The Rotation class represents a rotation around a 3-dimensional axis. More...

#include "rotation.h"

Public Types
typedef Angle< T >	AngleType
	Convenience typedefs for Angle and 3D vector of the correct type. More...

typedef Vector< 3, T >	VectorType

typedef Vector< 4, T >	QuaternionType

Public Member Functions
	Rotation ()
	The default constructor creates an identity Rotation, which has no effect. More...

bool	IsIdentity () const
	Returns true if this represents an identity Rotation. More...

void	SetQuaternion (const QuaternionType &quaternion)
	Sets the Rotation from a quaternion (4D vector), which is first normalized. More...

const QuaternionType &	GetQuaternion () const
	Returns the Rotation as a normalized quaternion (4D vector). More...

void	SetAxisAndAngle (const VectorType &axis, const AngleType &angle)
	Sets the Rotation to rotate by the given angle around the given axis, following the right-hand rule. More...

void	GetAxisAndAngle (VectorType axis, AngleType angle) const
	Returns the right-hand rule axis and angle corresponding to the Rotation. More...

void	GetEulerAngles (AngleType yaw, AngleType pitch, AngleType *roll) const
	Returns the Euler angles which would result in this rotation if done in the order of rotate-Y by yaw, rotate-X by pitch, rotate-Z by roll. More...

Rotation &	operator*= (const Rotation &r)
	Appends a rotation to this one. More...

const VectorType	operator* (const VectorType &v) const
	Multiply a Rotation and a Vector/Point to get a Vector/Point. More...

const Point< 3, T >	operator* (const Point< 3, T > &p) const

Static Public Member Functions
static Rotation	Identity ()
	Returns an identity Rotation, which has no effect. More...

static Rotation	FromAxisAndAngle (const VectorType &axis, const AngleType &angle)
	Convenience function that constructs and returns a Rotation given an axis and angle. More...

static Rotation	FromQuaternion (const QuaternionType &quat)
	Convienance function that constructs and returns a Rotation given a quaternion. More...

static Rotation	FromRotationMatrix (const Matrix< 3, T > &mat)
	Convienance function that constructs and returns a Rotation given a rotation matrix R with $R^ R = I && det(R) = 1$. More...

static Rotation	RotateInto (const VectorType &from, const VectorType &to)
	Constructs and returns a Rotation that rotates one vector to another along the shortest arc. More...

static Rotation	Slerp (const Rotation &r0, const Rotation &r1, T t)
	Performs spherical linear interpolation between two Rotation instances. More...

Friends
Rotation	operator- (const Rotation &r)
	The negation operator returns the inverse rotation. More...

const Rotation	operator* (const Rotation &r0, const Rotation &r1)
	Binary multiplication operator - returns a composite Rotation. More...

bool	operator== (const Rotation &v0, const Rotation &v1)
	Exact equality and inequality comparisons. More...

bool	operator!= (const Rotation &v0, const Rotation &v1)

Detailed Description

template<typename T>
class ion::math::Rotation< T >

The Rotation class represents a rotation around a 3-dimensional axis.

It uses normalized quaternions internally to make the math robust.

Definition at line 37 of file rotation.h.

Member Typedef Documentation

template<typename T>

typedef Angle<T> ion::math::Rotation< T >::AngleType

Convenience typedefs for Angle and 3D vector of the correct type.

Definition at line 40 of file rotation.h.

template<typename T>

typedef Vector<4, T> ion::math::Rotation< T >::QuaternionType

Definition at line 42 of file rotation.h.

template<typename T>

typedef Vector<3, T> ion::math::Rotation< T >::VectorType

Definition at line 41 of file rotation.h.

Constructor & Destructor Documentation

template<typename T>

ion::math::Rotation< T >::Rotation ( )

inline

The default constructor creates an identity Rotation, which has no effect.

Definition at line 45 of file rotation.h.

References ion::math::VectorBase< Dimension, T >::Set().

Referenced by ion::math::Rotation< T >::Identity().

Member Function Documentation

template<typename T>

static Rotation ion::math::Rotation< T >::FromAxisAndAngle	(	const VectorType &	axis,
		const AngleType &	angle
	)

inlinestatic

Convenience function that constructs and returns a Rotation given an axis and angle.

Definition at line 85 of file rotation.h.

References ion::math::Rotation< T >::SetAxisAndAngle().

template<typename T>

static Rotation ion::math::Rotation< T >::FromQuaternion ( const QuaternionType & quat )

inlinestatic

Convienance function that constructs and returns a Rotation given a quaternion.

Definition at line 94 of file rotation.h.

References ion::math::Rotation< T >::SetQuaternion().

Referenced by ion::math::Rotation< T >::FromRotationMatrix(), and ion::math::Rotation< T >::RotateInto().

template<typename T >

Rotation< T > ion::math::Rotation< T >::FromRotationMatrix ( const Matrix< 3, T > & mat )

static

Convienance function that constructs and returns a Rotation given a rotation matrix R with $R^ R = I && det(R) = 1$.

Definition at line 52 of file rotation.cc.

References ion::math::Rotation< T >::FromQuaternion(), and ion::math::Sqrt().

template<typename T >

void ion::math::Rotation< T >::GetAxisAndAngle	(	VectorType *	axis,
		AngleType *	angle
	)		const

Returns the right-hand rule axis and angle corresponding to the Rotation.

If the Rotation is the identity rotation, this returns the +X axis and an angle of 0.

Definition at line 100 of file rotation.cc.

References ion::math::ArcCosine(), DCHECK, DCHECK_NE, ion::math::Sqrt(), and ion::math::Square().

template<typename T >

void ion::math::Rotation< T >::GetEulerAngles	(	AngleType *	yaw,
		AngleType *	pitch,
		AngleType *	roll
	)		const

Returns the Euler angles which would result in this rotation if done in the order of rotate-Y by yaw, rotate-X by pitch, rotate-Z by roll.

Definition at line 115 of file rotation.cc.

References DCHECK.

template<typename T>

const QuaternionType& ion::math::Rotation< T >::GetQuaternion ( ) const

inline

Returns the Rotation as a normalized quaternion (4D vector).

Definition at line 67 of file rotation.h.

Referenced by ion::math::Rotation< T >::Slerp().

template<typename T>

static Rotation ion::math::Rotation< T >::Identity ( )

inlinestatic

Returns an identity Rotation, which has no effect.

Definition at line 51 of file rotation.h.

References ion::math::Rotation< T >::Rotation().

template<typename T>

bool ion::math::Rotation< T >::IsIdentity ( ) const

inline

Returns true if this represents an identity Rotation.

Definition at line 56 of file rotation.h.

template<typename T>

const VectorType ion::math::Rotation< T >::operator* ( const VectorType & v ) const

Multiply a Rotation and a Vector/Point to get a Vector/Point.

template<typename T >

const Point< 3, T > ion::math::Rotation< T >::operator* ( const Point< 3, T > & p ) const

Definition at line 179 of file rotation.h.

References ion::math::Point< Dimension, T >::Zero().

template<typename T>

Rotation& ion::math::Rotation< T >::operator*= ( const Rotation< T > & r )

inline

Appends a rotation to this one.

Definition at line 118 of file rotation.h.

References ion::math::Rotation< T >::SetQuaternion().

template<typename T >

Rotation< T > ion::math::Rotation< T >::RotateInto	(	const VectorType &	from,
		const VectorType &	to
	)

static

Constructs and returns a Rotation that rotates one vector to another along the shortest arc.

This returns an identity rotation if either vector has zero length.

Definition at line 150 of file rotation.cc.

References ion::math::Abs(), ion::math::Cross(), ion::math::Dot(), ion::math::Rotation< T >::FromQuaternion(), ion::math::LengthSquared(), and ion::math::Sqrt().

template<typename T >

void ion::math::Rotation< T >::SetAxisAndAngle	(	const VectorType &	axis,
		const AngleType &	angle
	)

Sets the Rotation to rotate by the given angle around the given axis, following the right-hand rule.

Rotation functions.

The axis does not need to be unit length. If it is zero length, this results in an identity Rotation.

Definition at line 39 of file rotation.cc.

References ion::math::Cosine(), ion::math::Normalize(), and ion::math::Sine().

Referenced by ion::math::Rotation< T >::FromAxisAndAngle(), and ion::math::operator>>().

template<typename T>

void ion::math::Rotation< T >::SetQuaternion ( const QuaternionType & quaternion )

inline

Sets the Rotation from a quaternion (4D vector), which is first normalized.

Definition at line 62 of file rotation.h.

References ion::math::Normalized().

Referenced by ion::math::Rotation< T >::FromQuaternion(), ion::math::Rotation< T >::operator*=(), and ion::math::Rotation< T >::Slerp().

template<typename T >

Rotation< T > ion::math::Rotation< T >::Slerp	(	const Rotation< T > &	r0,
		const Rotation< T > &	r1,
		T	t
	)

static

Performs spherical linear interpolation between two Rotation instances.

This returns r0 when t is 0 and r1 when t is 1; all other values of t interpolate appropriately.

Definition at line 178 of file rotation.cc.

References ion::math::ArcCosine(), ion::math::Clamp(), ion::math::Cosine(), ion::math::Dot(), ion::math::Rotation< T >::GetQuaternion(), ion::math::Normalized(), ion::math::Rotation< T >::SetQuaternion(), and ion::math::Sine().

Friends And Related Function Documentation

template<typename T>

bool operator!=	(	const Rotation< T > &	v0,
		const Rotation< T > &	v1
	)

friend

Definition at line 144 of file rotation.h.

template<typename T>

const Rotation operator*	(	const Rotation< T > &	r0,
		const Rotation< T > &	r1
	)

friend

Binary multiplication operator - returns a composite Rotation.

Definition at line 130 of file rotation.h.

template<typename T>

Rotation operator- ( const Rotation< T > & r )

friend

The negation operator returns the inverse rotation.

Definition at line 111 of file rotation.h.

template<typename T>

bool operator==	(	const Rotation< T > &	v0,
		const Rotation< T > &	v1
	)

friend

Exact equality and inequality comparisons.

Definition at line 141 of file rotation.h.

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

math/rotation.h
math/rotation.cc

Public Types

Public Member Functions

Static Public Member Functions

Friends

Detailed Description

template<typename T> class ion::math::Rotation< T >

Member Typedef Documentation

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

template<typename T>
class ion::math::Rotation< T >