#include <quaternion.h>

Detailed Description

template<typename ValueType>
class maxon::Quaternion< ValueType >

Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions. This avoids the problem of "gimbal-lock" and allows for the implementation of smooth and continuous rotation. In effect, they may be considered to add an additional rotation angle to spherical coordinates ie. Longitude, Latitude and Rotation angles. A Quaternion is defined using four floating point values |v.x v.y v.z w|. These are calculated from the combination of the three coordinates of the rotation axis and the rotation angle. Because the rotation axis is specified as a unit direction vector, it may be calculated through vector mathematics or from spherical coordinates ie. (longitude/latitude). Quaternions offer another advantage in that they be interpolated - this allows for smooth and predictable rotation effects.

Public Member Functions
	Quaternion ()

MAXON_IMPLICIT	Quaternion (const VectorType &v, const ValueType w)

MAXON_IMPLICIT	Quaternion (const ValueType x, const ValueType y, const ValueType z, const ValueType w)

const QuaternionType &	operator+= (const QuaternionType &v)

const QuaternionType &	operator-= (const QuaternionType &v)

const QuaternionType &	operator*= (const QuaternionType &v)

QuaternionType	operator+ (const QuaternionType &v) const

QuaternionType	operator- (const QuaternionType &v) const

QuaternionType	operator* (const QuaternionType &v) const

QuaternionType	operator* (const ValueType s) const

void	SetMatrix (const MatrixType &m)

void	SetRotation (const VectorType &rotation)

void	SetAxisRotation (const VectorType &axis, const ValueType rotation)

MatrixType	GetMatrix () const

Result< void >	GetAxisRotation (VectorType &axis, ValueType &angle) const

ValueType	GetSquaredLength () const

ValueType	GetLength () const

Result< QuaternionType >	GetNormalized () const

Result< QuaternionType >	GetInverse () const

QuaternionType	GetConjugate () const

Result< QuaternionType >	GetLog () const

Result< QuaternionType >	GetExp () const

Result< QuaternionType >	GetPow (const ValueType &t) const

String	ToString (const FormatStatement *formatStatement=nullptr) const

	MAXON_OPERATOR_EQUALITY_HASHCODE (Quaternion, v, w)

Static Public Member Functions
static ValueType	GetDot (const QuaternionType &q1, const QuaternionType &q2)

static Result< QuaternionType >	GetLerp (const QuaternionType &q1, const QuaternionType &q2, const ValueType t)

static Result< QuaternionType >	GetSlerp (const QuaternionType &q1, const QuaternionType &q2, const ValueType t)

static Result< QuaternionType >	GetSquad (const QuaternionType &qi, const QuaternionType &qi_p1, const QuaternionType &si, const QuaternionType &si_p1, const ValueType t)

static Result< QuaternionType >	GetInnerQuaternion (const QuaternionType &qi_m1, const QuaternionType &qi, const QuaternionType &qi_p1)

static Result< QuaternionType >	GetSpline (const QuaternionType &qi_m1, const QuaternionType &qi, const QuaternionType &qi_p1, const QuaternionType &qi_p2, const ValueType t)

static Result< void >	DescribeIO (const DataSerializeInterface &stream)

Public Attributes
VectorType	v

ValueType	w

Private Types
using	VectorType = Vec3< ValueType >

using	MatrixType = SqrMat3< Vec3< ValueType > >

using	QuaternionType = Quaternion< ValueType >

Private Member Functions
ValueType	MyCopysign (const ValueType &x, const ValueType &y) const

Friends
QuaternionType	operator* (const ValueType s, const QuaternionType &q)

Member Typedef Documentation

◆ VectorType

using VectorType = Vec3<ValueType>

private

◆ MatrixType

using MatrixType = SqrMat3<Vec3<ValueType> >

private

◆ QuaternionType

using QuaternionType = Quaternion<ValueType>

private

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

Quaternion

Creates a quaternion initialized with default values (all components 0.0).

◆ Quaternion() [2/3]

Quaternion	(	const VectorType &	v,
		const ValueType	w
	)

Creates a quaternion and initialize it with given quaternion values.

◆ Quaternion() [3/3]

Quaternion	(	const ValueType	x,
		const ValueType	y,
		const ValueType	z,
		const ValueType	w
	)

Creates a quaternion and initialize it with given quaternion values.

Member Function Documentation

◆ MyCopysign()

ValueType MyCopysign	(	const ValueType &	x,
		const ValueType &	y
	)		const

private

◆ operator+=()

const Quaternion< ValueType > & operator+= ( const QuaternionType & v )

Adds the components of two quaternions.

◆ operator-=()

const Quaternion< ValueType > & operator-= ( const QuaternionType & v )

Subtract the components of two quaternions.

◆ operator*=()

const Quaternion< ValueType > & operator*= ( const QuaternionType & v )

Concatenate two quaternion operations.

◆ operator+()

Quaternion< ValueType > operator+ ( const QuaternionType & v ) const

Adds the components of two quaternions.

◆ operator-()

Quaternion< ValueType > operator- ( const QuaternionType & v ) const

Subtracts the components of two quaternions.

◆ operator*() [1/2]

Quaternion< ValueType > operator* ( const QuaternionType & v ) const

Concatenates two quaternion operations.

◆ operator*() [2/2]

Quaternion< ValueType > operator* ( const ValueType s ) const

Scales the components of a quaternion.

◆ SetMatrix()

void SetMatrix ( const MatrixType & m )

Converts a rotation matrix into a quaternion.

Parameters

[in] m Rotation matrix (does not need to be normalized).

◆ SetRotation()

void SetRotation ( const VectorType & rotation )

Converts a rotation of order X -> Y -> Z into a quaternion.

Parameters

[in] rotation Rotation angle vector in radians.

◆ SetAxisRotation()

void SetAxisRotation	(	const VectorType &	axis,
		const ValueType	rotation
	)

Converts an axis and angle to a quaternion.

Parameters

[in]	axis	Axis (does not need to be normalized).
[in]	rotation	Rotation angle in radians.

◆ GetMatrix()

auto GetMatrix ( void ) const

Derives a rotation matrix from the quaternion.

◆ GetAxisRotation()

Result< void > GetAxisRotation	(	VectorType &	axis,
		ValueType &	angle
	)		const

Calculate axis and rotation angle from quaternion.

Parameters

[out]	axis	Axis vector.
[out]	angle	Angle value in radians.

Returns: OK on success. Returns an error if quaternion is not normalized or the direction of the axis is undefined (singularity at 0 / 180 degree)

◆ GetSquaredLength()

ValueType GetSquaredLength

Calculates the squared magntitude/length/norm of a quaternion.

◆ GetLength()

ValueType GetLength ( void ) const

Calculates the magntitude/length/norm of a quaternion.

◆ GetNormalized()

Result< Quaternion< ValueType > > GetNormalized

Calculates the normalized quaternion.

Returns: OK on sucess. Returns an error if the length of the quaternion is zero.

◆ GetInverse()

Result< Quaternion< ValueType > > GetInverse

Calculates the inverse of a quaternion.

Returns: OK on sucess. Returns an error if the length of the quaternion is zero.

◆ GetConjugate()

Quaternion< ValueType > GetConjugate

Calculates the conjugate of a quaternion.

Returns: Conjugated quaternion.

◆ GetLog()

Result< Quaternion< ValueType > > GetLog

Calculates the logarithm of a quaternion.

Returns: OK on sucess. Returns an error if the length of the quaternion axis is zero.

◆ GetExp()

Result< Quaternion< ValueType > > GetExp

Calculates the exponential of a quaternion.

Returns: OK on sucess. Returns an error if the length of the quaternion is zero.

◆ GetPow()

Result< Quaternion< ValueType > > GetPow ( const ValueType & t ) const

Calculates the quaternion power q^t.

Parameters

[in] t Exponent.

Returns: OK on sucess. Returns an error if the length of the quaternion is zero.

◆ GetDot()

ValueType GetDot	(	const QuaternionType &	q1,
		const QuaternionType &	q2
	)

static

Calculates the dot product of two quaternions.

◆ GetLerp()

Result< Quaternion< ValueType > > GetLerp	(	const QuaternionType &	q1,
		const QuaternionType &	q2,
		const ValueType	t
	)

static

Interpolates two quaternions linearly with blend parameter t.

Parameters

[in]	q1	First quaternion.
[in]	q2	Second quaternion.
[in]	t	Blend parameter [0.0, 1.0.]

Returns: The interpolated quaternion.

◆ GetSlerp()

Result< Quaternion< ValueType > > GetSlerp	(	const QuaternionType &	q1,
		const QuaternionType &	q2,
		const ValueType	t
	)

static

Interpolates two quaternions spherical linearly with blend parameter t.

Parameters

[in]	q1	First quaternion.
[in]	q2	Second quaternion.
[in]	t	Blend parameter [0.0, 1.0.]

Returns: The interpolated quaternion.

◆ GetSquad()

Result< Quaternion< ValueType > > GetSquad	(	const QuaternionType &	qi,
		const QuaternionType &	qi_p1,
		const QuaternionType &	si,
		const QuaternionType &	si_p1,
		const ValueType	t
	)

static

Spherical quadrangle interpolation of a sequence of quaternions qi and qi+1 with blend parameter t Additionally you have to specify the innner quaternions si and si+1.

Parameters

[in]	qi	Main quaternion at index i.
[in]	qi_p1	Main quaternion at index i+1
[in]	si	Inner quaterniona at index i.
[in]	si_p1	Inner quaternion at index i+1
[in]	t	Blend parameter [0.0, 1.0.]

Returns: The interpolated quaternion.

◆ GetInnerQuaternion()

Result< Quaternion< ValueType > > GetInnerQuaternion	(	const QuaternionType &	qi_m1,
		const QuaternionType &	qi,
		const QuaternionType &	qi_p1
	)

static

Computer the inner quaternion from the series of quaternions qi-1, qi and qi+1

Parameters

[in]	qi_m1	Quaternion at index i-1
[in]	qi	Quaternion at index i.
[in]	qi_p1	Quaternion at index i+1

Returns: The interpolated quaternion.

◆ GetSpline()

Result< Quaternion< ValueType > > GetSpline	(	const QuaternionType &	qi_m1,
		const QuaternionType &	qi,
		const QuaternionType &	qi_p1,
		const QuaternionType &	qi_p2,
		const ValueType	t
	)

static

Interpolates two quaternions qi and qi+1 smoothly using spherical spline interpolation with parameter t. qi-1 and qi+2 are used to provide C1 continuity at the borders.

Parameters

[in]	qi_m1	Quaternion at index i-1
[in]	qi	Quaternion at index i.
[in]	qi_p1	Quaternion at index i+1
[in]	qi_p2	Quaternion at index i+2
[in]	t	Blend parameter [0.0, 1.0.]

Returns: The interpolated quaternion.

◆ ToString()

String ToString ( const FormatStatement * formatStatement = nullptr ) const

Returns a readable string of the content.

Parameters

[in] formatStatement Nullptr or additional formatting instruction. See also Formatting Floating point values.

Returns: The converted result.

◆ DescribeIO()

Result< void > DescribeIO ( const DataSerializeInterface & stream )

static

Describe all elements of this class for I/O operations.

Parameters

[in] stream The stream that is used to register the class members.

Returns: OK on success.

◆ MAXON_OPERATOR_EQUALITY_HASHCODE()

MAXON_OPERATOR_EQUALITY_HASHCODE	(	Quaternion< ValueType >	,
		v	,
		w
	)

Friends And Related Function Documentation

◆ operator*

QuaternionType operator*	(	const ValueType	s,
		const QuaternionType &	q
	)

friend

Scales the components of a quaternion with a scalar.

Member Data Documentation

◆ v

VectorType v

direction vector component

◆ w

ValueType w

angle component

Detailed Description

template<typename ValueType> class maxon::Quaternion< ValueType >

Public Member Functions

Static Public Member Functions

Public Attributes

Private Types

Private Member Functions

Friends

Member Typedef Documentation

◆ VectorType

◆ MatrixType

◆ QuaternionType

Constructor & Destructor Documentation

◆ Quaternion() [1/3]

◆ Quaternion() [2/3]

◆ Quaternion() [3/3]

Member Function Documentation

◆ MyCopysign()

◆ operator+=()

◆ operator-=()

◆ operator*=()

◆ operator+()

◆ operator-()

◆ operator*() [1/2]

◆ operator*() [2/2]

◆ SetMatrix()

◆ SetRotation()

◆ SetAxisRotation()

◆ GetMatrix()

◆ GetAxisRotation()

◆ GetSquaredLength()

◆ GetLength()

◆ GetNormalized()

◆ GetInverse()

◆ GetConjugate()

◆ GetLog()

◆ GetExp()

◆ GetPow()

◆ GetDot()

◆ GetLerp()

◆ GetSlerp()

◆ GetSquad()

◆ GetInnerQuaternion()

◆ GetSpline()

◆ ToString()

◆ DescribeIO()

◆ MAXON_OPERATOR_EQUALITY_HASHCODE()

Friends And Related Function Documentation

◆ operator*

Member Data Documentation

◆ v

◆ w

template<typename ValueType>
class maxon::Quaternion< ValueType >