A quaternion. More...

#include <Quaternion.h>

Inheritance diagram for Quaternion:

Public Member Functions
	Quaternion ()
	Create a new identity quaternion.

	Quaternion (float _x, float _y, float _z, float _w)
	create a new quaternion with the given values

	Quaternion (Quat q)
	Create a quaternion from C-style Quat.

	~Quaternion ()

void	Normalize ()
	Convert to unit quaternion.

Vector3	operator* (const Vector3 &vector) const
	Rotate a vector using this quaterion.

Quaternion	operator* (const Quaternion &rotation) const
	Multiply this quaternion with another quaternion.

bool	operator== (const Quaternion &quaternion)
	Check the equality of two quaternions.

void	ToAngleAxis (float angle, Vector3 axis)
	Convert this quaternion to angle/axis representation.

Static Public Member Functions
static Quaternion	Normalize (const Quaternion &q)
	Convert to unity quaternion.

static Vector3	ToAngles (const Quaternion &q)
	Convert to euler angles.

static Quaternion	Inverse (Quaternion quaternion)
	The inverse of quaterion.

static Quaternion	LookRotation (const Vector3 &forward, const Vector3 &upwards)
	A rotation which looks in the given direction.

static Quaternion	LookRotation (const Vector3 &forward)
	Creates a quaternion with the given forward direction with up = Vector3::up.

static Quaternion	FromToRotation (Vector3 fromDirection, Vector3 toDirection)
	Calculat the rotation from on vector to another.

static Quaternion	RotateTowards (const Quaternion &from, const Quaternion &to, float maxDegreesDelta)
	Rotate form one orientation to anther with a maximum amount of degrees.

static Quaternion	AngleAxis (float angle, const Vector3 &axis)
	Convert an angle/axis representation to a quaternion.

static float	Angle (Quaternion orientation1, Quaternion orientation2)
	Get the angle between two orientations.

static Quaternion	Slerp (const Quaternion &rotation1, const Quaternion &rotation2, float factor)
	Sherical lerp between two rotations.

static Quaternion	SlerpUnclamped (const Quaternion &rotation1, const Quaternion &rotation2, float factor)
	Unclamped sherical lerp between two rotations.

static Quaternion	Euler (float x, float y, float z)
	Create a rotation from euler angles.

static Quaternion	Euler (Vector3 eulerAngles)
	Create a rotation from a vector containing euler angles.

static Quaternion	EulerXYZ (float x, float y, float z)
	Create a rotation from euler angles.

static Quaternion	EulerXYZ (Vector3 eulerAngles)
	Create a rotation from a vector containing euler angles.

static float	GetAngleAround (Vector3 axis, Quaternion rotation)
	Returns the angle of around the give axis for a rotation.

static Quaternion	GetRotationAround (Vector3 axis, Quaternion rotation)
	Returns the rotation limited around the given axis.

static void	GetSwingTwist (Vector3 axis, Quaternion rotation, Quaternion swing, Quaternion twist)
	Swing-twist decomposition of a rotation.

static float	Dot (Quaternion rotation1, Quaternion rotation2)
	Calculate the dot product of two quaternions.

Public Attributes
float	x
	The x component.

float	y
	The y component.

float	z
	The z component.

float	w
	The w component.

Static Public Attributes
static const Quaternion	identity = Quaternion(0, 0, 0, 1)
	An identity quaternion.

Detailed Description

A quaternion.

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

Quaternion::Quaternion ( )

Create a new identity quaternion.

◆ Quaternion() [2/3]

Quaternion::Quaternion	(	float	_x,
		float	_y,
		float	_z,
		float	_w
	)

create a new quaternion with the given values

Parameters

_x	x component
_y	y component
_z	z component
_w	w component

◆ Quaternion() [3/3]

Quaternion::Quaternion ( Quat q )

Create a quaternion from C-style Quat.

Parameters

q

◆ ~Quaternion()

Quaternion::~Quaternion ( )

Member Function Documentation

◆ Normalize() [1/2]

void Quaternion::Normalize ( )

Convert to unit quaternion.

This will preserve the orientation, but ensures that it is a unit quaternion.

◆ Normalize() [2/2]

Quaternion Quaternion::Normalize ( const Quaternion & q )

static

Convert to unity quaternion.

Parameters

q	The quaternion to convert

Returns: A unit quaternion

This will preserve the orientation, but ensures that it is a unit quaternion.

◆ ToAngles()

Vector3 Quaternion::ToAngles ( const Quaternion & q )

static

Convert to euler angles.

Parameters

q	The quaternion to convert

Returns: A vector containing euler angles

The euler angles performed in the order: Z, X, Y

◆ operator*() [1/2]

Vector3 Quaternion::operator* ( const Vector3 & vector ) const

Rotate a vector using this quaterion.

Parameters

vector The vector to rotate

Returns: The rotated vector

◆ operator*() [2/2]

Quaternion Quaternion::operator* ( const Quaternion & rotation ) const

Multiply this quaternion with another quaternion.

Parameters

rotation The quaternion to multiply with

Returns: The resulting rotation

The result will be this quaternion rotated according to the give rotation.

◆ operator==()

bool Quaternion::operator== ( const Quaternion & quaternion )

Check the equality of two quaternions.

Parameters

quaternion The quaternion to compare to

Returns: True when the components of the quaternions are identical

Note that this does not compare the rotations themselves. Two quaternions with the same rotational effect may have different components. Use Quaternion::Angle to check if the rotations are the same.

◆ Inverse()

Quaternion Quaternion::Inverse ( Quaternion quaternion )

static

The inverse of quaterion.

Parameters

quaternion The quaternion for which the inverse is needed

Returns: The inverted quaternion

◆ LookRotation() [1/2]

Quaternion Quaternion::LookRotation	(	const Vector3 &	forward,
		const Vector3 &	upwards
	)

static

A rotation which looks in the given direction.

Parameters

forward	The look direction
upwards	The up direction

Returns: The look rotation

◆ LookRotation() [2/2]

Quaternion Quaternion::LookRotation ( const Vector3 & forward )

static

Creates a quaternion with the given forward direction with up = Vector3::up.

Parameters

forward The look direction

Returns: The rotation for this direction

For the rotation, Vector::up is used for the up direction. Note: if the forward direction == Vector3::up, the result is Quaternion::identity

◆ FromToRotation()

Quaternion Quaternion::FromToRotation	(	Vector3	fromDirection,
		Vector3	toDirection
	)

static

Calculat the rotation from on vector to another.

Parameters

fromDirection	The from direction
toDirection	The to direction

Returns: The rotation from the first to the second vector

◆ RotateTowards()

Quaternion Quaternion::RotateTowards	(	const Quaternion &	from,
		const Quaternion &	to,
		float	maxDegreesDelta
	)

static

Rotate form one orientation to anther with a maximum amount of degrees.

Parameters

from	The from rotation
to	The destination rotation
maxDegreesDelta	The maximum amount of degrees to rotate

Returns: The possibly limited rotation

◆ AngleAxis()

Quaternion Quaternion::AngleAxis	(	float	angle,
		const Vector3 &	axis
	)

static

Convert an angle/axis representation to a quaternion.

Parameters

angle	The angle
axis	The axis

Returns: The resulting quaternion

◆ ToAngleAxis()

void Quaternion::ToAngleAxis	(	float *	angle,
		Vector3 *	axis
	)

Convert this quaternion to angle/axis representation.

Parameters

angle	A pointer to the angle for the result
axis	A pointer to the axis for the result

◆ Angle()

float Quaternion::Angle	(	Quaternion	orientation1,
		Quaternion	orientation2
	)

static

Get the angle between two orientations.

Parameters

orientation1	The first orientation
orientation2	The second orientation

Returns: The smallest angle in degrees between the two orientations

◆ Slerp()

Quaternion Quaternion::Slerp	(	const Quaternion &	rotation1,
		const Quaternion &	rotation2,
		float	factor
	)

static

Sherical lerp between two rotations.

Parameters

rotation1	The first rotation
rotation2	The second rotation
factor	The factor between 0 and 1.

Returns: The resulting rotation

A factor 0 returns rotation1, factor1 returns rotation2.

◆ SlerpUnclamped()

Quaternion Quaternion::SlerpUnclamped	(	const Quaternion &	rotation1,
		const Quaternion &	rotation2,
		float	factor
	)

static

Unclamped sherical lerp between two rotations.

Parameters

rotation1	The first rotation
rotation2	The second rotation
factor	The factor

Returns: The resulting rotation

A factor 0 returns rotation1, factor1 returns rotation2. Values outside the 0..1 range will result in extrapolated rotations

◆ Euler() [1/2]

Quaternion Quaternion::Euler	(	float	x,
		float	y,
		float	z
	)

static

Create a rotation from euler angles.

Parameters

x	The angle around the right axis
y	The angle around the upward axis
z	The angle around the forward axis

Returns: The resulting quaternion

Rotation are appied in the order Z, X, Y.

◆ Euler() [2/2]

Quaternion Quaternion::Euler ( Vector3 eulerAngles )

static

Create a rotation from a vector containing euler angles.

Parameters

eulerAngles Vector with the euler angles

Returns: The resulting quaternion

Rotation are appied in the order Z, X, Y.

◆ EulerXYZ() [1/2]

Quaternion Quaternion::EulerXYZ	(	float	x,
		float	y,
		float	z
	)

static

Create a rotation from euler angles.

Parameters

x	The angle around the right axis
y	The angle around the upward axis
z	The angle around the forward axis

Returns: The resulting quaternion

Rotation are appied in the order X, Y, Z.

◆ EulerXYZ() [2/2]

Quaternion Quaternion::EulerXYZ ( Vector3 eulerAngles )

static

Create a rotation from a vector containing euler angles.

Parameters

eulerAngles Vector with the euler angles

Returns: The resulting quaternion

Rotation are appied in the order X, Y, Z.

◆ GetAngleAround()

float Quaternion::GetAngleAround	(	Vector3	axis,
		Quaternion	rotation
	)

static

Returns the angle of around the give axis for a rotation.

Parameters

axis	The axis around which the angle should be computed
rotation	The source rotation

Returns: The signed angle around the axis

◆ GetRotationAround()

Quaternion Quaternion::GetRotationAround	(	Vector3	axis,
		Quaternion	rotation
	)

static

Returns the rotation limited around the given axis.

Parameters

axis	The axis which which the rotation should be limited
rotation	The source rotation

Returns: The rotation around the given axis

◆ GetSwingTwist()

void Quaternion::GetSwingTwist	(	Vector3	axis,
		Quaternion	rotation,
		Quaternion *	swing,
		Quaternion *	twist
	)

static

Swing-twist decomposition of a rotation.

Parameters

axis	The base direction for the decomposition
rotation	The source rotation
swing	A pointer to the quaternion for the swing result
twist	A pointer to the quaternion for the twist result

◆ Dot()

float Quaternion::Dot	(	Quaternion	rotation1,
		Quaternion	rotation2
	)

static

Calculate the dot product of two quaternions.

Parameters

rotation1	The first rotation
rotation2	The second rotation

Returns

Member Data Documentation

◆ identity

const Quaternion Quaternion::identity = Quaternion(0, 0, 0, 1)

static

An identity quaternion.

◆ x

float Quat::x

inherited

The x component.

◆ y

float Quat::y

inherited

The y component.

◆ z

float Quat::z

inherited

The z component.

◆ w

float Quat::w

inherited

The w component.

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

d:/PlatformIO/RoboidControlArduino/src/RoboidControl/VectorAlgebra/include/Quaternion.h
d:/PlatformIO/RoboidControlArduino/src/RoboidControl/VectorAlgebra/src/Quaternion.cpp

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

◆ Quaternion() [2/3]

◆ Quaternion() [3/3]

◆ ~Quaternion()

Member Function Documentation

◆ Normalize() [1/2]

◆ Normalize() [2/2]

◆ ToAngles()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ operator==()

◆ Inverse()

◆ LookRotation() [1/2]

◆ LookRotation() [2/2]

◆ FromToRotation()

◆ RotateTowards()

◆ AngleAxis()

◆ ToAngleAxis()

◆ Angle()

◆ Slerp()

◆ SlerpUnclamped()

◆ Euler() [1/2]

◆ Euler() [2/2]

◆ EulerXYZ() [1/2]

◆ EulerXYZ() [2/2]

◆ GetAngleAround()

◆ GetRotationAround()

◆ GetSwingTwist()

◆ Dot()

Member Data Documentation

◆ identity

◆ x

◆ y

◆ z

◆ w