This class represents a quaternion. More...

#include "Quaternion.hpp"

Public Member Functions
	QuaternionT (T x_=0, T y_=0, T z_=0, T w_=1)
	The default constructor. It initializes the quaternion from the given x_, y_, z_ and w_ respectively. More...

template<class C >
	QuaternionT (const C Values[])
	Constructs a quaternion from an array of (at least) four values. More...

	QuaternionT (const AnglesT< T > &Angles)
	Constructs a quaternion from the given angles. More...

	QuaternionT (const Matrix3x3T< T > &Mat)
	Constructs a quaternion from the given rotation matrix. More...

	QuaternionT (const Vector3T< T > &Axis, const T Angle)
	Constructs a quaternion from a rotation axis and angle. More...

Vector3T< T >	GetXYZ () const
	Returns the x, y and z components as a Vector3T<T>. More...

QuaternionT< T >	GetConjugate () const
	Returns the conjugate of this quaternion. More...

T	dot (const QuaternionT< T > &B) const
	Returns the dot product of this quaternion and B. More...

T	length () const
	Returns the length of this quaternion. More...

T	lengthSqr () const
	Returns the square of the length of this quaternion. More...

bool	IsNormal (const T Epsilon=0) const
	Returns if this quaternion is normal, i.e. More...

T &	operator[] (unsigned int Index)
	Component access by index number (0 to 3) rather than by name. More...

const T &	operator[] (unsigned int Index) const
	Component access by index number (0 to 3) rather than by name. More...

bool	operator== (const QuaternionT< T > &B) const
	Returns whether this quaternion and B are (bit-wise) identical. More...

bool	operator!= (const QuaternionT< T > &B) const
	Returns whether this quaternion and B are not equal (bit-wise). More...

QuaternionT< T >	operator- () const
	The unary minus operator. More...

QuaternionT< T >	operator+ (const QuaternionT< T > &B) const
	Returns the sum of this quaternion and B. More...

QuaternionT< T > &	operator+= (const QuaternionT< T > &B)
	Adds B to this quaternion. More...

QuaternionT< T >	operator- (const QuaternionT< T > &B) const
	Returns the difference between this quaternion and B. More...

QuaternionT< T > &	operator-= (const QuaternionT< T > &B)
	Subtracts B from this quaternion. More...

QuaternionT< T >	operator* (const QuaternionT< T > &B) const
	Returns the quaternion Q that expresses the combined rotation of this quaternion and `B`, `Q = this*B`. More...

QuaternionT< T >	operator* (const T s) const
	Returns a copy of this quaternion scaled by s. More...

QuaternionT< T > &	operator*= (const T s)
	Scales this quaternion by s. More...

QuaternionT< T >	operator/ (const T s) const
	Returns a copy of this quaternion divided by s, assuming that s is not 0. More...

QuaternionT< T > &	operator/= (const T s)
	Divides this quaternion by s, assuming that s is not 0. More...

Static Public Member Functions
static QuaternionT	FromXYZ (const Vector3T< T > &Vec)
	Constructs a quaternion from the first three components (x, y, z) of a unit quaternion. More...

static QuaternionT	Euler (const T Pitch, const T Yaw, const T Roll)
	Constructs a quaternion from three Euler angles. More...

Public Attributes
T	x

T	y

T	z

T	w

Detailed Description

template<class T>
class cf::math::QuaternionT< T >

This class represents a quaternion.

Constructor & Destructor Documentation

template<class T>

cf::math::QuaternionT< T >::QuaternionT	(	T	x_ = `0`,
		T	y_ = `0`,
		T	z_ = `0`,
		T	w_ = `1`
	)

inline

The default constructor. It initializes the quaternion from the given x_, y_, z_ and w_ respectively.

template<class T>

template<class C >

cf::math::QuaternionT< T >::QuaternionT ( const C Values[] )

inlineexplicit

Constructs a quaternion from an array of (at least) four values.

template<class T>

QuaternionT::QuaternionT ( const AnglesT< T > & Angles )

Constructs a quaternion from the given angles.

See the documentation of the AnglesT class for details.

template<class T>

QuaternionT::QuaternionT ( const Matrix3x3T< T > & Mat )

Constructs a quaternion from the given rotation matrix.

If the matrix is not orthonormal, the result is undefined.

template<class T>

QuaternionT::QuaternionT	(	const Vector3T< T > &	Axis,
		const T	Angle
	)

Constructs a quaternion from a rotation axis and angle.

This is useful, for example, to rotate one vector onto another, as is done in the implementation of cf::GameSys::ComponentTransformT::LookAt().

Parameters

Axis	The axis to rotate about. This given axis must be of unit length, or else the result is undefined.
Angle	The angle to rotate about, in radians.

Member Function Documentation

template<class T>

T cf::math::QuaternionT< T >::dot ( const QuaternionT< T > & B ) const

inline

Returns the dot product of this quaternion and B.

template<class T>

QuaternionT< T > QuaternionT::Euler	(	const T	Pitch,
		const T	Yaw,
		const T	Roll
	)

static

Constructs a quaternion from three Euler angles.

Parameters

Pitch	the Euler rotation about the x-axis, in radians.
Yaw	the Euler rotation about the y-axis, in radians.
Roll	the Euler rotation about the z-axis, in radians. Note that the assignment of angles to axes assumes a right-handed coordinate system where the z-axis points towards the viewer. This is especially different from the coordinate system that class cf::math::AnglesT<T> uses, which is also right-handed, but rotated by 90 degrees so that the z-axis points up and the y-axis away from the viewer!

template<class T>

static QuaternionT cf::math::QuaternionT< T >::FromXYZ ( const Vector3T< T > & Vec )

inlinestatic

Constructs a quaternion from the first three components (x, y, z) of a unit quaternion.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::GetConjugate ( ) const

inline

Returns the conjugate of this quaternion.

If the quaternion is of unit length, then the conjugate is also its inverse.

template<class T>

Vector3T<T> cf::math::QuaternionT< T >::GetXYZ ( ) const

inline

Returns the x, y and z components as a Vector3T<T>.

template<class T>

bool cf::math::QuaternionT< T >::IsNormal ( const T Epsilon = 0 ) const

inline

Returns if this quaternion is normal, i.e.

has length 1 within the given tolerance.

Parameters

Epsilon The tolerance value.

template<class T>

T cf::math::QuaternionT< T >::length ( ) const

inline

Returns the length of this quaternion.

template<class T>

T cf::math::QuaternionT< T >::lengthSqr ( ) const

inline

Returns the square of the length of this quaternion.

template<class T>

bool cf::math::QuaternionT< T >::operator!= ( const QuaternionT< T > & B ) const

inline

Returns whether this quaternion and B are not equal (bit-wise).

Use this operator with care, as it comes without any epsilon threshold to take rounding errors into account.

Parameters

B	Quaternion to compare to.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator* ( const QuaternionT< T > & B ) const

inline

Returns the quaternion Q that expresses the combined rotation of this quaternion and B, Q = this*B.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator* ( const T s ) const

inline

Returns a copy of this quaternion scaled by s.

template<class T>

QuaternionT<T>& cf::math::QuaternionT< T >::operator*= ( const T s )

inline

Scales this quaternion by s.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator+ ( const QuaternionT< T > & B ) const

inline

Returns the sum of this quaternion and B.

template<class T>

QuaternionT<T>& cf::math::QuaternionT< T >::operator+= ( const QuaternionT< T > & B )

inline

Adds B to this quaternion.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator- ( ) const

inline

The unary minus operator.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator- ( const QuaternionT< T > & B ) const

inline

Returns the difference between this quaternion and B.

template<class T>

QuaternionT<T>& cf::math::QuaternionT< T >::operator-= ( const QuaternionT< T > & B )

inline

Subtracts B from this quaternion.

template<class T>

QuaternionT<T> cf::math::QuaternionT< T >::operator/ ( const T s ) const

inline

Returns a copy of this quaternion divided by s, assuming that s is not 0.

template<class T>

QuaternionT<T>& cf::math::QuaternionT< T >::operator/= ( const T s )

inline

Divides this quaternion by s, assuming that s is not 0.

template<class T>

bool cf::math::QuaternionT< T >::operator== ( const QuaternionT< T > & B ) const

inline

Returns whether this quaternion and B are (bit-wise) identical.

Use this operator with care, as it comes without any epsilon threshold to take rounding errors into account.

Parameters

B	Quaternion to compare to.

template<class T>

T& cf::math::QuaternionT< T >::operator[] ( unsigned int Index )

inline

Component access by index number (0 to 3) rather than by name.

Parameters

Index Index of the component to access. Can only be 0, 1, 2 or 3 (for x, y, z, w).

Exceptions

InvalidOperationE if Index is not 0, 1, 2 or 3.

template<class T>

const T& cf::math::QuaternionT< T >::operator[] ( unsigned int Index ) const

inline

Component access by index number (0 to 3) rather than by name.

Parameters

Index Index of the component to access. Can only be 0, 1, 2 or 3 (for x, y, z, w).

Exceptions

InvalidOperationE if Index is not 0, 1, 2 or 3.

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

Libs/Math3D/Angles.hpp
Libs/Math3D/Quaternion.hpp
Libs/Math3D/Quaternion.cpp

Public Member Functions

Static Public Member Functions

Public Attributes

Detailed Description

template<class T> class cf::math::QuaternionT< T >

Constructor & Destructor Documentation

Member Function Documentation

template<class T>
class cf::math::QuaternionT< T >