Quaternion class for representing rotations. More...

#include <quaternion.h>

Public Member Functions
	quaternion ()
	Default Constructor.
	quaternion (const matrix4 &mat)
	Constructor which converts a matrix to a quaternion.
	quaternion (const vector3df &vec)
	Constructor which converts euler angles (radians) to a quaternion.
	quaternion (f32 x, f32 y, f32 z)
	Constructor which converts euler angles (radians) to a quaternion.
	quaternion (f32 x, f32 y, f32 z, f32 w)
	Constructor.
f32	dotProduct (const quaternion &other) const
	Calculates the dot product.
bool	equals (const quaternion &other, const f32 tolerance=ROUNDING_ERROR_f32) const
	returns if this quaternion equals the other one, taking floating point rounding errors into account
quaternion &	fromAngleAxis (f32 angle, const vector3df &axis)
	Create quaternion from rotation angle and rotation axis.
matrix4	getMatrix () const
	Creates a matrix from this quaternion.
void	getMatrix (matrix4 &dest, const core::vector3df &translation=core::vector3df()) const
	Creates a matrix from this quaternion.
void	getMatrix_transposed (matrix4 &dest) const
	Creates a matrix from this quaternion.
void	getMatrixCenter (matrix4 &dest, const core::vector3df &center, const core::vector3df &translation) const
quaternion &	lerp (quaternion q1, quaternion q2, f32 time)
	Set this quaternion to the linear interpolation between two quaternions.
quaternion &	makeIdentity ()
	Set quaternion to identity.
quaternion &	makeInverse ()
	Inverts this quaternion.
quaternion &	normalize ()
	Normalizes the quaternion.
bool	operator!= (const quaternion &other) const
	inequality operator
quaternion	operator* (const quaternion &other) const
	Multiplication operator.
vector3df	operator* (const vector3df &v) const
	Multiplication operator.
quaternion	operator* (f32 s) const
	Multiplication operator with scalar.
quaternion &	operator*= (const quaternion &other)
	Multiplication operator.
quaternion &	operator*= (f32 s)
	Multiplication operator with scalar.
quaternion	operator+ (const quaternion &other) const
	Add operator.
quaternion &	operator= (const matrix4 &other)
	Matrix assignment operator.
quaternion &	operator= (const quaternion &other)
	Assignment operator.
bool	operator== (const quaternion &other) const
	Equalilty operator.
quaternion &	rotationFromTo (const vector3df &from, const vector3df &to)
	Set quaternion to represent a rotation from one vector to another.
quaternion &	set (const core::quaternion &quat)
	Sets new quaternion from other quaternion.
quaternion &	set (const core::vector3df &vec)
	Sets new quaternion based on euler angles (radians).
quaternion &	set (f32 x, f32 y, f32 z)
	Sets new quaternion based on euler angles (radians).
quaternion &	set (f32 x, f32 y, f32 z, f32 w)
	Sets new quaternion.
quaternion &	slerp (quaternion q1, quaternion q2, f32 time, f32 threshold=.05f)
	Set this quaternion to the result of the spherical interpolation between two quaternions.
void	toAngleAxis (f32 &angle, core::vector3df &axis) const
	Fills an angle (radians) around an axis (unit vector).
void	toEuler (vector3df &euler) const
	Output this quaternion to an euler angle (radians).

Public Attributes
f32	W
f32	X
	Quaternion elements.
f32	Y
f32	Z

Detailed Description

Quaternion class for representing rotations.

It provides cheap combinations and avoids gimbal locks. Also useful for interpolations.

Definition at line 26 of file quaternion.h.

Constructor & Destructor Documentation

◆ quaternion() [1/5]

irr::core::quaternion::quaternion ( )

inline

Default Constructor.

Definition at line 31 of file quaternion.h.

References W, X, Y, and Z.

Referenced by dotProduct(), equals(), fromAngleAxis(), lerp(), makeInverse(), normalize(), operator!=(), operator*(), operator*(), operator*=(), operator*=(), operator+(), operator=(), operator=(), operator==(), set(), set(), set(), set(), and slerp().

◆ quaternion() [2/5]

irr::core::quaternion::quaternion	(	f32	x,
		f32	y,
		f32	z,
		f32	w )

inline

Constructor.

Definition at line 34 of file quaternion.h.

References W, X, Y, and Z.

◆ quaternion() [3/5]

irr::core::quaternion::quaternion	(	f32	x,
		f32	y,
		f32	z )

inline

Constructor which converts euler angles (radians) to a quaternion.

Definition at line 187 of file quaternion.h.

References set().

◆ quaternion() [4/5]

irr::core::quaternion::quaternion ( const vector3df & vec )

inline

Constructor which converts euler angles (radians) to a quaternion.

Definition at line 194 of file quaternion.h.

References set(), irr::core::vector3d< T >::X, irr::core::vector3d< T >::Y, and irr::core::vector3d< T >::Z.

◆ quaternion() [5/5]

irr::core::quaternion::quaternion ( const matrix4 & mat )

inline

Constructor which converts a matrix to a quaternion.

Definition at line 201 of file quaternion.h.

Member Function Documentation

◆ dotProduct()

f32 irr::core::quaternion::dotProduct ( const quaternion & other ) const

inline

Calculates the dot product.

Definition at line 556 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

Referenced by slerp().

◆ equals()

bool irr::core::quaternion::equals	(	const quaternion &	other,
		const f32	tolerance = ROUNDING_ERROR_f32 ) const

inline

returns if this quaternion equals the other one, taking floating point rounding errors into account

Definition at line 500 of file quaternion.h.

References quaternion(), irr::core::equals(), W, X, Y, and Z.

◆ fromAngleAxis()

quaternion & irr::core::quaternion::fromAngleAxis	(	f32	angle,
		const vector3df &	axis )

inline

Create quaternion from rotation angle and rotation axis.

axis must be unit length, angle in radians

Axis must be unit length. The quaternion representing the rotation is q = cos(A/2)+sin(A/2)*(x*i+y*j+z*k).

Parameters

angle	Rotation Angle in radians.
axis	Rotation axis.

Definition at line 563 of file quaternion.h.

References quaternion(), W, X, irr::core::vector3d< T >::X, Y, irr::core::vector3d< T >::Y, Z, and irr::core::vector3d< T >::Z.

◆ getMatrix() [1/2]

matrix4 irr::core::quaternion::getMatrix ( ) const

inline

Creates a matrix from this quaternion.

Definition at line 338 of file quaternion.h.

References getMatrix().

Referenced by getMatrix().

◆ getMatrix() [2/2]

void irr::core::quaternion::getMatrix	(	matrix4 &	dest,
		const core::vector3df &	center = core::vector3df() ) const

inline

Creates a matrix from this quaternion.

Creates a matrix from this quaternion

Definition at line 349 of file quaternion.h.

References irr::core::CMatrix4< T >::setDefinitelyIdentityMatrix(), W, X, irr::core::vector3d< T >::X, Y, irr::core::vector3d< T >::Y, Z, and irr::core::vector3d< T >::Z.

◆ getMatrix_transposed()

void irr::core::quaternion::getMatrix_transposed ( matrix4 & dest ) const

inline

Creates a matrix from this quaternion.

Definition at line 411 of file quaternion.h.

References irr::core::CMatrix4< T >::setDefinitelyIdentityMatrix(), W, X, Y, and Z.

◆ getMatrixCenter()

void irr::core::quaternion::getMatrixCenter	(	matrix4 &	dest,
		const core::vector3df &	center,
		const core::vector3df &	translation ) const

inline

Creates a matrix from this quaternion Rotate about a center point shortcut for core::quaternion q; q.rotationFromTo ( vin[i].Normal, forward ); q.getMatrixCenter ( lookat, center, newPos );

core::matrix4 m2; m2.setInverseTranslation ( center ); lookat *= m2;

core::matrix4 m3; m2.setTranslation ( newPos ); lookat *= m3;

Creates a matrix from this quaternion Rotate about a center point shortcut for core::quaternion q; q.rotationFromTo(vin[i].Normal, forward); q.getMatrix(lookat, center);

core::matrix4 m2; m2.setInverseTranslation(center); lookat *= m2;

Definition at line 388 of file quaternion.h.

References irr::core::CMatrix4< T >::setRotationCenter(), W, X, Y, and Z.

◆ lerp()

quaternion & irr::core::quaternion::lerp	(	quaternion	q1,
		quaternion	q2,
		f32	time )

inline

Set this quaternion to the linear interpolation between two quaternions.

Parameters

q1	First quaternion to be interpolated.
q2	Second quaternion to be interpolated.
time	Progress of interpolation. For time=0 the result is q1, for time=1 the result is q2. Otherwise interpolation between q1 and q2.

Definition at line 523 of file quaternion.h.

References quaternion().

Referenced by slerp().

◆ makeIdentity()

core::quaternion & irr::core::quaternion::makeIdentity ( )

inline

Set quaternion to identity.

Definition at line 649 of file quaternion.h.

References W, X, Y, and Z.

Referenced by rotationFromTo().

◆ makeInverse()

quaternion & irr::core::quaternion::makeInverse ( )

inline

Inverts this quaternion.

Definition at line 438 of file quaternion.h.

References quaternion(), X, Y, and Z.

◆ normalize()

quaternion & irr::core::quaternion::normalize ( )

inline

Normalizes the quaternion.

Definition at line 510 of file quaternion.h.

References quaternion(), irr::core::reciprocal_squareroot(), W, X, Y, and Z.

Referenced by operator=(), rotationFromTo(), and set().

◆ operator!=()

bool irr::core::quaternion::operator!= ( const quaternion & other ) const

inline

inequality operator

Definition at line 217 of file quaternion.h.

References quaternion().

◆ operator*() [1/3]

quaternion irr::core::quaternion::operator* ( const quaternion & other ) const

inline

Multiplication operator.

Definition at line 294 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ operator*() [2/3]

vector3df irr::core::quaternion::operator* ( const vector3df & v ) const

inline

Multiplication operator.

Definition at line 634 of file quaternion.h.

References irr::core::vector3d< T >::crossProduct(), W, X, Y, and Z.

◆ operator*() [3/3]

quaternion irr::core::quaternion::operator* ( f32 s ) const

inline

Multiplication operator with scalar.

Definition at line 308 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ operator*=() [1/2]

quaternion & irr::core::quaternion::operator*= ( const quaternion & other )

inline

Multiplication operator.

Definition at line 325 of file quaternion.h.

References quaternion().

◆ operator*=() [2/2]

quaternion & irr::core::quaternion::operator*= ( f32 s )

inline

Multiplication operator with scalar.

Definition at line 315 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ operator+()

quaternion irr::core::quaternion::operator+ ( const quaternion & other ) const

inline

Add operator.

Definition at line 331 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ operator=() [1/2]

quaternion & irr::core::quaternion::operator= ( const matrix4 & other )

inline

Matrix assignment operator.

Definition at line 234 of file quaternion.h.

References quaternion(), normalize(), W, X, Y, and Z.

◆ operator=() [2/2]

quaternion & irr::core::quaternion::operator= ( const quaternion & other )

inline

Assignment operator.

Definition at line 223 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ operator==()

bool irr::core::quaternion::operator== ( const quaternion & other ) const

inline

Equalilty operator.

Definition at line 208 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

◆ rotationFromTo()

core::quaternion & irr::core::quaternion::rotationFromTo	(	const vector3df &	from,
		const vector3df &	to )

inline

Set quaternion to represent a rotation from one vector to another.

Definition at line 658 of file quaternion.h.

References irr::core::vector3d< T >::crossProduct(), irr::core::vector3d< T >::dotProduct(), irr::core::vector3d< T >::getLength(), makeIdentity(), normalize(), irr::core::vector3d< T >::normalize(), set(), irr::core::vector3d< T >::set(), irr::core::vector3d< T >::X, irr::core::vector3d< T >::Y, and irr::core::vector3d< T >::Z.

◆ set() [1/4]

quaternion & irr::core::quaternion::set ( const core::quaternion & quat )

inline

Sets new quaternion from other quaternion.

Definition at line 493 of file quaternion.h.

References quaternion().

◆ set() [2/4]

quaternion & irr::core::quaternion::set ( const core::vector3df & vec )

inline

Sets new quaternion based on euler angles (radians).

Definition at line 487 of file quaternion.h.

References quaternion(), set(), irr::core::vector3d< T >::X, irr::core::vector3d< T >::Y, and irr::core::vector3d< T >::Z.

◆ set() [3/4]

quaternion & irr::core::quaternion::set	(	f32	x,
		f32	y,
		f32	z )

inline

Sets new quaternion based on euler angles (radians).

Definition at line 457 of file quaternion.h.

References quaternion(), normalize(), W, X, Y, and Z.

◆ set() [4/4]

quaternion & irr::core::quaternion::set	(	f32	x,
		f32	y,
		f32	z,
		f32	w )

inline

Sets new quaternion.

Definition at line 446 of file quaternion.h.

References quaternion(), W, X, Y, and Z.

Referenced by quaternion(), quaternion(), rotationFromTo(), and set().

◆ slerp()

quaternion & irr::core::quaternion::slerp	(	quaternion	q1,
		quaternion	q2,
		f32	time,
		f32	threshold = .05f )

inline

Set this quaternion to the result of the spherical interpolation between two quaternions.

Parameters

q1	First quaternion to be interpolated.
q2	Second quaternion to be interpolated.
time	Progress of interpolation. For time=0 the result is q1, for time=1 the result is q2. Otherwise interpolation between q1 and q2.
threshold	To avoid inaccuracies at the end (time=1) the interpolation switches to linear interpolation at some point. This value defines how much of the remaining interpolation will be calculated with lerp. Everything from 1-threshold up will be linear interpolation.

Definition at line 531 of file quaternion.h.

References quaternion(), dotProduct(), lerp(), and irr::core::reciprocal().