Holds a unit quaternion. More...

#include <Quaternion.hpp>

Public Member Functions
	Quaternion ()=default
	Quaternion (const NdArray< double > &inArray)
	Quaternion (const NdArray< double > &inAxis, double inAngle)
	Quaternion (const std::array< double, 4 > &components) noexcept
	Quaternion (const Vec3 &inAxis, double inAngle) noexcept
	Quaternion (double inI, double inJ, double inK, double inS) noexcept
	Quaternion (double roll, double pitch, double yaw) noexcept
double	angleOfRotation () const noexcept
NdArray< double >	angularVelocity (const Quaternion &inQuat2, double inTime) const
Vec3	axisOfRotation () const noexcept
Quaternion	conjugate () const noexcept
double	i () const noexcept
Quaternion	inverse () const noexcept
double	j () const noexcept
double	k () const noexcept
Quaternion	nlerp (const Quaternion &inQuat2, double inPercent) const
bool	operator!= (const Quaternion &inRhs) const noexcept
NdArray< double >	operator* (const NdArray< double > &inVec) const
Quaternion	operator* (const Quaternion &inRhs) const noexcept
Vec3	operator* (const Vec3 &inVec3) const
Quaternion	operator* (double inScalar) const noexcept
Quaternion &	operator*= (const Quaternion &inRhs) noexcept
Quaternion &	operator*= (double inScalar) noexcept
Quaternion	operator+ (const Quaternion &inRhs) const noexcept
Quaternion &	operator+= (const Quaternion &inRhs) noexcept
Quaternion	operator- () const noexcept
Quaternion	operator- (const Quaternion &inRhs) const noexcept
Quaternion &	operator-= (const Quaternion &inRhs) noexcept
Quaternion	operator/ (const Quaternion &inRhs) const noexcept
Quaternion &	operator/= (const Quaternion &inRhs) noexcept
bool	operator== (const Quaternion &inRhs) const noexcept
double	pitch () const noexcept
void	print () const
void	propagateBody (const Vec3 &inAngularVelocity, double inDeltaT)
void	propagateBodyPitch (double pitchRate, double inDeltaT)
void	propagateBodyRoll (double rollRate, double inDeltaT)
void	propagateBodyYaw (double yawRate, double inDeltaT)
void	propagateInertial (const Vec3 &inAngularVelocity, double inDeltaT)
void	propagateInertialPitch (double pitchRate, double inDeltaT)
void	propagateInertialRoll (double rollRate, double inDeltaT)
void	propagateInertialYaw (double yawRate, double inDeltaT)
double	roll () const noexcept
NdArray< double >	rotate (const NdArray< double > &inVector) const
Vec3	rotate (const Vec3 &inVec3) const
double	s () const noexcept
Quaternion	slerp (const Quaternion &inQuat2, double inPercent) const
std::string	str () const
NdArray< double >	toDCM () const
NdArray< double >	toNdArray () const
double	yaw () const noexcept

Static Public Member Functions
static NdArray< double >	angularVelocity (const Quaternion &inQuat1, const Quaternion &inQuat2, double inTime)
static Quaternion	identity () noexcept
static Quaternion	nlerp (const Quaternion &inQuat1, const Quaternion &inQuat2, double inPercent)
static Quaternion	pitchRotation (double inAngle) noexcept
static Quaternion	propagateBody (Quaternion inQuaternion, const Vec3 &inAngularVelocity, double inDeltaT)
static Quaternion	propagateBodyPitch (Quaternion inQuaternion, double pitchRate, double inDeltaT)
static Quaternion	propagateBodyRoll (Quaternion inQuaternion, double rollRate, double inDeltaT)
static Quaternion	propagateBodyYaw (Quaternion inQuaternion, double yawRate, double inDeltaT)
static Quaternion	propagateInertial (Quaternion inQuaternion, const Vec3 &inAngularVelocity, double inDeltaT)
static Quaternion	propagateInertialPitch (Quaternion inQuaternion, double pitchRate, double inDeltaT)
static Quaternion	propagateInertialRoll (Quaternion inQuaternion, double rollRate, double inDeltaT)
static Quaternion	propagateInertialYaw (Quaternion inQuaternion, double yawRate, double inDeltaT)
static Quaternion	rollRotation (double inAngle) noexcept
static Quaternion	slerp (const Quaternion &inQuat1, const Quaternion &inQuat2, double inPercent)
static Quaternion	xRotation (double inAngle) noexcept
static Quaternion	yawRotation (double inAngle) noexcept
static Quaternion	yRotation (double inAngle) noexcept
static Quaternion	zRotation (double inAngle) noexcept

Friends
std::ostream &	operator<< (std::ostream &inOStream, const Quaternion &inQuat)

Detailed Description

Holds a unit quaternion.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

nc::rotations::Quaternion::Quaternion ( )

default

Default Constructor

◆ Quaternion() [2/7]

nc::rotations::Quaternion::Quaternion	(	double	roll,
		double	pitch,
		double	yaw )

inlinenoexcept

Constructor

Parameters

roll	euler roll angle in radians
pitch	euler pitch angle in radians
yaw	euler yaw angle in radians

◆ Quaternion() [3/7]

nc::rotations::Quaternion::Quaternion	(	double	inI,
		double	inJ,
		double	inK,
		double	inS )

inlinenoexcept

Constructor

Parameters

inI
inJ
inK
inS

◆ Quaternion() [4/7]

nc::rotations::Quaternion::Quaternion ( const std::array< double, 4 > & components )

inlinenoexcept

Constructor

Parameters

components

◆ Quaternion() [5/7]

nc::rotations::Quaternion::Quaternion ( const NdArray< double > & inArray )

inline

Constructor

Parameters

inArray if size = 3 the roll, pitch, yaw euler angles if size = 4 the i, j, k, s components if shape = [3, 3] then direction cosine matrix

◆ Quaternion() [6/7]

nc::rotations::Quaternion::Quaternion	(	const Vec3 &	inAxis,
		double	inAngle )

inlinenoexcept

Constructor

Parameters

inAxis	Euler axis
inAngle	Euler angle in radians

◆ Quaternion() [7/7]

nc::rotations::Quaternion::Quaternion	(	const NdArray< double > &	inAxis,
		double	inAngle )

inline

Constructor

Parameters

inAxis	Euler axis x,y,z vector components
inAngle	Euler angle in radians

Member Function Documentation

◆ angleOfRotation()

double nc::rotations::Quaternion::angleOfRotation ( ) const

inlinenodiscardnoexcept

the angle of rotation around the rotation axis that is described by the quaternion

Returns: radians

◆ angularVelocity() [1/2]

NdArray< double > nc::rotations::Quaternion::angularVelocity	(	const Quaternion &	inQuat1,
		const Quaternion &	inQuat2,
		double	inTime )

inlinestatic

angular velocity vector between the two quaternions. The norm of the array is the magnitude

Parameters

inQuat1
inQuat2
inTime	(seperation time)

Returns: NdArray<double>

◆ angularVelocity() [2/2]

NdArray< double > nc::rotations::Quaternion::angularVelocity	(	const Quaternion &	inQuat2,
		double	inTime ) const

inlinenodiscard

angular velocity vector between the two quaternions. The norm of the array is the magnitude

Parameters

inQuat2
inTime	(seperation time)

Returns: NdArray<double>

◆ axisOfRotation()

Vec3 nc::rotations::Quaternion::axisOfRotation ( ) const

inlinenodiscardnoexcept

the axis of rotation described by the quaternion

Returns: Vec3

◆ conjugate()

Quaternion nc::rotations::Quaternion::conjugate ( ) const

inlinenodiscardnoexcept

quaternion conjugate

Returns: Quaternion

◆ i()

double nc::rotations::Quaternion::i ( ) const

inlinenodiscardnoexcept

returns the i component

Returns: double

◆ identity()

Quaternion nc::rotations::Quaternion::identity ( )

inlinestaticnoexcept

quaternion identity (0,0,0,1)

Returns: Quaternion

◆ inverse()

Quaternion nc::rotations::Quaternion::inverse ( ) const

inlinenodiscardnoexcept

quaternion inverse

Returns: Quaterion

◆ j()

double nc::rotations::Quaternion::j ( ) const

inlinenodiscardnoexcept

returns the j component

Returns: double

◆ k()

double nc::rotations::Quaternion::k ( ) const

inlinenodiscardnoexcept

returns the k component

Returns: double

◆ nlerp() [1/2]

Quaternion nc::rotations::Quaternion::nlerp	(	const Quaternion &	inQuat1,
		const Quaternion &	inQuat2,
		double	inPercent )

inlinestatic

linearly interpolates between the two quaternions

Parameters

inQuat1
inQuat2
inPercent	[0, 1]

Returns: Quaternion

◆ nlerp() [2/2]

Quaternion nc::rotations::Quaternion::nlerp	(	const Quaternion &	inQuat2,
		double	inPercent ) const

inlinenodiscard

linearly interpolates between the two quaternions

Parameters

inQuat2
inPercent	(0, 1)

Returns: Quaternion

◆ operator!=()

bool nc::rotations::Quaternion::operator!= ( const Quaternion & inRhs ) const

inlinenoexcept

equality operator

Parameters

inRhs

Returns: bool

◆ operator*() [1/4]

NdArray< double > nc::rotations::Quaternion::operator* ( const NdArray< double > & inVec ) const

inline

multiplication operator

Parameters

inVec

Returns: NdArray<double>

◆ operator*() [2/4]

Quaternion nc::rotations::Quaternion::operator* ( const Quaternion & inRhs ) const

inlinenoexcept

multiplication operator

Parameters

inRhs

Returns: Quaternion

◆ operator*() [3/4]

Vec3 nc::rotations::Quaternion::operator* ( const Vec3 & inVec3 ) const

inline

multiplication operator

Parameters

inVec3

Returns: Vec3

◆ operator*() [4/4]

Quaternion nc::rotations::Quaternion::operator* ( double inScalar ) const

inlinenoexcept

multiplication operator, only useful for multiplying by negative 1, all others will be renormalized back out

Parameters

inScalar

Returns: Quaternion

◆ operator*=() [1/2]

Quaternion & nc::rotations::Quaternion::operator*= ( const Quaternion & inRhs )

inlinenoexcept

multiplication assignment operator

Parameters

inRhs

Returns: Quaternion

◆ operator*=() [2/2]

Quaternion & nc::rotations::Quaternion::operator*= ( double inScalar )

inlinenoexcept

multiplication operator, only useful for multiplying by negative 1, all others will be renormalized back out

Parameters

inScalar

Returns: Quaternion

◆ operator+()

Quaternion nc::rotations::Quaternion::operator+ ( const Quaternion & inRhs ) const

inlinenoexcept

addition operator

Parameters

inRhs

Returns: Quaternion

◆ operator+=()

Quaternion & nc::rotations::Quaternion::operator+= ( const Quaternion & inRhs )

inlinenoexcept

addition assignment operator

Parameters

inRhs

Returns: Quaternion

◆ operator-() [1/2]

Quaternion nc::rotations::Quaternion::operator- ( ) const

inlinenoexcept

negative operator

Returns: Quaternion

◆ operator-() [2/2]

Quaternion nc::rotations::Quaternion::operator- ( const Quaternion & inRhs ) const

inlinenoexcept

subtraction operator

Parameters

inRhs

Returns: Quaternion

◆ operator-=()

Quaternion & nc::rotations::Quaternion::operator-= ( const Quaternion & inRhs )

inlinenoexcept

subtraction assignment operator

Parameters

inRhs

Returns: Quaternion

◆ operator/()

Quaternion nc::rotations::Quaternion::operator/ ( const Quaternion & inRhs ) const

inlinenoexcept

division operator

Parameters

inRhs

Returns: Quaternion

◆ operator/=()

Quaternion & nc::rotations::Quaternion::operator/= ( const Quaternion & inRhs )

inlinenoexcept

division assignment operator

Parameters

inRhs

Returns: Quaternion

◆ operator==()

bool nc::rotations::Quaternion::operator== ( const Quaternion & inRhs ) const

inlinenoexcept

equality operator

Parameters

inRhs

Returns: bool

◆ pitch()

double nc::rotations::Quaternion::pitch ( ) const

inlinenodiscardnoexcept

The euler pitch angle in radians

Returns: euler pitch angle in radians

◆ pitchRotation()

Quaternion nc::rotations::Quaternion::pitchRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the pitch axis

Parameters

inAngle (radians)

Returns: Quaternion

◆ print()

void nc::rotations::Quaternion::print ( ) const

inline

prints the Quaternion to the console

◆ propagateBody() [1/2]

void nc::rotations::Quaternion::propagateBody	(	const Vec3 &	inAngularVelocity,
		double	inDeltaT )

inline

Propagate the quaternion forward in time using the body angular velocity vector

Parameters

inAngularVelocity	the body angular velocity vector (rad/s)
inDeltaT	the time step

◆ propagateBody() [2/2]

Quaternion nc::rotations::Quaternion::propagateBody	(	Quaternion	inQuaternion,
		const Vec3 &	inAngularVelocity,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time using the body angular velocity vector

Parameters

inQuaternion	the quaternion to propagate
inAngularVelocity	the body angular velocity vector (rad/s)
inDeltaT	the time step

◆ propagateBodyPitch() [1/2]

void nc::rotations::Quaternion::propagateBodyPitch	(	double	pitchRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along body the pitch axis

Parameters

pitchRate	the body pitch rate (rad/s)
inDeltaT	the time step

◆ propagateBodyPitch() [2/2]

Quaternion nc::rotations::Quaternion::propagateBodyPitch	(	Quaternion	inQuaternion,
		double	pitchRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along body the pitch axis

Parameters

inQuaternion	the quaternion to propagate
pitchRate	the body pitch rate (rad/s)
inDeltaT	the time step

◆ propagateBodyRoll() [1/2]

void nc::rotations::Quaternion::propagateBodyRoll	(	double	rollRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along body the roll axis

Parameters

rollRate	the body roll rate (rad/s)
inDeltaT	the time step

◆ propagateBodyRoll() [2/2]

Quaternion nc::rotations::Quaternion::propagateBodyRoll	(	Quaternion	inQuaternion,
		double	rollRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along body the roll axis

Parameters

inQuaternion	the quaternion to propagate
rollRate	the body roll rate (rad/s)
inDeltaT	the time step

◆ propagateBodyYaw() [1/2]

void nc::rotations::Quaternion::propagateBodyYaw	(	double	yawRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along body the yaw axis

Parameters

yawRate	the body yaw rate (rad/s)
inDeltaT	the time step

◆ propagateBodyYaw() [2/2]

Quaternion nc::rotations::Quaternion::propagateBodyYaw	(	Quaternion	inQuaternion,
		double	yawRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along body the yaw axis

Parameters

inQuaternion	the quaternion to propagate
yawRate	the body yaw rate (rad/s)
inDeltaT	the time step

◆ propagateInertial() [1/2]

void nc::rotations::Quaternion::propagateInertial	(	const Vec3 &	inAngularVelocity,
		double	inDeltaT )

inline

Propagate the quaternion forward in time using the inertial angular velocity vector

Parameters

inAngularVelocity	the inertial angular velocity vector (rad/s)
inDeltaT	the time step

◆ propagateInertial() [2/2]

Quaternion nc::rotations::Quaternion::propagateInertial	(	Quaternion	inQuaternion,
		const Vec3 &	inAngularVelocity,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time using the inertial angular velocity vector

Parameters

inQuaternion	the quaternion to propagate
inAngularVelocity	the inertial angular velocity vector (rad/s)
inDeltaT	the time step

◆ propagateInertialPitch() [1/2]

void nc::rotations::Quaternion::propagateInertialPitch	(	double	pitchRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along inertial the pitch axis

Parameters

pitchRate	the body pitch rate (rad/s)
inDeltaT	the time step

◆ propagateInertialPitch() [2/2]

Quaternion nc::rotations::Quaternion::propagateInertialPitch	(	Quaternion	inQuaternion,
		double	pitchRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along inertial the pitch axis

Parameters

inQuaternion	the quaternion to propagate
pitchRate	the body pitch rate (rad/s)
inDeltaT	the time step

◆ propagateInertialRoll() [1/2]

void nc::rotations::Quaternion::propagateInertialRoll	(	double	rollRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along inertial the roll axis

Parameters

rollRate	the body roll rate (rad/s)
inDeltaT	the time step

◆ propagateInertialRoll() [2/2]

Quaternion nc::rotations::Quaternion::propagateInertialRoll	(	Quaternion	inQuaternion,
		double	rollRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along inertial the roll axis

Parameters

inQuaternion	the quaternion to propagate
rollRate	the body roll rate (rad/s)
inDeltaT	the time step

◆ propagateInertialYaw() [1/2]

void nc::rotations::Quaternion::propagateInertialYaw	(	double	yawRate,
		double	inDeltaT )

inline

Propagate the quaternion forward in time along inertial the yaw axis

Parameters

yawRate	the body yaw rate (rad/s)
inDeltaT	the time step

◆ propagateInertialYaw() [2/2]

Quaternion nc::rotations::Quaternion::propagateInertialYaw	(	Quaternion	inQuaternion,
		double	yawRate,
		double	inDeltaT )

inlinestatic

Propagate the quaternion forward in time along inertial the yaw axis

Parameters

inQuaternion	the quaternion to propagate
yawRate	the body yaw rate (rad/s)
inDeltaT	the time step

◆ roll()

double nc::rotations::Quaternion::roll ( ) const

inlinenodiscardnoexcept

The euler roll angle in radians

Returns: euler roll angle in radians

◆ rollRotation()

Quaternion nc::rotations::Quaternion::rollRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the roll axis

Parameters

inAngle (radians)

Returns: Quaternion

◆ rotate() [1/2]

NdArray< double > nc::rotations::Quaternion::rotate ( const NdArray< double > & inVector ) const

inlinenodiscard

rotate a vector using the quaternion

Parameters

inVector (cartesian vector with x,y,z components)

Returns: NdArray<double> (cartesian vector with x,y,z components)

◆ rotate() [2/2]

Vec3 nc::rotations::Quaternion::rotate ( const Vec3 & inVec3 ) const

inlinenodiscard

rotate a vector using the quaternion

Parameters

inVec3

Returns: Vec3

◆ s()

double nc::rotations::Quaternion::s ( ) const

inlinenodiscardnoexcept

returns the s component

Returns: double

◆ slerp() [1/2]

Quaternion nc::rotations::Quaternion::slerp	(	const Quaternion &	inQuat1,
		const Quaternion &	inQuat2,
		double	inPercent )

inlinestatic

spherical linear interpolates between the two quaternions

Parameters

inQuat1
inQuat2
inPercent	(0, 1)

Returns: Quaternion

◆ slerp() [2/2]

Quaternion nc::rotations::Quaternion::slerp	(	const Quaternion &	inQuat2,
		double	inPercent ) const

inlinenodiscard

spherical linear interpolates between the two quaternions

Parameters

inQuat2
inPercent	(0, 1)

Returns: Quaternion

◆ str()

std::string nc::rotations::Quaternion::str ( ) const

inlinenodiscard

returns the quaternion as a string representation

Returns: std::string

◆ toDCM()

NdArray< double > nc::rotations::Quaternion::toDCM ( ) const

inlinenodiscard

returns the direction cosine matrix

Returns: NdArray<double>

◆ toNdArray()

NdArray< double > nc::rotations::Quaternion::toNdArray ( ) const

inlinenodiscard

returns the quaternion as an NdArray

Returns: NdArray<double>

◆ xRotation()

Quaternion nc::rotations::Quaternion::xRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the x-axis by the input angle

Parameters

inAngle (radians)

Returns: Quaternion

◆ yaw()

double nc::rotations::Quaternion::yaw ( ) const

inlinenodiscardnoexcept

The euler yaw angle in radians

Returns: euler yaw angle in radians

◆ yawRotation()

Quaternion nc::rotations::Quaternion::yawRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the yaw axis

Parameters

inAngle (radians)

Returns: Quaternion

◆ yRotation()

Quaternion nc::rotations::Quaternion::yRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the y-axis by the input angle

Parameters

inAngle (radians)

Returns: Quaternion

◆ zRotation()

Quaternion nc::rotations::Quaternion::zRotation ( double inAngle )

inlinestaticnoexcept

returns a quaternion to rotate about the y-axis by the input angle

Parameters

inAngle (radians)

Returns: Quaternion

◆ operator<<

std::ostream & operator<<	(	std::ostream &	inOStream,
		const Quaternion &	inQuat )

friend

IO operator for the Quaternion class

Parameters

inOStream
inQuat

Returns: std::ostream&

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

Quaternion.hpp

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

Member Function Documentation

◆ angleOfRotation()

◆ angularVelocity() [1/2]

◆ angularVelocity() [2/2]

◆ axisOfRotation()

◆ conjugate()

◆ i()

◆ identity()

◆ inverse()

◆ j()

◆ k()

◆ nlerp() [1/2]

◆ nlerp() [2/2]

◆ operator!=()

◆ operator*() [1/4]

◆ operator*() [2/4]

◆ operator*() [3/4]

◆ operator*() [4/4]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator+()

◆ operator+=()

◆ operator-() [1/2]

◆ operator-() [2/2]

◆ operator-=()

◆ operator/()

◆ operator/=()

◆ operator==()

◆ pitch()

◆ pitchRotation()

◆ print()

◆ propagateBody() [1/2]

◆ propagateBody() [2/2]

◆ propagateBodyPitch() [1/2]

◆ propagateBodyPitch() [2/2]

◆ propagateBodyRoll() [1/2]

◆ propagateBodyRoll() [2/2]

◆ propagateBodyYaw() [1/2]

◆ propagateBodyYaw() [2/2]

◆ propagateInertial() [1/2]

◆ propagateInertial() [2/2]

◆ propagateInertialPitch() [1/2]

◆ propagateInertialPitch() [2/2]

◆ propagateInertialRoll() [1/2]

◆ propagateInertialRoll() [2/2]

◆ propagateInertialYaw() [1/2]

◆ propagateInertialYaw() [2/2]

◆ roll()

◆ rollRotation()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ s()

◆ slerp() [1/2]

◆ slerp() [2/2]

◆ str()

◆ toDCM()

◆ toNdArray()

◆ xRotation()

◆ yaw()

◆ yawRotation()

◆ yRotation()

◆ zRotation()

Friends And Related Symbol Documentation

◆ operator<<