This class implements a unit quaternion rotation. More...

Inheritance diagram for Ocean::QuaternionT< T >:

Public Types
typedef T	Type
	Definition of the used data type. More...

Public Member Functions
	QuaternionT ()=default
	Creates a new quaternion with default values, representation an identity rotation. More...

	QuaternionT (const bool toIdentity)
	Creates a new quaternion with either default values (representation an identity rotation) or an invalid rotation. More...

template<typename U >
	QuaternionT (const QuaternionT< U > &quaternion)
	Copies a quaternion with different element data type than T. More...

	QuaternionT (const T w, const T x, const T y, const T z)
	Creates a new quaternion by four given values. More...

	QuaternionT (const VectorT3< T > &axis, const T angle)
	Creates a new quaternion by a given axis and rotation angle. More...

	QuaternionT (const VectorT3< T > &reference, const VectorT3< T > &offset)
	Creates a quaternion object based on two given unit vectors. More...

	QuaternionT (const RotationT< T > &rotation)
	Creates a new quaternion by a given angle-axis rotation. More...

	QuaternionT (const EulerT< T > &euler)
	Creates a new quaternion by a given Euler rotation. More...

	QuaternionT (const SquareMatrixT3< T > &matrix)
	Creates a new quaternion by a given 3x3 rotation matrix. More...

	QuaternionT (const HomogenousMatrixT4< T > &transformation)
	Creates a new quaternion by a given 4x4 homogeneous transformation matrix. More...

	QuaternionT (const VectorT4< T > &vector)
	Creates a new quaternion by a 4D vector. More...

	QuaternionT (const T *arrayValue)
	Creates a new quaternion by an array with at least four elements. More...

QuaternionT< T >	normalized () const
	Returns the normalized quaternion. More...

bool	normalize ()
	Normalizes the quaternion in place. More...

bool	normalize (QuaternionT< T > &normalizedQuaternion) const
	Normalizes the quaternion and returns the result as parameter. More...

QuaternionT< T >	inverted () const
	Returns the inverted quaternion. More...

bool	invert ()
	Inverts this quaternion in place. More...

bool	invert (QuaternionT< T > &invertedQuaternion) const
	Inverts this quaternion and returns the result as parameter. More...

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

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

T	sqr () const
	Returns the square of the quaternion norm. More...

T	dot (const QuaternionT< T > &quaternion) const
	Returns the dot product between this quaternion and a second quaternion. More...

T	angle () const
	Returns the rotation angle defined by the quaternion. More...

T	angle (const QuaternionT< T > &quaternion) const
	Returns the angle between two quaternion rotations. More...

T	smallestAngle (const QuaternionT< T > &quaternion) const
	Returns the smallest angle between two quaternion rotations. More...

T	cos2 (const QuaternionT< T > &quaternion) const
	Returns the cosine value of the half angle between two quaternion rotations. More...

QuaternionT< T >	slerp (const QuaternionT< T > &quaternion, T factor) const
	Spherical linear interpolation between two quaternions. More...

bool	isValid () const
	Returns whether this quaternion is a valid unit quaternion. More...

const T &	w () const
	Returns the w value of the quaternion. More...

T &	w ()
	Returns the w value of the quaternion. More...

const T &	x () const
	Returns the x value of the quaternion. More...

T &	x ()
	Returns the x value of the quaternion. More...

const T &	y () const
	Returns the y value of the quaternion. More...

T &	y ()
	Returns the y value of the quaternion. More...

const T &	z () const
	Returns the z value of the quaternion. More...

T &	z ()
	Returns the z value of the quaternion. More...

bool	isEqual (const QuaternionT< T > &quaternion, const T eps) const
	Returns whether two quaternions are equal up to a specified epsilon. More...

bool	operator== (const QuaternionT< T > &right) const
	Returns whether two quaternions are identical up to a small epsilon. More...

bool	operator!= (const QuaternionT< T > &right) const
	Returns whether two quaternions are not identical up to a small epsilon. More...

QuaternionT< T >	operator* (const QuaternionT< T > &right) const
	Combines two quaternion to a new combined rotation. More...

QuaternionT< T >	operator* (const RotationT< T > &right) const
	Combines a angle-axis rotation with this quaternion. More...

VectorT3< T >	operator* (const VectorT3< T > &vector) const
	Rotates a 3D vector by this quaternion. More...

QuaternionT< T > &	operator*= (const QuaternionT< T > &right)
	Combines and assigns two quaternions. More...

QuaternionT< T > &	operator*= (const RotationT< T > &right)
	Combines and assigns a quaternion with a rotation. More...

T	operator[] (const unsigned int index) const
	Element operator. More...

T &	operator[] (const unsigned int index)
	Element operator. More...

T	operator() (const unsigned int index) const
	Element operator. More...

T &	operator() (const unsigned int index)
	Element operator. More...

const T *	operator() () const
	Access operator. More...

T *	operator() ()
	Access operator. More...

Protected Attributes
T	values_ [4] = {T(1), T(0), T(0), T(0)}
	The four values of the quaternion. More...

Detailed Description

template<typename T>
class Ocean::QuaternionT< T >

This class implements a unit quaternion rotation.

A quaternion is defined by four values:

w + xi + yj + zk
with
i * i = -1, j * j = -1, k * k = -1

The elements are stored in the following order: w, x, y, z

Template Parameters

T	Data type used to represent the quaternion values

See also: Quaternion, QuaternionF, QuaternionD, Rotation, Euler, SquareMatrix3, ExponentialMap.

Member Typedef Documentation

◆ Type

template<typename T >

typedef T Ocean::QuaternionT< T >::Type

Definition of the used data type.

Constructor & Destructor Documentation

◆ QuaternionT() [1/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( )

default

Creates a new quaternion with default values, representation an identity rotation.

◆ QuaternionT() [2/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const bool toIdentity )

explicit

Creates a new quaternion with either default values (representation an identity rotation) or an invalid rotation.

Parameters

toIdentity True, to create an identity rotation; False, to created an invalid rotation

◆ QuaternionT() [3/12]

template<typename T >

template<typename U >

Ocean::QuaternionT< T >::QuaternionT ( const QuaternionT< U > & quaternion )

inlineexplicit

Copies a quaternion with different element data type than T.

Parameters

quaternion The quaternion object to be copied

Template Parameters

U	The element data type of the given quaternion

◆ QuaternionT() [4/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT	(	const T	w,
		const T	x,
		const T	y,
		const T	z
	)

Creates a new quaternion by four given values.

Parameters

w	W value of the quaternion, with range (-infinity, infinity)
x	X value of the quaternion, with range (-infinity, infinity)
y	Y value of the quaternion, with range (-infinity, infinity)
z	Z value of the quaternion, with range (-infinity, infinity)

◆ QuaternionT() [5/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT	(	const VectorT3< T > &	axis,
		const T	angle
	)

Creates a new quaternion by a given axis and rotation angle.

Parameters

axis	The axis of the angle-axis rotation with unit length
angle	The angle of the angle-axis rotation in radian, with range (-infinity, infinity), however will be converted to the range [0.0, 2 * PI)

◆ QuaternionT() [6/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT	(	const VectorT3< T > &	reference,
		const VectorT3< T > &	offset
	)

Creates a quaternion object based on two given unit vectors.

The resulting rotation defines a transformation that rotates that reference vector into the offset vector: Quaternion(reference, offset) = offset_Q_reference.
The following equation holds:

offset = Quaternion(reference, offset) * reference.

Parameters

reference	The reference vector, with length 1
offset	The offset vector, with length 1

◆ QuaternionT() [7/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const RotationT< T > & rotation )

explicit

Creates a new quaternion by a given angle-axis rotation.

Parameters

rotation The rotation to create the quaternion from, must be valid

◆ QuaternionT() [8/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const EulerT< T > & euler )

explicit

Creates a new quaternion by a given Euler rotation.

Parameters

euler Rotation to create the quaternion from, must be valid

◆ QuaternionT() [9/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const SquareMatrixT3< T > & matrix )

explicit

Creates a new quaternion by a given 3x3 rotation matrix.

Parameters

matrix Rotation matrix to create the quaternion from, with determinant 1

◆ QuaternionT() [10/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const HomogenousMatrixT4< T > & transformation )

explicit

Creates a new quaternion by a given 4x4 homogeneous transformation matrix.

Parameters

transformation The transformation matrix to create the quaternion from

◆ QuaternionT() [11/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const VectorT4< T > & vector )

explicit

Creates a new quaternion by a 4D vector.

Parameters

vector The vector holding the four quaternion parameter

◆ QuaternionT() [12/12]

template<typename T >

Ocean::QuaternionT< T >::QuaternionT ( const T * arrayValue )

explicit

Creates a new quaternion by an array with at least four elements.

Parameters

arrayValue Array with elements, must be valid

Member Function Documentation

◆ angle() [1/2]

template<typename T >

T Ocean::QuaternionT< T >::angle

Returns the rotation angle defined by the quaternion.

This angle is calculated based on the real part of the quaternion.
Beware: Ensure that this quaternion is valid.

Returns: Rotation angle in radian, with range [0, 2PI), 0 in case of an invalid quaternion

◆ angle() [2/2]

template<typename T >

T Ocean::QuaternionT< T >::angle ( const QuaternionT< T > & quaternion ) const

Returns the angle between two quaternion rotations.

This function may return angles larger than PI. Beware: Ensure that this quaternion is valid.

Parameters

quaternion Second quaternion for angle determination, must be valid

Returns: Rotation angle in radian, with range [0, 2PI), 0 in case of an invalid quaternion

See also: smallestAngle().

◆ conjugate()

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::conjugate

Returns the conjugate of this quaternion.

The conjugated quaternion is defined as: (w - xi - yj - zk)

Returns: Conjugate quaternion

◆ cos2()

template<typename T >

T Ocean::QuaternionT< T >::cos2 ( const QuaternionT< T > & quaternion ) const

Returns the cosine value of the half angle between two quaternion rotations.

To determine whether two quaternion rotations have a lesser angle offset than 30 degrees
this cos2 value must be larger than the cosine of 15 degrees.
Beware: Ensure that this quaternion is valid.

Parameters

quaternion Second quaternion for value determination, must be valid

Returns: Cosine value of the half angle

◆ dot()

template<typename T >

T Ocean::QuaternionT< T >::dot ( const QuaternionT< T > & quaternion ) const

Returns the dot product between this quaternion and a second quaternion.

The function actually returns: w0 * w1 + x0 * x1 + y0 * y1 + z0 * z1, with quaternions (w0, x0, y0, z0) and (w1, x1, y1, z1).

Parameters

quaternion The second quaternion for dot product calculation

Returns: The dot product between both quaternions

◆ invert() [1/2]

template<typename T >

bool Ocean::QuaternionT< T >::invert

Inverts this quaternion in place.

Returns: True, if the quaternion is not singular and could be inverted.

See also: inverted().

◆ invert() [2/2]

template<typename T >

bool Ocean::QuaternionT< T >::invert ( QuaternionT< T > & invertedQuaternion ) const

Inverts this quaternion and returns the result as parameter.

Parameters

invertedQuaternion The resulting inverted quaternion

Returns: True, if the quaternion is not singular and could be inverted.

See also: inverted().

◆ inverted()

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::inverted

Returns the inverted quaternion.

Beware: This function does not throw an exception if the quaternion is singular and cannot be inverted.
Thus ensure that the quaternion is valid before calling this function.
In case, this quaternion is not valid, a default quaternion will be returned.

Returns: Inverted quaternion

See also: isValid(), invert().

◆ isEqual()

template<typename T >

bool Ocean::QuaternionT< T >::isEqual	(	const QuaternionT< T > &	quaternion,
		const T	eps
	)		const

inline

Returns whether two quaternions are equal up to a specified epsilon.

Parameters

quaternion	Second quaternion to compare
eps	The epsilon to be used, with range [0, infinity)

Returns: True, if so

◆ isValid()

template<typename T >

bool Ocean::QuaternionT< T >::isValid

Returns whether this quaternion is a valid unit quaternion.

Returns: True, if so

◆ norm()

template<typename T >

T Ocean::QuaternionT< T >::norm

Returns the norm of this quaternion.

Returns: Quaternion norm

◆ normalize() [1/2]

template<typename T >

bool Ocean::QuaternionT< T >::normalize

Normalizes the quaternion in place.

Returns: True, if the quaternion is not singular and could be normalized.

See also: normalized().

◆ normalize() [2/2]

template<typename T >

bool Ocean::QuaternionT< T >::normalize ( QuaternionT< T > & normalizedQuaternion ) const

Normalizes the quaternion and returns the result as parameter.

Parameters

normalizedQuaternion The resulting normalized quaternion

Returns: True, if the quaternion is not singular and could be normalized.

See also: normalized().

◆ normalized()

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::normalized

Returns the normalized quaternion.

Beware: This function does not throw an exception if the quaternion is singular and cannot be normalized.
Thus ensure that the quaternion is valid before calling this function.
In case, this quaternion is not valid, a default quaternion will be returned.

Returns: Normalized quaternion

See also: isValid(), normalize().

◆ operator!=()

template<typename T >

bool Ocean::QuaternionT< T >::operator!= ( const QuaternionT< T > & right ) const

inline

Returns whether two quaternions are not identical up to a small epsilon.

Parameters

right The right quaternion

Returns: True, if so

◆ operator()() [1/4]

template<typename T >

T * Ocean::QuaternionT< T >::operator()

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [2/4]

template<typename T >

const T * Ocean::QuaternionT< T >::operator()

inline

Access operator.

Returns: Pointer to the internal values

◆ operator()() [3/4]

template<typename T >

T & Ocean::QuaternionT< T >::operator() ( const unsigned int index )

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 3]

Returns: Specified element

◆ operator()() [4/4]

template<typename T >

T Ocean::QuaternionT< T >::operator() ( const unsigned int index ) const

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 3]

Returns: Specified element

◆ operator*() [1/3]

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::operator* ( const QuaternionT< T > & right ) const

Combines two quaternion to a new combined rotation.

Parameters

right The right quaternion

Returns: Combined quaternion

◆ operator*() [2/3]

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::operator* ( const RotationT< T > & right ) const

inline

Combines a angle-axis rotation with this quaternion.

Parameters

right The right angle-axis rotation

Returns: Combined quaternion rotation

◆ operator*() [3/3]

template<typename T >

VectorT3< T > Ocean::QuaternionT< T >::operator* ( const VectorT3< T > & vector ) const

Rotates a 3D vector by this quaternion.

Parameters

vector 3D vector to rotate

Returns: Rotated 3D vector

◆ operator*=() [1/2]

template<typename T >

QuaternionT< T > & Ocean::QuaternionT< T >::operator*= ( const QuaternionT< T > & right )

inline

Combines and assigns two quaternions.

Parameters

right The right quaternion

Returns: Reference to this quaternion

◆ operator*=() [2/2]

template<typename T >

QuaternionT< T > & Ocean::QuaternionT< T >::operator*= ( const RotationT< T > & right )

inline

Combines and assigns a quaternion with a rotation.

Parameters

right The right quaternion

Returns: Reference to this quaternion

◆ operator==()

template<typename T >

bool Ocean::QuaternionT< T >::operator== ( const QuaternionT< T > & right ) const

Returns whether two quaternions are identical up to a small epsilon.

Parameters

right The right quaternion

Returns: True, if so

◆ operator[]() [1/2]

template<typename T >

T & Ocean::QuaternionT< T >::operator[] ( const unsigned int index )

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 3]

Returns: Specified element

◆ operator[]() [2/2]

template<typename T >

T Ocean::QuaternionT< T >::operator[] ( const unsigned int index ) const

inline

Element operator.

Beware: No range check will be done!

Parameters

index The index of the element to return [0, 3]

Returns: Specified element

◆ slerp()

template<typename T >

QuaternionT< T > Ocean::QuaternionT< T >::slerp	(	const QuaternionT< T > &	quaternion,
		T	factor
	)		const

Spherical linear interpolation between two quaternions.

This quaternion will be the resulting interpolation if 'factor == 0'.

Parameters

quaternion	The right quaternion which will be the resulting interpolation if 'factor == 1'
factor	Interpolation factor has to be between [0, 1]

Returns: The interpolated quaternion

◆ smallestAngle()

template<typename T >

T Ocean::QuaternionT< T >::smallestAngle ( const QuaternionT< T > & quaternion ) const

Returns the smallest angle between two quaternion rotations.

In contrast to angle(), this function returns the smallest (absolute) angle with range [0, PI). Beware: Ensure that this quaternion is valid.

Parameters

quaternion Second quaternion for angle determination, must be valid

Returns: Rotation angle in radian, with range [0, PI), 0 in case of an invalid quaternion

See also: angle().

◆ sqr()

template<typename T >

T Ocean::QuaternionT< T >::sqr

Returns the square of the quaternion norm.

Returns: Square of quaternion norm

◆ w() [1/2]

template<typename T >

T & Ocean::QuaternionT< T >::w

inline

Returns the w value of the quaternion.

Returns: w value

◆ w() [2/2]

template<typename T >

const T & Ocean::QuaternionT< T >::w

inline

Returns the w value of the quaternion.

Returns: w value

◆ x() [1/2]

template<typename T >

T & Ocean::QuaternionT< T >::x

inline

Returns the x value of the quaternion.

Returns: x value

◆ x() [2/2]

template<typename T >

const T & Ocean::QuaternionT< T >::x

inline

Returns the x value of the quaternion.

Returns: x value

◆ y() [1/2]

template<typename T >

T & Ocean::QuaternionT< T >::y

inline

Returns the y value of the quaternion.

Returns: x value

◆ y() [2/2]

template<typename T >

const T & Ocean::QuaternionT< T >::y

inline

Returns the y value of the quaternion.

Returns: x value

◆ z() [1/2]

template<typename T >

T & Ocean::QuaternionT< T >::z

inline

Returns the z value of the quaternion.

Returns: z value

◆ z() [2/2]

template<typename T >

const T & Ocean::QuaternionT< T >::z

inline

Returns the z value of the quaternion.

Returns: z value

Field Documentation

◆ values_

template<typename T >

T Ocean::QuaternionT< T >::values_[4] = {T(1), T(0), T(0), T(0)}

protected

The four values of the quaternion.

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

Public Types

Public Member Functions

Protected Attributes

Detailed Description

template<typename T> class Ocean::QuaternionT< T >

Member Typedef Documentation

◆ Type

Constructor & Destructor Documentation

◆ QuaternionT() [1/12]

◆ QuaternionT() [2/12]

◆ QuaternionT() [3/12]

◆ QuaternionT() [4/12]

◆ QuaternionT() [5/12]

◆ QuaternionT() [6/12]

◆ QuaternionT() [7/12]

◆ QuaternionT() [8/12]

◆ QuaternionT() [9/12]

◆ QuaternionT() [10/12]

◆ QuaternionT() [11/12]

◆ QuaternionT() [12/12]

Member Function Documentation

◆ angle() [1/2]

◆ angle() [2/2]

◆ conjugate()

◆ cos2()

◆ dot()

◆ invert() [1/2]

◆ invert() [2/2]

◆ inverted()

◆ isEqual()

◆ isValid()

◆ norm()

◆ normalize() [1/2]

◆ normalize() [2/2]

◆ normalized()

◆ operator!=()

◆ operator()() [1/4]

◆ operator()() [2/4]

◆ operator()() [3/4]

◆ operator()() [4/4]

◆ operator*() [1/3]

◆ operator*() [2/3]

◆ operator*() [3/3]

◆ operator*=() [1/2]

◆ operator*=() [2/2]

◆ operator==()

◆ operator[]() [1/2]

◆ operator[]() [2/2]

◆ slerp()

◆ smallestAngle()

◆ sqr()

◆ w() [1/2]

◆ w() [2/2]

◆ x() [1/2]

◆ x() [2/2]

◆ y() [1/2]

◆ y() [2/2]

◆ z() [1/2]

◆ z() [2/2]

Field Documentation

◆ values_

template<typename T>
class Ocean::QuaternionT< T >