Public Member Functions
	Quaternion ()=default
	Default constructor, components are uninitialized.

	Quaternion (const Quaternion &q)
	Copy constructor, clones the provided quaternion.

	Quaternion (float x)
	Constructs quaternion with all components set to the same specified value.

	Quaternion (float x, float y, float z, float w)
	Constructs quaternion with all components set to the provided values.

	Quaternion (const Vector3 &v, float w)
	Constructs quaternion from a vector3 and scalar w value.

	Quaternion (Simd::Vec4::FloatArgType value)

void	StoreToFloat4 (float *values) const
	Stores the vector to an array of 4 floats. The floats need only be 4 byte aligned, 16 byte alignment is not required.

float	GetElement (int index) const
	We recommend using GetX,Y,Z,W. GetElement can be slower.

void	SetElement (int index, float v)
	We recommend using SetX,Y,Z,W. SetElement can be slower.

float	operator() (int index) const

void	Set (float x)

void	Set (float x, float y, float z, float w)

void	Set (const Vector3 &v, float w)

void	Set (const float values[])

Quaternion	GetConjugate () const
	The conjugate of a quaternion is (-x, -y, -z, w).

float	Dot (const Quaternion &q) const
	Dot product.

float	GetLengthSq () const

float	GetLength () const
	Returns length of the quaternion, full accuracy.

float	GetLengthEstimate () const
	Returns length of the quaternion, fast but low accuracy, uses raw estimate instructions.

float	GetLengthReciprocal () const
	Returns 1/length, full accuracy.

float	GetLengthReciprocalEstimate () const
	Returns 1/length of the quaternion, fast but low accuracy, uses raw estimate instructions.

Quaternion	GetNormalized () const
	Returns normalized quaternion, full accuracy.

Quaternion	GetNormalizedEstimate () const
	Returns normalized quaternion, fast but low accuracy, uses raw estimate instructions.

void	Normalize ()
	Normalizes the quaternion in-place, full accuracy.

void	NormalizeEstimate ()
	Normalizes the quaternion in-place, fast but low accuracy, uses raw estimate instructions.

Quaternion	Lerp (const Quaternion &dest, float t) const

Quaternion	NLerp (const Quaternion &dest, float t) const

Quaternion	Slerp (const Quaternion &dest, float t) const
	Spherical linear interpolation. Result is not normalized.

Quaternion	Squad (const Quaternion &dest, const Quaternion &in, const Quaternion &out, float t) const

bool	IsClose (const Quaternion &q, float tolerance=Constants::Tolerance) const
	Checks if the quaternion is close to another quaternion with a given floating point tolerance.

bool	IsIdentity (float tolerance=Constants::Tolerance) const

bool	IsZero (float tolerance=Constants::FloatEpsilon) const

Quaternion &	operator= (const Quaternion &rhs)

Quaternion	operator- () const

Quaternion	operator+ (const Quaternion &q) const

Quaternion	operator- (const Quaternion &q) const

Quaternion	operator* (const Quaternion &q) const

Quaternion	operator* (float multiplier) const

Quaternion	operator/ (float divisor) const

Quaternion &	operator+= (const Quaternion &q)

Quaternion &	operator-= (const Quaternion &q)

Quaternion &	*operator=** (const Quaternion &q)

Quaternion &	*operator=** (float multiplier)

Quaternion &	operator/= (float divisor)

bool	operator== (const Quaternion &rhs) const

bool	operator!= (const Quaternion &rhs) const

Vector3	TransformVector (const Vector3 &v) const
	Transforms a vector using the rotation described by this quaternion.

Vector3	GetEulerDegrees () const

Vector3	GetEulerRadians () const

Vector3	GetEulerDegreesXYZ () const

Vector3	GetEulerRadiansXYZ () const

Vector3	GetEulerDegreesYXZ () const

Vector3	GetEulerRadiansYXZ () const

Vector3	GetEulerDegreesZYX () const

Vector3	GetEulerRadiansZYX () const

void	SetFromEulerRadians (const Vector3 &eulerRadians)

void	SetFromEulerDegrees (const Vector3 &eulerDegrees)

void	ConvertToAxisAngle (Vector3 &outAxis, float &outAngle) const

Vector3	ConvertToScaledAxisAngle () const
	Convert the quaternion into scaled axis-angle representation.

Vector3	GetImaginary () const
	Returns the imaginary (X/Y/Z) portion of the quaternion.

float	GetAngle () const
	Return angle in radians.

bool	IsFinite () const

Simd::Vec4::FloatType	GetSimdValue () const


float	GetX () const

float	GetY () const

float	GetZ () const

float	GetW () const

void	SetX (float x)

void	SetY (float y)

void	SetZ (float z)

void	SetW (float w)


Quaternion	GetInverseFast () const

void	InvertFast ()


Quaternion	GetInverseFull () const

void	InvertFull ()


float	NormalizeWithLength ()

float	NormalizeWithLengthEstimate ()


Quaternion	GetShortestEquivalent () const

void	ShortestEquivalent ()

Static Public Member Functions
static void	Reflect (ReflectContext *context)

static Quaternion	CreateIdentity ()

static Quaternion	CreateZero ()

static Quaternion	CreateFromFloat4 (const float *values)
	Sets components from an array of 4 floats, stored in xyzw order.

static Quaternion	CreateFromVector3 (const Vector3 &v)
	Sets components using a Vector3 for the imaginary part and setting the real part to zero.

static Quaternion	CreateFromVector3AndValue (const Vector3 &v, float w)
	Sets components using a Vector3 for the imaginary part and a float for the real part.

static Quaternion	CreateFromEulerRadiansXYZ (const Vector3 &eulerRadians)

static Quaternion	CreateFromEulerRadiansYXZ (const Vector3 &eulerRadians)

static Quaternion	CreateFromEulerRadiansZYX (const Vector3 &eulerRadians)

static Quaternion	CreateFromEulerDegreesXYZ (const Vector3 &eulerDegrees)

static Quaternion	CreateFromEulerDegreesYXZ (const Vector3 &eulerDegrees)

static Quaternion	CreateFromEulerDegreesZYX (const Vector3 &eulerDegrees)

static Quaternion	CreateFromMatrix3x3 (const class Matrix3x3 &m)
	Creates a quaternion from a Matrix3x3.

static Quaternion	CreateFromMatrix3x4 (const class Matrix3x4 &m)

static Quaternion	CreateFromMatrix4x4 (const class Matrix4x4 &m)
	Creates a quaternion using the rotation part of a Matrix4x4.

static Quaternion	CreateFromBasis (const Vector3 &basisX, const Vector3 &basisY, const Vector3 &basisZ)
	Creates a quaternion from a set of basis vectors.

static Quaternion	CreateFromAxisAngle (const Vector3 &axis, float angle)

static Quaternion	CreateFromScaledAxisAngle (const Vector3 &scaledAxisAngle)
	Create a quaternion from a scaled axis-angle representation.

static Quaternion	CreateShortestArc (const Vector3 &v1, const Vector3 &v2)

static const Quaternion	CreateFromEulerAnglesDegrees (const Vector3 &anglesInDegrees)

static const Quaternion	CreateFromEulerAnglesRadians (const Vector3 &anglesInRadians)


static Quaternion	CreateRotationX (float angleInRadians)

static Quaternion	CreateRotationY (float angleInRadians)

static Quaternion	CreateRotationZ (float angleInRadians)

Constructor & Destructor Documentation

◆ Quaternion()

AZ_MATH_INLINE AZ::Quaternion::Quaternion ( Simd::Vec4::FloatArgType value )

explicit

Constructs quaternion from a SIMD type. For internal use only, arrangement of values in SIMD type is not guaranteed.

Member Function Documentation

◆ ConvertToAxisAngle()

void AZ::Quaternion::ConvertToAxisAngle	(	Vector3 &	outAxis,
		float &	outAngle
	)		const

Populate axis and angle of rotation from Quaternion

Parameters

[out]	outAxis	A Vector3 defining the rotation axis.
[out]	outAngle	A float rotation angle around the axis in radians.

◆ CreateFromEulerAnglesDegrees()

static const Quaternion AZ::Quaternion::CreateFromEulerAnglesDegrees ( const Vector3 & anglesInDegrees )

static

O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use CreateFromEulerDegreesXYZ() Creates a quaternion using rotation in degrees about the axes. First rotated about the X axis, followed by the Y axis, then the Z axis.

◆ CreateFromEulerAnglesRadians()

static const Quaternion AZ::Quaternion::CreateFromEulerAnglesRadians ( const Vector3 & anglesInRadians )

static

O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use CreateFromEulerRadiansXYZ() Creates a quaternion using rotation in radians about the axes. First rotated about the X axis, followed by the Y axis, then the Z axis.

◆ CreateFromMatrix3x4()

static Quaternion AZ::Quaternion::CreateFromMatrix3x4 ( const class Matrix3x4 & m )

static

Creates a quaternion using the left 3x3 part of a Matrix3x4.

Note: If the matrix has a scale other than (1, 1, 1) be sure to extract the scale first with AZ::Matrix3x4::ExtractScale or ::ExtractScaleExact.

◆ CreateRotationX()

AZ_MATH_INLINE Quaternion AZ::Quaternion::CreateRotationX ( float angleInRadians )

static

Sets the quaternion to be a rotation around a specified axis in radians.

◆ GetEulerDegrees()

AZ_MATH_INLINE Vector3 AZ::Quaternion::GetEulerDegrees ( ) const

Create, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first x-axis, then y-axis and then z-axis.

Returns: Vector3 A vector containing component-wise rotation angles in degrees. O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use GetEulerDegreesXYZ()

◆ GetEulerDegreesXYZ()

AZ_MATH_INLINE Vector3 AZ::Quaternion::GetEulerDegreesXYZ ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first x-axis (roll), then y-axis (pitch) and then z-axis (yaw). The quaternion us supposed to be created with CreateFromEulerRadiansXYZ() or CreateFromEulerDegreesXYZ(). Note that a gimbal lock occurs with the y-axis rotation equal to +-90 degrees, loosing information on initial yaw and roll, and then roll is deliberately zeroed.

Returns: Vector3 A vector containing component-wise rotation angles in degrees.

◆ GetEulerDegreesYXZ()

AZ_MATH_INLINE Vector3 AZ::Quaternion::GetEulerDegreesYXZ ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first y-axis (pitch), then x-axis (roll) and then z-axis (yaw). The quaternion us supposed to be created with CreateFromEulerRadiansYXZ() or CreateFromEulerDegreesYXZ().

Returns: Vector3 A vector containing component-wise rotation angles in degrees.

◆ GetEulerDegreesZYX()

AZ_MATH_INLINE Vector3 AZ::Quaternion::GetEulerDegreesZYX ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first z-axis (yaw), then y-axis (pitch) and then x-axis (roll). The quaternion us supposed to be created with CreateFromEulerRadiansZYX() or CreateFromEulerDegreesZYX(). Note that a gimbal lock occurs with the y-axis rotation equal to +-90 degrees, loosing information on initial yaw and roll, and then roll is deliberately zeroed.

Returns: Vector3 A vector containing component-wise rotation angles in degrees.

◆ GetEulerRadians()

Vector3 AZ::Quaternion::GetEulerRadians ( ) const

Create, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first x-axis, then y-axis and then z-axis.

Returns: Vector3 A vector containing component-wise rotation angles in radians. O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use GetEulerRadiansXYZ()

◆ GetEulerRadiansXYZ()

Vector3 AZ::Quaternion::GetEulerRadiansXYZ ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first x-axis (roll), then y-axis (pitch) and then z-axis (yaw). The quaternion us supposed to be created with CreateFromEulerRadiansXYZ() or CreateFromEulerDegreesXYZ(). Note that a gimbal lock occurs with the y-axis rotation equal to +-90 degrees, loosing information on initial yaw and roll, and then roll is deliberately zeroed.

Returns: Vector3 A vector containing component-wise rotation angles in radians.

◆ GetEulerRadiansYXZ()

Vector3 AZ::Quaternion::GetEulerRadiansYXZ ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first y-axis (pitch), then x-axis (roll) and then z-axis (yaw). The quaternion us supposed to be created with CreateFromEulerRadiansYXZ() or CreateFromEulerDegreesYXZ().

Returns: Vector3 A vector containing component-wise rotation angles in radians.

◆ GetEulerRadiansZYX()

Vector3 AZ::Quaternion::GetEulerRadiansZYX ( ) const

Compute, from the quaternion, a set of Euler (actually Tait-Bryan) angles of rotations around: first z-axis (yaw), then y-axis (pitch) and then x-axis (roll). The quaternion us supposed to be created with CreateFromEulerRadiansZYX() or CreateFromEulerDegreesZYX(). Note that a gimbal lock occurs with the y-axis rotation equal to +-90 degrees, loosing information on initial yaw and roll, and then roll is deliberately zeroed.

Returns: Vector3 A vector containing component-wise rotation angles in radians.

◆ GetInverseFast()

AZ_MATH_INLINE Quaternion AZ::Quaternion::GetInverseFast ( ) const

For a unit quaternion, the inverse is just the conjugate. This function assumes a unit quaternion.

◆ GetInverseFull()

AZ_MATH_INLINE Quaternion AZ::Quaternion::GetInverseFull ( ) const

This is the inverse for any quaternion, not just unit quaternions.

◆ GetShortestEquivalent()

AZ_MATH_INLINE Quaternion AZ::Quaternion::GetShortestEquivalent ( ) const

Get the shortest equivalent of the rotation. In case the w component of the quaternion is negative the rotation is > 180° and taking the longer path. The quaternion will be inverted in that case to take the shortest path of rotation.

◆ GetX()

AZ_MATH_INLINE float AZ::Quaternion::GetX ( ) const

Component access

◆ Lerp()

AZ_MATH_INLINE Quaternion AZ::Quaternion::Lerp	(	const Quaternion &	dest,
		float	t
	)		const

Linearly interpolate towards a destination quaternion.

Parameters

[in]	dest	The quaternion to interpolate towards.
[in]	t	Normalized interpolation value where 0.0 represents the current and 1.0 the destination value.

Returns: The interpolated quaternion at the given interpolation point.

◆ NLerp()

AZ_MATH_INLINE Quaternion AZ::Quaternion::NLerp	(	const Quaternion &	dest,
		float	t
	)		const

Linearly interpolate towards a destination quaternion, and normalize afterwards.

Parameters

[in]	dest	The quaternion to interpolate towards.
[in]	t	Normalized interpolation value where 0.0 represents the current and 1.0 the destination value.

Returns: The interpolated and normalized quaternion at the given interpolation point.

◆ NormalizeWithLength()

AZ_MATH_INLINE float AZ::Quaternion::NormalizeWithLength ( )

Normalizes the vector in-place and returns the previous length. This takes a few more instructions than calling just Normalize().

◆ operator()()

AZ_MATH_INLINE float AZ::Quaternion::operator() ( int index ) const

Indexed access using operator(). It's just for convenience.

Note: This can be slower than using GetX,GetY, etc.

◆ Reflect()

static void AZ::Quaternion::Reflect ( ReflectContext * context )

static

AzCore Reflection.

Parameters

context reflection context

◆ SetFromEulerDegrees()

AZ_MATH_INLINE void AZ::Quaternion::SetFromEulerDegrees ( const Vector3 & eulerDegrees )

Parameters

eulerDegrees A vector containing component-wise rotation angles in degrees. O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use CreateFromEulerDegreesXYZ()

◆ SetFromEulerRadians()

void AZ::Quaternion::SetFromEulerRadians ( const Vector3 & eulerRadians )

Parameters

eulerRadians A vector containing component-wise rotation angles in radians. O3DE_DEPRECATION_NOTICE(GHI-10929)

Deprecated:: use CreateFromEulerRadiansXYZ()

◆ Squad()

AZ_MATH_INLINE Quaternion AZ::Quaternion::Squad	(	const Quaternion &	dest,
		const Quaternion &	in,
		const Quaternion &	out,
		float	t
	)		const

Spherical linear interpolation, but with in/out tangent quaternions. Squad(p,a,b,q,t) = Slerp(Slerp(p,q,t), Slerp(a,b,t); 2(1-t)t).

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

Code/Framework/AzCore/AzCore/Math/Quaternion.h
Code/Framework/AzCore/AzCore/Math/Quaternion.inl

Public Member Functions

Static Public Member Functions

Constructor & Destructor Documentation

◆ Quaternion()

Member Function Documentation

◆ ConvertToAxisAngle()

◆ CreateFromEulerAnglesDegrees()

◆ CreateFromEulerAnglesRadians()

◆ CreateFromMatrix3x4()

◆ CreateRotationX()

◆ GetEulerDegrees()

◆ GetEulerDegreesXYZ()

◆ GetEulerDegreesYXZ()

◆ GetEulerDegreesZYX()

◆ GetEulerRadians()

◆ GetEulerRadiansXYZ()

◆ GetEulerRadiansYXZ()

◆ GetEulerRadiansZYX()

◆ GetInverseFast()

◆ GetInverseFull()

◆ GetShortestEquivalent()

◆ GetX()

◆ Lerp()

◆ NLerp()

◆ NormalizeWithLength()

◆ operator()()

◆ Reflect()

◆ SetFromEulerDegrees()

◆ SetFromEulerRadians()

◆ Squad()