Quaternions represent rotation around an axis, defined by quaternion components x, y, z and w. More...

#include <kanzi/core/math/quaternion.hpp>

Inheritance diagram for kanzi::Quaternion:

Public Member Functions
Quaternion	conjugated () const
	Get conjugated copy of this quaternion. More...

float	getW () const
	Get the w component of the quaternion. More...

float	getX () const
	Get the x component of the quaternion. More...

float	getY () const
	Get the y component of the quaternion. More...

float	getZ () const
	Get the z component of the quaternion. More...

KZ_NO_DISCARD Quaternion	normalized () const
	Get normalized copy of this quaternion. More...

Quaternion	operator* (float scalar) const
	Multiplies each quaternion component with a scalar and returns the result. More...

Quaternion &	operator*= (float scalar)
	Multiplies each quaternion component with a scalar. More...

Quaternion	operator/ (float scalar) const
	Divides each quaternion component with a scalar and returns the result. More...

Quaternion &	operator/= (float scalar)
	Divides each quaternion component with a scalar. More...

float &	operator[] (size_t index)
	Access individual components of a quaternion. More...

const float &	operator[] (size_t index) const
	Access individual components of a quaternion. More...

	Quaternion ()
	Default constructor, initializes the quaternion components to identity, representing no rotation (x=0, y=0, z=0, w=1). More...

	Quaternion (const float x, const float y, const float z, const float w)
	Constructor, initializes the quaternion components to x, y, z and w. More...

void	setW (float w)
	Sets the w component of the quaternion. More...

void	setX (float x)
	Sets the x component of the quaternion. More...

void	setY (float y)
	Sets the y component of the quaternion. More...

void	setZ (float z)
	Sets the z component of the quaternion. More...

Static Public Member Functions
static Quaternion	createFromEulerAngles (Vector3 anglesInRadians)
	Creates a quaternion from Euler angles. More...

static Quaternion	createFromEulerAngles (float rotationX, float rotationY, float rotationZ)
	Creates a quaternion from Euler angles. More...

static Quaternion	createFromVector (Vector3 axis, float angleInRadians)
	Creates quaternion from axis and angle. More...

Detailed Description

Quaternions represent rotation around an axis, defined by quaternion components x, y, z and w.

Quaternions are compact, do not suffer from gimbal lock and can be easily interpolated. Kanzi Engine uses quaternions internally to represent all rotations. Quaternions are based on complex numbers and are not easy to understand intuitively. You almost never access or modify the individual components. In most cases you take existing rotations and use them to construct new rotations (e.g. to smoothly interpolate between two rotations). You can use the Quaternion operator * to rotate one rotation by another, or to rotate a vector by a rotation.

See also: operator*().; rotateVector().

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

kanzi::Quaternion::Quaternion ( )

inlineexplicit

Default constructor, initializes the quaternion components to identity, representing no rotation (x=0, y=0, z=0, w=1).

◆ Quaternion() [2/2]

kanzi::Quaternion::Quaternion	(	const float	x,
		const float	y,
		const float	z,
		const float	w
	)

inlineexplicit

Constructor, initializes the quaternion components to x, y, z and w.

Parameters

x	x component of the quaternion.
y	y component of the quaternion.
z	z component of the quaternion.
w	w component of the quaternion.

Member Function Documentation

◆ createFromVector()

static Quaternion kanzi::Quaternion::createFromVector	(	Vector3	axis,
		float	angleInRadians
	)

static

Creates quaternion from axis and angle.

Use this to create a quaternion from axis of rotation and angle in radians.

Parameters

axis	Axis components in Vector3(x, y, z).
angleInRadians	Angle in radians.

Returns: Rotated quaternion.

◆ createFromEulerAngles() [1/2]

static Quaternion kanzi::Quaternion::createFromEulerAngles ( Vector3 anglesInRadians )

static

Creates a quaternion from Euler angles.

Kanzi Engine represents Euler angles as Tait-Bryan angles where the rotations are applied in the order x, y and z.

Parameters

anglesInRadians Euler angles in radians.

Returns: Rotated quaternion.

◆ createFromEulerAngles() [2/2]

static Quaternion kanzi::Quaternion::createFromEulerAngles	(	float	rotationX,
		float	rotationY,
		float	rotationZ
	)

static

Creates a quaternion from Euler angles.

Kanzi Engine represents Euler angles as Tait-Bryan angles where the rotations are applied in the order x, y and z.

Parameters

rotationX	Rotation angle around the x axis in radians.
rotationY	Rotation angle around the y axis in radians.
rotationZ	Rotation angle around the z axis in radians.

Returns: Rotated quaternion.

◆ normalized()

KZ_NO_DISCARD Quaternion kanzi::Quaternion::normalized ( ) const

Get normalized copy of this quaternion.

Normalized quaternion is called an unit quaternion. Calculates the magnitude from the dot product of the quaternion components, and divides all the quaternion components with the magnitude. Use this when rotating or transforming a vector with a quaternion, and when generating a rotation or transformation matrix from quaternion. Using unnormalized quaternion in calculations can lead to floating point rounding errors. The errors that result from using an unnormalized quaternion in calculations are proportional to the square of the quaternion's magnitude.

Returns: Normalized quaternion.

◆ conjugated()

Quaternion kanzi::Quaternion::conjugated ( ) const

inline

Get conjugated copy of this quaternion.

Conjugation inverses the quaternion axis components x, y and z. Use this to get the inverse rotation of a quaternion.

Returns: Conjugated quaternion.

◆ getX()

float kanzi::Quaternion::getX ( ) const

inline

Get the x component of the quaternion.

Returns: The x component.

◆ getY()

float kanzi::Quaternion::getY ( ) const

inline

Get the y component of the quaternion.

Returns: The y component.

◆ getZ()

float kanzi::Quaternion::getZ ( ) const

inline

Get the z component of the quaternion.

Returns: The z component.

◆ getW()

float kanzi::Quaternion::getW ( ) const

inline

Get the w component of the quaternion.

Returns: The w component.

◆ setX()

void kanzi::Quaternion::setX ( float x )

inline

Sets the x component of the quaternion.

Parameters

x	The new value of the x component.

◆ setY()

void kanzi::Quaternion::setY ( float y )

inline

Sets the y component of the quaternion.

Parameters

y	The new value of the y component.

◆ setZ()

void kanzi::Quaternion::setZ ( float z )

inline

Sets the z component of the quaternion.

Parameters

z	The new value of the z component.

◆ setW()

void kanzi::Quaternion::setW ( float w )

inline

Sets the w component of the quaternion.

Parameters

w	The new value of the w component.

◆ operator[]() [1/2]

float& kanzi::Quaternion::operator[] ( size_t index )

inline

Access individual components of a quaternion.

Parameters

index Index of the accessed component. Should be either 0, 1, 2, or 3.

Returns: If index is 0, x component. If index is 1, y component. If index is 2, z component. If index is 3, w component.

◆ operator[]() [2/2]

const float& kanzi::Quaternion::operator[] ( size_t index ) const

inline

Access individual components of a quaternion.

Parameters

index Index of the accessed component. Should be either 0, 1, 2, or 3.

Returns: If index is 0, x component. If index is 1, y component. If index is 2, z component. If index is 3, w component.

◆ operator*()

Quaternion kanzi::Quaternion::operator* ( float scalar ) const

inline

Multiplies each quaternion component with a scalar and returns the result.

Parameters

scalar Multiplier for each quaternion component.

Returns: Result quaternion.

◆ operator*=()

Quaternion& kanzi::Quaternion::operator*= ( float scalar )

inline

Multiplies each quaternion component with a scalar.

Parameters

scalar Multiplier for each quaternion component.

Returns: This quaternion.

◆ operator/()

Quaternion kanzi::Quaternion::operator/ ( float scalar ) const

inline

Divides each quaternion component with a scalar and returns the result.

Parameters

scalar Divisor for each quaternion component.

Returns: Result quaternion.

◆ operator/=()

Quaternion& kanzi::Quaternion::operator/= ( float scalar )

inline

Divides each quaternion component with a scalar.

Parameters

scalar Divisor for each quaternion component.

Returns: This quaternion.

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

kanzi/core/math/quaternion.hpp

Public Member Functions

Static Public Member Functions

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/2]

◆ Quaternion() [2/2]

Member Function Documentation

◆ createFromVector()

◆ createFromEulerAngles() [1/2]

◆ createFromEulerAngles() [2/2]

◆ normalized()

◆ conjugated()

◆ getX()

◆ getY()

◆ getZ()

◆ getW()

◆ setX()

◆ setY()

◆ setZ()

◆ setW()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ operator*()

◆ operator*=()

◆ operator/()

◆ operator/=()