The Quaternion class encapsulates the mathematics of the quaternion. More...

Public Member Functions
	Quaternion ()
	Default Constructor.
	Quaternion (float cosThetaBy2, float iBySineTheta, float jBySineTheta, float kBySineTheta)
	Constructs from a quaternion represented by floats.
	Quaternion (const Vector4 &vector)
	Constructs from a quaternion represented by a vector.
	Quaternion (Radian angle, const Vector3 &axis)
	Constructor from an axis and angle.
	Quaternion (Radian pitch, Radian yaw, Radian roll)
	Constructs from Euler angles.
	Quaternion (const Matrix &matrix)
	Constructs from a matrix.
	Quaternion (const Vector3 &xAxis, const Vector3 &yAxis, const Vector3 &zAxis)
	Constructs from 3 orthonormal axes.
	Quaternion (const Vector3 &v0, const Vector3 &v1)
	Constructs quaternion which describes minimum rotation to align v0 with v1.
	~Quaternion ()
	Destructor, nonvirtual as this is not a base class.
bool	IsIdentity () const
	Helper to check if this is an identity quaternion.
bool	ToAxisAngle (Vector3 &axis, Radian &angle) const
	Converts the quaternion to an axis/angle pair.
const Vector4 &	AsVector () const
	Returns the quaternion as a vector.
void	SetEuler (Radian pitch, Radian yaw, Radian roll)
	SetEuler sets the quaternion from the Euler angles applied in x, y, z order.
Vector4	EulerAngles () const
	Returns the Euler angles from a rotation Quaternion.
const Quaternion	operator+ (const Quaternion &other) const
	Addition operator.
const Quaternion	operator- (const Quaternion &other) const
	Subtraction operator.
const Quaternion	operator* (const Quaternion &other) const
	Multiplication operator.
Vector3	operator* (const Vector3 &other) const
	Multiplication operator.
const Quaternion	operator/ (const Quaternion &other) const
	Division operator.
const Quaternion	operator* (float scale) const
	Scale operator.
const Quaternion	operator/ (float scale) const
	Scale operator.
Quaternion	operator- () const
	Unary Negation operator.
const Quaternion &	operator+= (const Quaternion &other)
	Addition with Assignment operator.
const Quaternion &	operator-= (const Quaternion &other)
	Subtraction with Assignment operator.
const Quaternion &	operator*= (const Quaternion &other)
	Multiplication with Assignment operator.
const Quaternion &	operator*= (float scale)
	Scale with Assignment operator.
const Quaternion &	operator/= (float scale)
	Scale with Assignment operator.
bool	operator== (const Quaternion &rhs) const
	Equality operator.
bool	operator!= (const Quaternion &rhs) const
	Inequality operator.
float	Length () const
	Returns the length of the quaternion.
float	LengthSquared () const
	Returns the squared length of the quaternion.
void	Normalize ()
	Normalizes this to unit length.
Quaternion	Normalized () const
	Normalized.
void	Conjugate ()
	Conjugates this quaternion.
void	Invert ()
	Inverts this quaternion.
Quaternion	Log () const
	Performs the logarithm of a Quaternion = va where q = (cos(a),vsin(a)).
Quaternion	Exp () const
	Performs an exponent e^Quaternion = Exp(v*a) = (cos(a),vsin(a)).
Vector4	Rotate (const Vector4 &vector) const
	Rotates v by this Quaternion (Quaternion must be unit).
Vector3	Rotate (const Vector3 &vector) const
	Rotates v by this Quaternion (Quaternion must be unit).
Static Public Member Functions
static float	Dot (const Quaternion &q1, const Quaternion &q2)
	Returns the dot product of two quaternions.
static Quaternion	Lerp (const Quaternion &q1, const Quaternion &q2, float t)
	Linear Interpolation (using a straight line between the two quaternions).
static Quaternion	Slerp (const Quaternion &q1, const Quaternion &q2, float progress)
	Spherical Linear Interpolation (using the shortest arc of a great circle between the two quaternions).
static Quaternion	SlerpNoInvert (const Quaternion &q1, const Quaternion &q2, float t)
	This version of Slerp, used by Squad, does not check for theta > 90.
static Quaternion	Squad (const Quaternion &start, const Quaternion &end, const Quaternion &ctrl1, const Quaternion &ctrl2, float t)
	Spherical Cubic Interpolation.
static float	AngleBetween (const Quaternion &q1, const Quaternion &q2)
	Returns the shortest angle between two quaternions in Radians.
Public Attributes
Vector4	mVector
Static Public Attributes
static const Quaternion	IDENTITY
	(0.0f,0.0f,0.0f,1.0f)

Detailed Description

The Quaternion class encapsulates the mathematics of the quaternion.

Since:: 3.0, DALi version 1.0.0

Constructor & Destructor Documentation

Dali::Quaternion::Quaternion ( )

Default Constructor.

Since:: 3.0, DALi version 1.0.0

Dali::Quaternion::Quaternion	(	float	cosThetaBy2,
		float	iBySineTheta,
		float	jBySineTheta,
		float	kBySineTheta
	)

Constructs from a quaternion represented by floats.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	cosThetaBy2
[in]	iBySineTheta
[in]	jBySineTheta
[in]	kBySineTheta

Dali::Quaternion::Quaternion ( const Vector4 & vector ) [explicit]

Constructs from a quaternion represented by a vector.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] vector x,y,z fields represent i,j,k coefficients, w represents cos(theta/2)

Dali::Quaternion::Quaternion	(	Radian	angle,
		const Vector3 &	axis
	)

Constructor from an axis and angle.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	angle	The angle around the axis
[in]	axis	The vector of the axis

Dali::Quaternion::Quaternion	(	Radian	pitch,
		Radian	yaw,
		Radian	roll
	)

Constructs from Euler angles.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	pitch
[in]	yaw
[in]	roll

Dali::Quaternion::Quaternion ( const Matrix & matrix ) [explicit]

Constructs from a matrix.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] matrix

Dali::Quaternion::Quaternion	(	const Vector3 &	xAxis,
		const Vector3 &	yAxis,
		const Vector3 &	zAxis
	)		`[explicit]`

Constructs from 3 orthonormal axes.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	xAxis	The X axis
[in]	yAxis	The Y axis
[in]	zAxis	The Z axis

Dali::Quaternion::Quaternion	(	const Vector3 &	v0,
		const Vector3 &	v1
	)		`[explicit]`

Constructs quaternion which describes minimum rotation to align v0 with v1.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	v0	First normalized vector
[in]	v1	Second normalized vector

Precondition:: v0 and v1 should be normalized

Dali::Quaternion::~Quaternion ( )

Destructor, nonvirtual as this is not a base class.

Since:: 3.0, DALi version 1.0.0

Member Function Documentation

static float Dali::Quaternion::AngleBetween	(	const Quaternion &	q1,
		const Quaternion &	q2
	)		`[static]`

Returns the shortest angle between two quaternions in Radians.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	q1	The first quaternion
[in]	q2	The second quaternion

Returns:: The angle between the two quaternions

const Vector4& Dali::Quaternion::AsVector ( ) const

Returns the quaternion as a vector.

Since:: 3.0, DALi version 1.0.0

Returns:: The vector representation of the quaternion

void Dali::Quaternion::Conjugate ( )

Conjugates this quaternion.

Since:: 3.0, DALi version 1.0.0

static float Dali::Quaternion::Dot	(	const Quaternion &	q1,
		const Quaternion &	q2
	)		`[static]`

Returns the dot product of two quaternions.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	q1	The first quaternion
[in]	q2	The second quaternion

Returns:: The dot product of the two quaternions

Vector4 Dali::Quaternion::EulerAngles ( ) const

Returns the Euler angles from a rotation Quaternion.

Since:: 3.0, DALi version 1.0.0

Returns:: A vector of Euler angles (x == pitch, y == yaw, z == roll)

Quaternion Dali::Quaternion::Exp ( ) const

Performs an exponent e^Quaternion = Exp(v*a) = (cos(a),vsin(a)).

Since:: 3.0, DALi version 1.0.0

Returns:: A quaternion representing the exponent

void Dali::Quaternion::Invert ( )

Inverts this quaternion.

Since:: 3.0, DALi version 1.0.0

bool Dali::Quaternion::IsIdentity ( ) const

Helper to check if this is an identity quaternion.

Since:: 3.0, DALi version 1.0.0

Returns:: True if this is identity quaternion

float Dali::Quaternion::Length ( ) const

Returns the length of the quaternion.

Since:: 3.0, DALi version 1.0.0

Returns:: The length of the quaternion

float Dali::Quaternion::LengthSquared ( ) const

Returns the squared length of the quaternion.

Since:: 3.0, DALi version 1.0.0

Returns:: The squared length of the quaternion

static Quaternion Dali::Quaternion::Lerp	(	const Quaternion &	q1,
		const Quaternion &	q2,
		float	t
	)		`[static]`

Linear Interpolation (using a straight line between the two quaternions).

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	q1	The start quaternion
[in]	q2	The end quaternion
[in]	t	A progress value between 0 and 1

Returns:: The interpolated quaternion

Quaternion Dali::Quaternion::Log ( ) const

Performs the logarithm of a Quaternion = v*a where q = (cos(a),v*sin(a)).

Since:: 3.0, DALi version 1.0.0

Returns:: A quaternion representing the logarithm

void Dali::Quaternion::Normalize ( )

Normalizes this to unit length.

Since:: 3.0, DALi version 1.0.0

Quaternion Dali::Quaternion::Normalized ( ) const

Normalized.

Since:: 3.0, DALi version 1.0.0

Returns:: A normalized version of this quaternion

bool Dali::Quaternion::operator!= ( const Quaternion & rhs ) const

Inequality operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] rhs The quaternion to compare with

Returns:: True if the quaternions are not equal

const Quaternion Dali::Quaternion::operator* ( const Quaternion & other ) const

Multiplication operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to multiply

Returns:: A quaternion containing the result

Vector3 Dali::Quaternion::operator* ( const Vector3 & other ) const

Multiplication operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The vector to multiply

Returns:: A vector containing the result of the multiplication

const Quaternion Dali::Quaternion::operator* ( float scale ) const

Scale operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] scale A value to scale by

Returns:: A quaternion containing the result

const Quaternion& Dali::Quaternion::operator*= ( const Quaternion & other )

Multiplication with Assignment operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to multiply

Returns:: A reference to this

const Quaternion& Dali::Quaternion::operator*= ( float scale )

Scale with Assignment operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] scale the value to scale by

Returns:: A reference to this

const Quaternion Dali::Quaternion::operator+ ( const Quaternion & other ) const

Addition operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to add

Returns:: A quaternion containing the result of the addition

const Quaternion& Dali::Quaternion::operator+= ( const Quaternion & other )

Addition with Assignment operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to add

Returns:: A reference to this

const Quaternion Dali::Quaternion::operator- ( const Quaternion & other ) const

Subtraction operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to subtract

Returns:: A quaternion containing the result of the subtract

Quaternion Dali::Quaternion::operator- ( ) const

Unary Negation operator.

Since:: 3.0, DALi version 1.0.0

Returns:: A quaternion containing the negated result

const Quaternion& Dali::Quaternion::operator-= ( const Quaternion & other )

Subtraction with Assignment operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other The quaternion to subtract

Returns:: A reference to this

const Quaternion Dali::Quaternion::operator/ ( const Quaternion & other ) const

Division operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] other A quaternion to divide by

Returns:: A quaternion containing the result

const Quaternion Dali::Quaternion::operator/ ( float scale ) const

Scale operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] scale A value to scale by

Returns:: A quaternion containing the result

const Quaternion& Dali::Quaternion::operator/= ( float scale )

Scale with Assignment operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] scale The value to scale by

Returns:: A reference to this

bool Dali::Quaternion::operator== ( const Quaternion & rhs ) const

Equality operator.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] rhs The quaternion to compare with

Returns:: True if the quaternions are equal

Vector4 Dali::Quaternion::Rotate ( const Vector4 & vector ) const

Rotates v by this Quaternion (Quaternion must be unit).

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] vector A vector to rotate

Returns:: The rotated vector

Vector3 Dali::Quaternion::Rotate ( const Vector3 & vector ) const

Rotates v by this Quaternion (Quaternion must be unit).

Since:: 3.0, DALi version 1.0.0

Parameters:

[in] vector A vector to rotate

Returns:: The rotated vector

void Dali::Quaternion::SetEuler	(	Radian	pitch,
		Radian	yaw,
		Radian	roll
	)

SetEuler sets the quaternion from the Euler angles applied in x, y, z order.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	pitch
[in]	yaw
[in]	roll

static Quaternion Dali::Quaternion::Slerp	(	const Quaternion &	q1,
		const Quaternion &	q2,
		float	progress
	)		`[static]`

Spherical Linear Interpolation (using the shortest arc of a great circle between the two quaternions).

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	q1	The start quaternion
[in]	q2	The end quaternion
[in]	progress	A progress value between 0 and 1

Returns:: The interpolated quaternion

static Quaternion Dali::Quaternion::SlerpNoInvert	(	const Quaternion &	q1,
		const Quaternion &	q2,
		float	t
	)		`[static]`

This version of Slerp, used by Squad, does not check for theta > 90.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	q1	The start quaternion
[in]	q2	The end quaternion
[in]	t	A progress value between 0 and 1

Returns:: The interpolated quaternion

static Quaternion Dali::Quaternion::Squad	(	const Quaternion &	start,
		const Quaternion &	end,
		const Quaternion &	ctrl1,
		const Quaternion &	ctrl2,
		float	t
	)		`[static]`

Spherical Cubic Interpolation.

Since:: 3.0, DALi version 1.0.0

Parameters:

[in]	start	The start quaternion
[in]	end	The end quaternion
[in]	ctrl1	The control quaternion for q1
[in]	ctrl2	The control quaternion for q2
[in]	t	A progress value between 0 and 1

Returns:: The interpolated quaternion

bool Dali::Quaternion::ToAxisAngle	(	Vector3 &	axis,
		Radian &	angle
	)		const

Converts the quaternion to an axis/angle pair.

Since:: 3.0, DALi version 1.0.0

Parameters:

[out]	axis
[out]	angle	Angle in radians

Returns:: True if converted correctly

Member Data Documentation

Vector4 Dali::Quaternion::mVector

w component is s ( = cos(theta/2.0) )

Public Member Functions

Static Public Member Functions

Public Attributes

Static Public Attributes

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation