PLMath::Quaternion Class Reference

Quaternion. More...

#include <Quaternion.h>

List of all members.

Public Types
enum	Component { W = 0, X = 1, Y = 2, Z = 3 }
	Component. More...
Public Member Functions
	Quaternion ()
	Default constructor setting an identity quaternion.
	Quaternion (float fW, float fX, float fY, float fZ)
	Quaternion (const float fQ[])
	Quaternion (const Quaternion &qQ)
	Quaternion (const Vector3 &vAxis, float fAngle)
PLMATH_API	Quaternion (const Matrix3x3 &mRot)
PLMATH_API	Quaternion (const Matrix3x4 &mRot)
PLMATH_API	Quaternion (const Matrix4x4 &mRot)
	~Quaternion ()
Quaternion	operator+ (const Quaternion &qQ) const
Quaternion &	operator+= (const Quaternion &qQ)
Quaternion	operator- () const
Quaternion	operator- (const Quaternion &qQ) const
Quaternion &	operator-= (const Quaternion &qQ)
Quaternion	operator* (float f) const
Quaternion &	operator*= (float f)
Quaternion	operator* (const Quaternion &qQ) const
Quaternion &	operator*= (const Quaternion &qQ)
Vector3	operator* (const Vector3 &vV) const
Vector4	operator* (const Vector4 &vV) const
Quaternion	operator/ (float f) const
Quaternion &	operator/= (float f)
Quaternion &	operator= (const Quaternion &qQ)
bool	operator== (const Quaternion &qQ) const
bool	operator!= (const Quaternion &qQ) const
	operator float * ()
	operator const float * () const
Quaternion &	SetWXYZ (float fW, float fX, float fY, float fZ)
	Sets the component of the quaternion.
Quaternion &	SetWXYZ (const float fValues[])
	Sets the component of the quaternion.
PLMATH_API void	ToAxisAngle (float &fX, float &fY, float &fZ, float &fAngle) const
	Returns a selected axis and angle from the rotation quaternion.
PLMATH_API Quaternion &	FromAxisAngle (float fX, float fY, float fZ, float fAngle)
	Sets a rotation quaternion by using a selected axis and angle.
PLMATH_API Vector3	GetXAxis () const
	Returns the x (left) axis.
PLMATH_API Vector3	GetYAxis () const
	Returns the y (up) axis.
PLMATH_API Vector3	GetZAxis () const
	Returns the z (forward) axis.
PLMATH_API void	ToRotationMatrix (Matrix3x3 &mRot) const
	Returns the rotation quaternion as 3x3 matrix.
PLMATH_API Quaternion &	FromRotationMatrix (const Matrix3x3 &mRot)
	Sets a rotation quaternion by using a 3x3 rotation matrix.
PLMATH_API void	ToRotationMatrix (Matrix3x4 &mRot) const
	Returns the rotation quaternion as 3x4 matrix.
PLMATH_API Quaternion &	FromRotationMatrix (const Matrix3x4 &mRot)
	Sets a rotation quaternion by using a 3x4 rotation matrix.
PLMATH_API void	ToRotationMatrix (Matrix4x4 &mRot) const
	Returns the rotation quaternion as 4x4 matrix.
PLMATH_API Quaternion &	FromRotationMatrix (const Matrix4x4 &mRot)
	Sets a rotation quaternion by using a 4x4 rotation matrix.
bool	Compare (const Quaternion &qQ, float fEpsilon=Math::Epsilon) const
	Compares two quaternions using an epsilon environment.
float	GetLength () const
	Returns the length (also called magnitude) of the quaternion.
float	GetSquaredLength () const
	Returns the squared length (norm) of the quaternion.
float	DotProduct (const Quaternion &qQ) const
	Returns the dot product of this quaternion and another one.
Quaternion &	Normalize ()
	Normalizes the quaternion.
Quaternion	GetNormalized () const
	Returns a normalized quaternion.
void	Conjugate ()
	Conjugates the quaternion.
Quaternion	GetConjugated () const
	Returns the conjugated of the quaternion.
void	Invert ()
	Inverts the quaternion.
Quaternion	GetInverted () const
	Returns the inverted quaternion.
void	UnitInvert ()
	Inverts the normalized quaternion.
Quaternion	GetUnitInverted () const
	Returns the inverted normalized quaternion.
Quaternion &	Exp ()
	Calculates the exponential of the quaternion.
Quaternion	GetExp () const
	Returns the exponential of the quaternion.
Quaternion &	Log ()
Quaternion	GetLog () const
Quaternion &	Power (float fPower)
	Calculates the power of the quaternion.
Quaternion	GetPower (float fPower) const
	Returns the power of the quaternion.
PLMATH_API void	Slerp (const Quaternion &qQ1, const Quaternion &qQ2, float fTime)
	Computes spherical linear interpolation between qQ1 and qQ2 with time 0-1.
PLMATH_API PLCore::String	ToString () const
	To string.
PLMATH_API bool	FromString (const PLCore::String &sString)
	From string.
Public Attributes
union {
float   fQ [4]
struct {
float   w
float   x
float   y
float   z
}
};
	Some direct quaternion element accesses.
Static Public Attributes
static PLMATH_API const Quaternion	Zero
static PLMATH_API const Quaternion	Identity

---

Detailed Description

Quaternion.

Note:

• Orientation quaternions are unit quaternions

---

Member Enumeration Documentation

enum PLMath::Quaternion::Component

Component.

Enumerator:

W	W component
X	X component
Y	Y component
Z	Z component

---

Constructor & Destructor Documentation

PLMath::Quaternion::Quaternion

(

)

[inline]

Default constructor setting an identity quaternion.

PLMath::Quaternion::Quaternion	(	float	fW,
		float	fX,
		float	fY,
		float	fZ
	)		[inline]

PLMath::Quaternion::Quaternion

(

const float

fQ[]

)

[inline]

PLMath::Quaternion::Quaternion

(

const Quaternion &

qQ

)

[inline]

PLMath::Quaternion::Quaternion	(	const Vector3 &	vAxis,
		float	fAngle
	)		[inline]

PLMATH_API PLMath::Quaternion::Quaternion

(

const Matrix3x3 &

mRot

)

PLMATH_API PLMath::Quaternion::Quaternion

(

const Matrix3x4 &

mRot

)

PLMATH_API PLMath::Quaternion::Quaternion

(

const Matrix4x4 &

mRot

)

PLMath::Quaternion::~Quaternion

(

)

[inline]

---

Member Function Documentation

Quaternion PLMath::Quaternion::operator+

(

const Quaternion &

qQ

)

const [inline]

Quaternion & PLMath::Quaternion::operator+=

(

const Quaternion &

qQ

)

[inline]

Quaternion PLMath::Quaternion::operator-

(

)

const [inline]

Quaternion PLMath::Quaternion::operator-

(

const Quaternion &

qQ

)

const [inline]

Quaternion & PLMath::Quaternion::operator-=

(

const Quaternion &

qQ

)

[inline]

Quaternion PLMath::Quaternion::operator*

(

float

f

)

const [inline]

Quaternion & PLMath::Quaternion::operator*=

(

float

f

)

[inline]

Quaternion PLMath::Quaternion::operator*

(

const Quaternion &

qQ

)

const [inline]

Quaternion & PLMath::Quaternion::operator*=

(

const Quaternion &

qQ

)

[inline]

Vector3 PLMath::Quaternion::operator*

(

const Vector3 &

vV

)

const [inline]

Vector4 PLMath::Quaternion::operator*

(

const Vector4 &

vV

)

const [inline]

Quaternion PLMath::Quaternion::operator/

(

float

f

)

const [inline]

Quaternion & PLMath::Quaternion::operator/=

(

float

f

)

[inline]

Quaternion & PLMath::Quaternion::operator=

(

const Quaternion &

qQ

)

[inline]

bool PLMath::Quaternion::operator==

(

const Quaternion &

qQ

)

const [inline]

bool PLMath::Quaternion::operator!=

(

const Quaternion &

qQ

)

const [inline]

PLMath::Quaternion::operator float *

(

)

[inline]

PLMath::Quaternion::operator const float *

(

)

const [inline]

Quaternion & PLMath::Quaternion::SetWXYZ	(	float	fW,
		float	fX,
		float	fY,
		float	fZ
	)		[inline]

Sets the component of the quaternion.

Parameters:

[in]	fW	W component
[in]	fX	X component
[in]	fY	Y component
[in]	fZ	Z component

Returns:

This quaternion

Quaternion & PLMath::Quaternion::SetWXYZ

(

const float

fValues[]

)

[inline]

Sets the component of the quaternion.

Parameters:

[in]

fValues

Array of at least 4 floats

Returns:

This quaternion

PLMATH_API void PLMath::Quaternion::ToAxisAngle	(	float &	fX,
		float &	fY,
		float &	fZ,
		float &	fAngle
	)		const

Returns a selected axis and angle from the rotation quaternion.

Parameters:

[out]	fX	Will receive the x component of the selected axis
[out]	fY	Will receive the y component of the selected axis
[out]	fZ	Will receive the z component of the selected axis
[out]	fAngle	Will receive the rotation angle around the selected axis (in radian, between [0, Math::Pi])

Note:

• The quaternion must be normalized

PLMATH_API Quaternion& PLMath::Quaternion::FromAxisAngle	(	float	fX,
		float	fY,
		float	fZ,
		float	fAngle
	)

Sets a rotation quaternion by using a selected axis and angle.

Parameters:

[in]	fX	X component of the selected axis
[in]	fY	Y component of the selected axis
[in]	fZ	Z component of the selected axis
[in]	fAngle	Rotation angle around the selected axis (in radian, between [0, Math::Pi])

Returns:

This quaternion

Note:

• The given selected axis must be normalized!

PLMATH_API Vector3 PLMath::Quaternion::GetXAxis

(

)

const

Returns the x (left) axis.

Returns:

The x (left) axis, already normalized for rotation quaternions

PLMATH_API Vector3 PLMath::Quaternion::GetYAxis

(

)

const

Returns the y (up) axis.

Returns:

The y (up) axis, already normalized for rotation quaternions

PLMATH_API Vector3 PLMath::Quaternion::GetZAxis

(

)

const

Returns the z (forward) axis.

Returns:

The z (forward) axis, already normalized for rotation quaternions

PLMATH_API void PLMath::Quaternion::ToRotationMatrix

(

Matrix3x3 &

mRot

)

const

Returns the rotation quaternion as 3x3 matrix.

Parameters:

[out]

mRot

Will receive the rotation matrix

PLMATH_API Quaternion& PLMath::Quaternion::FromRotationMatrix

(

const Matrix3x3 &

mRot

)

Sets a rotation quaternion by using a 3x3 rotation matrix.

Parameters:

[in]

mRot

Rotation matrix

Returns:

This quaternion

PLMATH_API void PLMath::Quaternion::ToRotationMatrix

(

Matrix3x4 &

mRot

)

const

Returns the rotation quaternion as 3x4 matrix.

Parameters:

[out]

mRot

Will receive the rotation matrix

PLMATH_API Quaternion& PLMath::Quaternion::FromRotationMatrix

(

const Matrix3x4 &

mRot

)

Sets a rotation quaternion by using a 3x4 rotation matrix.

Parameters:

[in]

mRot

Rotation matrix

Returns:

This quaternion

PLMATH_API void PLMath::Quaternion::ToRotationMatrix

(

Matrix4x4 &

mRot

)

const

Returns the rotation quaternion as 4x4 matrix.

Parameters:

[out]

mRot

Will receive the rotation matrix

PLMATH_API Quaternion& PLMath::Quaternion::FromRotationMatrix

(

const Matrix4x4 &

mRot

)

Sets a rotation quaternion by using a 4x4 rotation matrix.

Parameters:

[in]

mRot

Rotation matrix

Returns:

This quaternion

bool PLMath::Quaternion::Compare	(	const Quaternion &	qQ,
		float	fEpsilon = Math::Epsilon
	)		const [inline]

Compares two quaternions using an epsilon environment.

Parameters:

[in]	qQ	Quaternion to compare with
[in]	fEpsilon	Epsilon environment

Returns:

'true' if the both quaternions are equal, else 'false'

float PLMath::Quaternion::GetLength

(

)

const [inline]

Returns the length (also called magnitude) of the quaternion.

Returns:

The length (also called magnitude) of the quaternion

float PLMath::Quaternion::GetSquaredLength

(

)

const [inline]

Returns the squared length (norm) of the quaternion.

Returns:

The squared length (norm) of the quaternion

float PLMath::Quaternion::DotProduct

(

const Quaternion &

qQ

)

const [inline]

Returns the dot product of this quaternion and another one.

Parameters:

[in]

qQ

Second quaternion

Returns:

The dot product of the two quaternions

Quaternion & PLMath::Quaternion::Normalize

(

)

[inline]

Normalizes the quaternion.

Normalizes the vector.

Returns:

This quaternion

Quaternion PLMath::Quaternion::GetNormalized

(

)

const [inline]

Returns a normalized quaternion.

Returns:

Normalized quaternion

void PLMath::Quaternion::Conjugate

(

)

[inline]

Conjugates the quaternion.

Quaternion PLMath::Quaternion::GetConjugated

(

)

const [inline]

Returns the conjugated of the quaternion.

Returns:

The conjugated of the quaternion

void PLMath::Quaternion::Invert

(

)

[inline]

Inverts the quaternion.

Quaternion PLMath::Quaternion::GetInverted

(

)

const [inline]

Returns the inverted quaternion.

Returns:

Inverted quaternion

void PLMath::Quaternion::UnitInvert

(

)

[inline]

Inverts the normalized quaternion.

Remarks:

This function can only be used if the quaternion is normalized! (rotation quaternions are normally always normalized) If the quaternion is not normalized, use Invert() instead.

Quaternion PLMath::Quaternion::GetUnitInverted

(

)

const [inline]

Returns the inverted normalized quaternion.

Returns:

Inverted normalized quaternion

See also:

• UnitInvert()

Quaternion & PLMath::Quaternion::Exp

(

)

[inline]

Calculates the exponential of the quaternion.

Returns:

This quaternion

Quaternion PLMath::Quaternion::GetExp

(

)

const [inline]

Returns the exponential of the quaternion.

Returns:

The exponential of the quaternion

Quaternion & PLMath::Quaternion::Log

(

)

[inline]

Quaternion PLMath::Quaternion::GetLog

(

)

const [inline]

Quaternion & PLMath::Quaternion::Power

(

float

fPower

)

[inline]

Calculates the power of the quaternion.

Parameters:

[in]

fPower

Power to calculate

Returns:

This quaternion

Quaternion PLMath::Quaternion::GetPower

(

float

fPower

)

const [inline]

Returns the power of the quaternion.

Parameters:

[in]

fPower

Power to calculate

Returns:

The power of the quaternion

PLMATH_API void PLMath::Quaternion::Slerp	(	const Quaternion &	qQ1,
		const Quaternion &	qQ2,
		float	fTime
	)

Computes spherical linear interpolation between qQ1 and qQ2 with time 0-1.

Parameters:

[in]	qQ1	Start quaternion (time: 0)
[in]	qQ2	End quaternion (time: 1)
[in]	fTime	Time from 0-1

PLMATH_API PLCore::String PLMath::Quaternion::ToString

(

)

const

To string.

Returns:

String with the data

PLMATH_API bool PLMath::Quaternion::FromString

(

const PLCore::String &

sString

)

From string.

Parameters:

[in]

sString

String with the data

---

Member Data Documentation

PLMATH_API const Quaternion PLMath::Quaternion::Zero [static]

0.0, 0.0, 0.0, 0.0

PLMATH_API const Quaternion PLMath::Quaternion::Identity [static]

1.0, 0.0, 0.0, 0.0

float PLMath::Quaternion::fQ[4]

float PLMath::Quaternion::w

float PLMath::Quaternion::x

float PLMath::Quaternion::y

float PLMath::Quaternion::z

union { ... }

Some direct quaternion element accesses.

---

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

• Quaternion.h
• Quaternion.inl