A normalized quaternion. More...

#include <quaternion.h>

Classes
class	Identity

Public Member Functions
	Quaternion (const Identity &)

	Quaternion ()
	Construct a Quaternion. More...

	Quaternion (CoordType w_in, CoordType x_in, CoordType y_in, CoordType z_in)
	Construct a Quaternion from (w, x, y, z) components. More...

	Quaternion (int axis, CoordType angle)
	Construct a Quaternion giving a rotation around axis by angle. More...

	Quaternion (const Vector< 3 > &axis, CoordType angle)
	Construct a Quaternion giving a rotation around the Vector axis by angle. More...

	Quaternion (const Vector< 3 > &axis)
	Construct a Quaternion giving a rotation around the Vector axis. More...

	Quaternion (const Quaternion &p)=default
	Construct a copy of a Quaternion. More...

	Quaternion (const AtlasInType &a)
	Construct a Quaternion from an Atlas::Message::Object. More...

AtlasOutType	toAtlas () const
	Create an Atlas object from the Quaternion. More...

void	fromAtlas (const AtlasInType &a)
	Set the Quaternion's value to that given by an Atlas object. More...

Quaternion &	operator= (const Quaternion &rhs)=default

bool	isEqualTo (const Quaternion &q, CoordType epsilon=numeric_constants< CoordType >::epsilon()) const

bool	operator== (const Quaternion &rhs) const

bool	operator!= (const Quaternion &rhs) const

bool	isValid () const

Quaternion &	identity ()
	Set the Quaternion to the identity rotation. More...

Quaternion &	*operator=** (const Quaternion &rhs)

Quaternion &	operator/= (const Quaternion &rhs)

Quaternion	operator* (const Quaternion &rhs) const

Quaternion	operator/ (const Quaternion &rhs) const

bool	fromRotMatrix (const RotMatrix< 3 > &m)
	set a Quaternion's value from a RotMatrix More...

Quaternion	inverse () const
	returns the inverse of the Quaternion More...

Quaternion &	rotate (const RotMatrix< 3 > &)
	Rotate quaternion using the matrix. More...

Quaternion &	rotate (const Quaternion &q)
	rotate the quaternion using another quaternion More...

Quaternion &	rotation (int axis, CoordType angle)
	sets the Quaternion to a rotation by angle around axis More...

Quaternion &	rotation (const Vector< 3 > &axis, CoordType angle)
	sets the Quaternion to a rotation by angle around the Vector axis More...

Quaternion &	rotation (const Vector< 3 > &axis)
	sets the Quaternion to a rotation around the Vector axis More...

Quaternion &	rotation (const Vector< 3 > &from, const Vector< 3 > &to)
	Sets the Quaternion to rotate 'from' to be parallel to 'to'. More...

Quaternion &	rotation (const Vector< 3 > &from, const Vector< 3 > &to, const Vector< 3 > &fallbackAxis)
	Sets the Quaternion to rotate 'from' to be parallel to 'to'. More...

CoordType	scalar () const
	returns the scalar (w) part of the Quaternion More...

const Vector< 3 > &	vector () const
	returns the Vector (x, y, z) part of the quaternion More...

void	normalize ()
	normalize to remove accumulated round-off error More...

unsigned	age () const
	current round-off age More...

Static Public Member Functions
static const Quaternion &	IDENTITY ()

Friends
std::ostream &	operator<< (std::ostream &os, const Quaternion &p)

std::istream &	operator>> (std::istream &is, Quaternion &p)

Detailed Description

A normalized quaternion.

Definition at line 35 of file quaternion.h.

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

WFMath::Quaternion::Quaternion ( )

inline

Construct a Quaternion.

Definition at line 51 of file quaternion.h.

Referenced by IDENTITY().

◆ Quaternion() [2/7]

WFMath::Quaternion::Quaternion	(	CoordType	w_in,
		CoordType	x_in,
		CoordType	y_in,
		CoordType	z_in
	)

Construct a Quaternion from (w, x, y, z) components.

This normalizes the components so the sum of their squares is one.

Definition at line 49 of file quaternion.cpp.

References WFMath::Vector< dim >::setValid().

◆ Quaternion() [3/7]

WFMath::Quaternion::Quaternion	(	int	axis,
		CoordType	angle
	)

inline

Construct a Quaternion giving a rotation around axis by angle.

Definition at line 58 of file quaternion.h.

References rotation().

◆ Quaternion() [4/7]

WFMath::Quaternion::Quaternion	(	const Vector< 3 > &	axis,
		CoordType	angle
	)

inline

Construct a Quaternion giving a rotation around the Vector axis by angle.

Definition at line 62 of file quaternion.h.

References rotation().

◆ Quaternion() [5/7]

WFMath::Quaternion::Quaternion ( const Vector< 3 > & axis )

inlineexplicit

Construct a Quaternion giving a rotation around the Vector axis.

The angle of rotating is equal to the magnitude of the Vector

Definition at line 70 of file quaternion.h.

References rotation().

◆ Quaternion() [6/7]

WFMath::Quaternion::Quaternion ( const Quaternion & p )

default

Construct a copy of a Quaternion.

◆ Quaternion() [7/7]

WFMath::Quaternion::Quaternion ( const AtlasInType & a )

inlineexplicit

Construct a Quaternion from an Atlas::Message::Object.

Definition at line 76 of file quaternion.h.

References fromAtlas().

Member Function Documentation

◆ age()

unsigned WFMath::Quaternion::age ( ) const

inline

current round-off age

Definition at line 187 of file quaternion.h.

◆ fromAtlas()

void WFMath::Quaternion::fromAtlas ( const AtlasInType & a )

inline

Set the Quaternion's value to that given by an Atlas object.

Definition at line 127 of file atlasconv.h.

Referenced by Quaternion().

◆ fromRotMatrix()

bool WFMath::Quaternion::fromRotMatrix ( const RotMatrix< 3 > & m )

set a Quaternion's value from a RotMatrix

Since a Quaternion can only represent an even-parity RotMatrix, this function returns false if the parity of m is odd. In this case, the quaternion is set to the value of m multiplied by a fixed parity-odd RotMatrix, so the full RotMatrix can be recovered by passing the Quaternion and the value of 'not_flip' returned by this function to RotMatrix::fromQuaternion().

Definition at line 138 of file quaternion.cpp.

References WFMath::RotMatrix< dim >::age(), WFMath::RotMatrix< dim >::elem(), WFMath::RotMatrix< dim >::parity(), WFMath::Prod(), WFMath::Vector< dim >::setValid(), and WFMath::RotMatrix< dim >::trace().

Referenced by rotate().

◆ IDENTITY()

const Quaternion & WFMath::Quaternion::IDENTITY ( )

static

Gets a static identity quaternion.

Returns: A static identity quaternion.

Definition at line 64 of file quaternion.cpp.

References Quaternion().

◆ identity()

Quaternion& WFMath::Quaternion::identity ( )

inline

Set the Quaternion to the identity rotation.

Definition at line 102 of file quaternion.h.

References WFMath::Vector< dim >::zero().

◆ inverse()

Quaternion WFMath::Quaternion::inverse ( ) const

returns the inverse of the Quaternion

Definition at line 189 of file quaternion.cpp.

◆ normalize()

void WFMath::Quaternion::normalize ( )

normalize to remove accumulated round-off error

Definition at line 322 of file quaternion.cpp.

References WFMath::Vector< dim >::sqrMag().

◆ rotate() [1/2]

Quaternion& WFMath::Quaternion::rotate ( const Quaternion & q )

inline

rotate the quaternion using another quaternion

Definition at line 145 of file quaternion.h.

◆ rotate() [2/2]

Quaternion & WFMath::Quaternion::rotate ( const RotMatrix< 3 > & m )

Rotate quaternion using the matrix.

Definition at line 198 of file quaternion.cpp.

References fromRotMatrix().

◆ rotation() [1/5]

Quaternion & WFMath::Quaternion::rotation ( const Vector< 3 > & axis )

sets the Quaternion to a rotation around the Vector axis

The rotation angle is given by the magnitude of the Vector

Definition at line 247 of file quaternion.cpp.

References WFMath::Vector< dim >::mag().

◆ rotation() [2/5]

Quaternion & WFMath::Quaternion::rotation	(	const Vector< 3 > &	axis,
		CoordType	angle
	)

sets the Quaternion to a rotation by angle around the Vector axis

Definition at line 228 of file quaternion.cpp.

References WFMath::Vector< dim >::mag().

◆ rotation() [3/5]

Quaternion & WFMath::Quaternion::rotation	(	const Vector< 3 > &	from,
		const Vector< 3 > &	to
	)

Sets the Quaternion to rotate 'from' to be parallel to 'to'.

Parameters

from	The vector to rotate from.
to	The vector to rotate to.

If the vectors are colinear a ColinearVectors exception is thrown. If this is undesirable see rotation(const Vector<3>&, const Vector<3>&, const Vector<3>&) instead

Definition at line 266 of file quaternion.cpp.

References WFMath::Cross(), and WFMath::Vector< dim >::sqrMag().

◆ rotation() [4/5]

Quaternion & WFMath::Quaternion::rotation	(	const Vector< 3 > &	from,
		const Vector< 3 > &	to,
		const Vector< 3 > &	fallbackAxis
	)

Sets the Quaternion to rotate 'from' to be parallel to 'to'.

Parameters

from	The vector to rotate from.
to	The vector to rotate to.
fallbackAxis	If the vectors are colinear, rotate around this axis instead.

Definition at line 294 of file quaternion.cpp.

References WFMath::Cross(), rotation(), and WFMath::Vector< dim >::sqrMag().

◆ rotation() [5/5]

Quaternion & WFMath::Quaternion::rotation	(	int	axis,
		CoordType	angle
	)

sets the Quaternion to a rotation by angle around axis

Definition at line 207 of file quaternion.cpp.

References WFMath::Vector< dim >::setValid().

Referenced by Quaternion(), and rotation().

◆ scalar()

CoordType WFMath::Quaternion::scalar ( ) const

inline

returns the scalar (w) part of the Quaternion

Definition at line 180 of file quaternion.h.

◆ toAtlas()

AtlasOutType WFMath::Quaternion::toAtlas ( ) const

inline

Create an Atlas object from the Quaternion.

Definition at line 172 of file atlasconv.h.

◆ vector()

const Vector<3>& WFMath::Quaternion::vector ( ) const

inline

returns the Vector (x, y, z) part of the quaternion

Definition at line 182 of file quaternion.h.

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

Classes

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

Constructor & Destructor Documentation

◆ Quaternion() [1/7]

◆ Quaternion() [2/7]

◆ Quaternion() [3/7]

◆ Quaternion() [4/7]

◆ Quaternion() [5/7]

◆ Quaternion() [6/7]

◆ Quaternion() [7/7]

Member Function Documentation

◆ age()

◆ fromAtlas()

◆ fromRotMatrix()

◆ IDENTITY()

◆ identity()

◆ inverse()

◆ normalize()

◆ rotate() [1/2]

◆ rotate() [2/2]

◆ rotation() [1/5]

◆ rotation() [2/5]

◆ rotation() [3/5]

◆ rotation() [4/5]

◆ rotation() [5/5]

◆ scalar()

◆ toAtlas()

◆ vector()