/2]

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromMatrix	(	const biorbd::utils::RotoTrans &	rt,
		double	kStab = `1`
	)

static

Construct Quaternion from a RotoTrans matrix.

Parameters

rt	RotoTrans matrix
kStab	The value of the kstabilizer

Definition at line 155 of file Quaternion.cpp.

◆ fromXYZAngles()

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromXYZAngles	(	const biorbd::utils::Vector3d &	xyz_angles,
		double	kStab = `1`
	)

static

Construct Quaternion from Euler angles (sequece XYZ)

Parameters

xyz_angles	The Euler angles in a sequence where the first element is the X-component
kStab	The value of the kstabilizer

Definition at line 189 of file Quaternion.cpp.

◆ fromYXZAngles()

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromYXZAngles	(	const biorbd::utils::Vector3d &	yxz_angles,
		double	kStab = `1`
	)

static

Construct Quaternion from Euler angles (sequece YXZ)

Parameters

yxz_angles	The Euler angles in a sequence where the first element is the Y-component
kStab	The value of the kstabilizer

Definition at line 181 of file Quaternion.cpp.

◆ fromZYXAngles()

biorbd::utils::Quaternion biorbd::utils::Quaternion::fromZYXAngles	(	const biorbd::utils::Vector3d &	zyx_angles,
		double	kStab = `1`
	)

static

Construct Quaternion from Euler angles (sequece ZYX)

Parameters

zyx_angles	The Euler angles in a sequence where the first element is the Z-component
kStab	The value of the kstabilizer

Definition at line 173 of file Quaternion.cpp.

◆ kStab()

double biorbd::utils::Quaternion::kStab ( ) const

Return the k stabilizer.

Returns: The k stabilizer

The k statilizer value is used during several operation to make the quaternion tending toward a norm of

Definition at line 75 of file Quaternion.cpp.

◆ normalize()

void biorbd::utils::Quaternion::normalize ( )

Force the normalization of the quaternion.

Definition at line 353 of file Quaternion.cpp.

◆ omegaToQDot()

biorbd::utils::Quaternion biorbd::utils::Quaternion::omegaToQDot ( const biorbd::utils::Vector3d & omega ) const

Converts a 3d angular velocity vector.

Parameters

omega the angular velocity

Returns: a 4d vector containing the derivatives of the 4 components of the quaternion corresponding to omega

Converts a 3d angular velocity vector into a 4d derivative of the components of the quaternion

Definition at line 287 of file Quaternion.cpp.

◆ operator*() [1/3]

biorbd::utils::Quaternion biorbd::utils::Quaternion::operator* ( const biorbd::utils::Quaternion & other ) const

Quaternion multiplication.

Parameters

other The other quaternion

Definition at line 80 of file Quaternion.cpp.

◆ operator*() [2/3]

biorbd::utils::Quaternion biorbd::utils::Quaternion::operator* ( const biorbd::utils::Scalar & scalar ) const

Multiply the quaternion with a scalar.

Parameters

scalar The scalar to multiply with

Definition at line 91 of file Quaternion.cpp.

◆ operator*() [3/3]

biorbd::utils::Quaternion biorbd::utils::Quaternion::operator* ( float scalar ) const

Multiply the quaternion with a scalar.

Parameters

scalar The scalar to multiply with

Definition at line 98 of file Quaternion.cpp.

◆ operator+()

biorbd::utils::Quaternion biorbd::utils::Quaternion::operator+ ( const biorbd::utils::Quaternion & other ) const

Add the quaternion to another.

Parameters

other The other quaternion to add

Definition at line 116 of file Quaternion.cpp.

◆ operator-()

biorbd::utils::Quaternion biorbd::utils::Quaternion::operator- ( const biorbd::utils::Quaternion & other ) const

Subtract the quaternion to another.

Parameters

other Other quaternion to substract

Definition at line 123 of file Quaternion.cpp.

◆ rotate()

biorbd::utils::Vector3d biorbd::utils::Quaternion::rotate ( const biorbd::utils::Vector3d & vec ) const

Return a rotated vector from the quaternion.

Parameters

vec	The vector to rotate

Returns: The rotated vector

Definition at line 276 of file Quaternion.cpp.

◆ setKStab()

void biorbd::utils::Quaternion::setKStab ( double newKStab )

Set the k stabilizer.

Parameters

newKStab The new value

Definition at line 70 of file Quaternion.cpp.

◆ slerp()

biorbd::utils::Quaternion biorbd::utils::Quaternion::slerp	(	double	alpha,
		const Quaternion &	quat
	)		const

Interpolation of the quaternion between to position.

Parameters

alpha	The proportion of the rotation
quat	The quaternion to targe

Definition at line 219 of file Quaternion.cpp.

◆ timeStep()

biorbd::utils::Quaternion biorbd::utils::Quaternion::timeStep	(	const biorbd::utils::Vector3d &	omega,
		double	dt
	)

Integrate the quaternion from its velocity.

Parameters

omega	3D vector of the angular velocity
dt	The time step to intergrate on

Returns: The rotated quaternion

Definition at line 268 of file Quaternion.cpp.

◆ toMatrix()

biorbd::utils::Rotation biorbd::utils::Quaternion::toMatrix ( bool skipAsserts = false ) const

Convert the quaternion to a RotoTrans.

Parameters

skipAsserts Check if the norm of the quaternion is approximately 1

Returns: The rotation matrix

The function throws a runtime_error if the skipAsserts is false and the norm of the quaternion is not almost one. In order to accelerate the computation of the norm, the norm-squared is evaluated. The threshold is 1e-10 for the norm-squared

Definition at line 197 of file Quaternion.cpp.

◆ w()

biorbd::utils::Scalar biorbd::utils::Quaternion::w ( ) const

Return the real part (w) the Quaternion.

Returns: The real part of the Quaternion

Definition at line 53 of file Quaternion.cpp.

◆ x()

biorbd::utils::Scalar biorbd::utils::Quaternion::x ( ) const

Return the X-Component of the imaginary part of the Quaternion.

Returns: The X-Component of the imaginary part of the Quaternion

Definition at line 57 of file Quaternion.cpp.

◆ y()

biorbd::utils::Scalar biorbd::utils::Quaternion::y ( ) const

Return the Y-Component of the imaginary part of the Quaternion.

Returns: The Y-Component of the imaginary part of the Quaternion

Definition at line 61 of file Quaternion.cpp.

◆ z()

biorbd::utils::Scalar biorbd::utils::Quaternion::z ( ) const

Return the Z-Component of the imaginary part of the Quaternion.

Returns: The Z-Component of the imaginary part of the Quaternion

Definition at line 65 of file Quaternion.cpp.

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

Public Member Functions

Static Public Member Functions

Protected Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/5]

◆ Quaternion() [2/5]

◆ Quaternion() [3/5]

◆ Quaternion() [4/5]

◆ Quaternion() [5/5]

Member Function Documentation

◆ conjugate()

◆ derivate()

◆ eulerDotToOmega()

◆ fromAxisAngle()

◆ fromGLRotate()

◆ fromMatrix() [1/2]

◆ fromMatrix() [2/2]

◆ fromXYZAngles()

◆ fromYXZAngles()

◆ fromZYXAngles()

◆ kStab()

◆ normalize()

◆ omegaToQDot()

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator+()

◆ operator-()

◆ rotate()

◆ setKStab()

◆ slerp()

◆ timeStep()

◆ toMatrix()

◆ w()

◆ x()

◆ y()

◆ z()