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openvrml::quatf Class Reference
[Base Types]

List of all members.

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Detailed Description

A quaternion.

Public Member Functions
	quatf () throw ()
	Default constructor.
	quatf (float x, float y, float z, float w) throw ()
	Construct from four values.
	quatf (const float(&quat)[4]) throw ()
	Construct from an array of four values.
	quatf (const rotation &rot) throw ()
	Construct from an rotation.
	quatf (const mat4f &mat) throw ()
	Construct from a rotation matrix.
quatf &	operator *= (const quatf &quat) throw ()
	Multiply by a quaternion.
quatf &	operator *= (float scalar) throw ()
	Multiply by a scalar.
quatf &	operator/= (float scalar) throw ()
	Divide by a scalar.
quatf &	operator+= (const quatf &quat) throw ()
	Add a quaternion.
quatf &	operator-= (const quatf &quat) throw ()
	Subtract a quaternion.
const float &	operator[] (size_t index) const throw ()
	Array element dereference operator (const version).
float &	operator[] (size_t index) throw ()
	Array element dereference operator (non-const version).
float	x () const throw ()
	Get the x component.
float	y () const throw ()
	Get the y component.
float	z () const throw ()
	Get the z component.
float	w () const throw ()
	Get the w component.
void	x (float value) throw ()
	Set the x component.
void	y (float value) throw ()
	Set the y component.
void	z (float value) throw ()
	Set the z component.
void	w (float value) throw ()
	Set the w component.
const quatf	conjugate () const throw ()
	Get the conjugate.
const quatf	inverse () const throw ()
	Get the inverse.
float	norm () const throw ()
	Get the norm.
const quatf	normalize () const throw ()
	Normalize the quaternion.
Private Attributes
float	quat [4]
	An array comprising the quaternion components.
Related Functions
(Note that these are not member functions.)
const quatf	operator * (const quatf &lhs, const quatf &rhs) throw()
	Multiply two quaternions.
const quatf	operator * (const quatf &quat, const float scalar) throw()
	Multiply a quaternion by a scalar.
const quatf	operator * (const float scalar, const quatf &quat) throw()
	Multiply a scalar by a quaternion.
const quatf	operator/ (const quatf &quat, const float scalar) throw()
	Divide a quaternion by a scalar.
const quatf	operator+ (const quatf &lhs, const quatf &rhs) throw()
	Add two quaternions.
const quatf	operator- (const quatf &lhs, const quatf &rhs) throw()
	Take the difference between two quaternions.
std::ostream &	operator<< (std::ostream &out, const quatf &quat)
	Stream output.
bool	operator== (const quatf &lhs, const quatf &rhs) throw()
	Compare for equality.
bool	operator!= (const quatf &lhs, const quatf &rhs) throw()
	Compare for inequality.

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Constructor & Destructor Documentation

openvrml::quatf::quatf

(

)

throw ()

Default constructor.

openvrml::quatf::quatf	(	float	x,
		float	y,
		float	z,
		float	w
	)			throw ()

Construct from four values.

Parameters:

	x	the x vector component.
	y	the y vector component.
	z	the z vector component.
	w	the scalar value w.

openvrml::quatf::quatf

(

const float &

quat[4]

)

throw () [explicit]

Construct from an array of four values.

Parameters:

quat

the first three values in the array are used for the x, y, and z vector components, respectively. The fourth value in the array is used for the scalar part of the quaternion.

openvrml::quatf::quatf

(

const rotation &

rot

)

throw () [explicit]

Construct from an rotation.

Parameters:

rot

a rotation.

openvrml::quatf::quatf

(

const mat4f &

mat

)

throw () [explicit]

Construct from a rotation matrix.

Parameters:

mat

a rotation matrix.

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Member Function Documentation

quatf & openvrml::quatf::operator *=

(

const quatf &

quat

)

throw ()

Multiply by a quaternion.

Note:

qr = (q_v x r_v + r_wq_v + q_wr_v, q_wr_w

• q_v . r_v)

Parameters:

quat

the quaternion by which to multiply.

Returns:

a reference to the object.

quatf & openvrml::quatf::operator *=

(

float

scalar

)

throw ()

Multiply by a scalar.

Parameters:

scalar

value by which to multiply.

Returns:

a reference to the object.

quatf & openvrml::quatf::operator/=

(

float

scalar

)

throw ()

Divide by a scalar.

Parameters:

scalar

value by which to divide.

Returns:

a reference to the object.

quatf & openvrml::quatf::operator+=

(

const quatf &

quat

)

throw ()

Add a quaternion.

Parameters:

quat

the quaternion to add.

Returns:

a reference to the object.

quatf & openvrml::quatf::operator-=

(

const quatf &

quat

)

throw ()

Subtract a quaternion.

Parameters:

quat

the quaternion to subtract.

Returns:

a reference to the object.

const float & openvrml::quatf::operator[]

(

size_t

index

)

const throw () [inline]

Array element dereference operator (const version).

Parameters:

index

an index from 0 - 3.

Precondition:

index is not larger than 3.

float & openvrml::quatf::operator[]

(

size_t

index

)

throw () [inline]

Array element dereference operator (non-const version).

Parameters:

index

an index from 0 - 3.

Precondition:

index is not larger than 3.

float openvrml::quatf::x

(

)

const throw () [inline]

Get the x component.

Returns:

the x component value.

float openvrml::quatf::y

(

)

const throw () [inline]

Get the y component.

Returns:

the y component value.

float openvrml::quatf::z

(

)

const throw () [inline]

Get the z component.

Returns:

the z component value.

float openvrml::quatf::w

(

)

const throw () [inline]

Get the w component.

Returns:

the w component value.

void openvrml::quatf::x

(

float

value

)

throw () [inline]

Set the x component.

Parameters:

value

x component value.

void openvrml::quatf::y

(

float

value

)

throw () [inline]

Set the y component.

Parameters:

value

y component value.

void openvrml::quatf::z

(

float

value

)

throw () [inline]

Set the z component.

Parameters:

value

z component value.

void openvrml::quatf::w

(

float

value

)

throw () [inline]

Set the w component.

Parameters:

value

w component value.

const quatf openvrml::quatf::conjugate

(

)

const throw ()

Get the conjugate.

Note:

q^* = (-q_v, q_w)

Returns:

the conjugate of the quaternion.

const quatf openvrml::quatf::inverse

(

)

const throw ()

Get the inverse.

Note:

q^-1 = q^* / n(q)

Returns:

the multiplicative inverse.

float openvrml::quatf::norm

(

)

const throw ()

Get the norm.

Note:

n(q) = q_x² + q_y² + q_z² + q_w²

Returns:

the norm.

const quatf openvrml::quatf::normalize

(

)

const throw ()

Normalize the quaternion.

Returns:

a unit quaternion derived from the quaternion.

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Friends And Related Function Documentation

const quatf operator *	(	const quatf &	lhs,
		const quatf &	rhs
	)			throw() [related]

Multiply two quaternions.

Parameters:

	lhs	left-hand operand.
	rhs	right-hand operand.

Returns:

the product of lhs and rhs.

const quatf operator *	(	const quatf &	quat,
		const float	scalar
	)			throw() [related]

Multiply a quaternion by a scalar.

Parameters:

	quat	quaternion.
	scalar	scalar.

Returns:

the product of quat and scalar.

const quatf operator *	(	const float	scalar,
		const quatf &	quat
	)			throw() [related]

Multiply a scalar by a quaternion.

Parameters:

	scalar	scalar.
	quat	quaternion.

Returns:

the product of scalar and quat.

const quatf operator/	(	const quatf &	quat,
		const float	scalar
	)			throw() [related]

Divide a quaternion by a scalar.

Parameters:

	quat	quaternion.
	scalar	scalar.

Returns:

the result of dividing quat by scalar.

const quatf operator+	(	const quatf &	lhs,
		const quatf &	rhs
	)			throw() [related]

Add two quaternions.

Parameters:

	lhs	left-hand operand.
	rhs	right-hand operand.

Returns:

the sum of lhs and rhs.

const quatf operator-	(	const quatf &	lhs,
		const quatf &	rhs
	)			throw() [related]

Take the difference between two quaternions.

Parameters:

	lhs	left-hand operand.
	rhs	right-hand operand.

Returns:

the difference between lhs and rhs.

std::ostream & operator<<	(	std::ostream &	out,
		const quatf &	quat
	)			[related]

Stream output.

Parameters:

	out	an output stream.
	quat	a quaternion.

Returns:

out.

bool operator==	(	const quatf &	lhs,
		const quatf &	rhs
	)			throw() [related]

Compare for equality.

Parameters:

	lhs	left-hand operand.
	rhs	right-hand operand.

Returns:

true if lhs and rhs are equal; false otherwise.

bool operator!=	(	const quatf &	lhs,
		const quatf &	rhs
	)			throw() [related]

Compare for inequality.

Parameters:

	lhs	left-hand operand.
	rhs	right-hand operand.

Returns:

true if lhs and rhs are not equal; false otherwise.

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Member Data Documentation

float openvrml::quatf::quat[4] [private]

An array comprising the quaternion components.

For internal use only.