Definitions of quaternion types. More...

#include <math.h>
#include <Eigen/Core>
#include <Eigen/Geometry>

Namespaces
	SurgSim
	Wraps glewInit() to separate the glew opengl definitions from the osg opengl definitions only imgui needs glew but we need to call glewInit() from a osg callback, using this call we avoid getting warnings about redefinitions.

Typedefs
typedef Eigen::Quaternion< float >	SurgSim::Math::Quaternionf
	A quaternion of floats. More...

typedef Eigen::Quaternion< double >	SurgSim::Math::Quaterniond
	A quaternion of doubles. More...

Functions
template<typename T , int VOpt>
Eigen::Quaternion< T >	SurgSim::Math::makeRotationQuaternion (const T &angle, const Eigen::Matrix< T, 3, 1, VOpt > &axis)
	Create a quaternion rotation corresponding to the specified angle (in radians) and axis. More...

template<typename T , int QOpt>
Eigen::Quaternion< T, QOpt >	SurgSim::Math::negate (const Eigen::Quaternion< T, QOpt > &q)
	Quaternion negation (i.e. More...

template<typename T , int QOpt, int VOpt>
void	SurgSim::Math::computeAngleAndAxis (const Eigen::Quaternion< T, QOpt > &quaternion, T angle, Eigen::Matrix< T, 3, 1, VOpt > axis)
	Get the angle (in radians) and axis corresponding to a quaternion's rotation. More...

template<typename T , int QOpt>
T	SurgSim::Math::computeAngle (const Eigen::Quaternion< T, QOpt > &quaternion)
	Get the angle corresponding to a quaternion's rotation, in radians. More...

template<typename T , int TOpt, int VOpt>
void	SurgSim::Math::computeRotationVector (const Eigen::Transform< T, 3, Eigen::Isometry, TOpt > &end, const Eigen::Transform< T, 3, Eigen::Isometry, TOpt > &start, Eigen::Matrix< T, 3, 1, VOpt > *rotationVector)
	Get the vector corresponding to the rotation between transforms. More...

template<typename T , int QOpt>
Eigen::Quaternion< T, QOpt >	SurgSim::Math::interpolate (const Eigen::Quaternion< T, QOpt > &q0, const Eigen::Quaternion< T, QOpt > &q1, T t)
	Interpolate (slerp) between 2 quaternions. More...

template<typename T >
::std::ostream &	Eigen::operator<< (::std::ostream &os, const Eigen::Quaternion< T > &quaternion)

Detailed Description

Definitions of quaternion types.

Typedef Documentation

§ Quaterniond

typedef Eigen::Quaternion<double> SurgSim::Math::Quaterniond

A quaternion of doubles.

This type (and any structs that contain it) can be safely allocated via new.

§ Quaternionf

typedef Eigen::Quaternion<float> SurgSim::Math::Quaternionf

A quaternion of floats.

This type (and any structs that contain it) can be safely allocated via new.

Function Documentation

§ computeAngle()

template<typename T , int QOpt>

T SurgSim::Math::computeAngle ( const Eigen::Quaternion< T, QOpt > & quaternion )

inline

Get the angle corresponding to a quaternion's rotation, in radians.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
QOpt	the option flags (alignment etc.) used for the quaternion argument. Can be deduced.

Parameters

quaternion the rotation quaternion to inspect.

Returns: the angle of the rotation within [0 +pi], in radians.

§ computeAngleAndAxis()

template<typename T , int QOpt, int VOpt>

void SurgSim::Math::computeAngleAndAxis	(	const Eigen::Quaternion< T, QOpt > &	quaternion,
		T *	angle,
		Eigen::Matrix< T, 3, 1, VOpt > *	axis
	)

inline

Get the angle (in radians) and axis corresponding to a quaternion's rotation.

Note: Unit quaternions cover the unit sphere twice (q=-q). To make sure that the same rotation (q or -q); returns the same Axis/Angle, we need a pi range for the angle.; We choose to enforce half the angle in the quadrant [0 +pi/2], which leads to an output angle in [0 +pi].

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
QOpt	the option flags (alignment etc.) used for the quaternion argument. Can be deduced.
VOpt	the option flags (alignment etc.) used for the axis vector argument. Can be deduced.

Parameters

	quaternion	the rotation quaternion to inspect.
[out]	angle	the angle of the rotation in [0 +pi], in radians.
[out]	axis	the axis of the rotation.

§ computeRotationVector()

template<typename T , int TOpt, int VOpt>

void SurgSim::Math::computeRotationVector	(	const Eigen::Transform< T, 3, Eigen::Isometry, TOpt > &	end,
		const Eigen::Transform< T, 3, Eigen::Isometry, TOpt > &	start,
		Eigen::Matrix< T, 3, 1, VOpt > *	rotationVector
	)

Get the vector corresponding to the rotation between transforms.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
TOpt	the option flags (alignment etc.) used for the transform arguments. Can be deduced.
VOpt	the option flags (alignment etc.) used for the vector argument. Can be deduced.

Parameters

	end	the transform after the rotation.
	start	the transform before the rotation.
[out]	rotationVector	a vector describing the rotation.

§ interpolate()

template<typename T , int QOpt>

Eigen::Quaternion<T, QOpt> SurgSim::Math::interpolate	(	const Eigen::Quaternion< T, QOpt > &	q0,
		const Eigen::Quaternion< T, QOpt > &	q1,
		T	t
	)

inline

Interpolate (slerp) between 2 quaternions.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
QOpt	the option flags (alignment etc.) used for the quaternion arguments. Can be deduced.

Parameters

q0	The start quaternion (at time 0.0).
q1	The end quaternion (at time 1.0).
t	The interpolation time requested. Within [0..1].

Returns: the quaternion resulting in the slerp interpolation at time t, between q0 and q1.

Note: t=0 => returns either q0 or -q0; t=1 => returns either q1 or -q1; 'Interpolate' has been created because slerp might not be enough in certain cases. This gives room for correction and special future treatment

§ makeRotationQuaternion()

template<typename T , int VOpt>

Eigen::Quaternion<T> SurgSim::Math::makeRotationQuaternion	(	const T &	angle,
		const Eigen::Matrix< T, 3, 1, VOpt > &	axis
	)

inline

Create a quaternion rotation corresponding to the specified angle (in radians) and axis.

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
VOpt	the option flags (alignment etc.) used for the axis vector argument. Can be deduced.

Parameters

angle	the angle of the rotation, in radians.
axis	the axis of the rotation.

Returns: the rotation quaternion.

§ negate()

template<typename T , int QOpt>

Eigen::Quaternion<T, QOpt> SurgSim::Math::negate ( const Eigen::Quaternion< T, QOpt > & q )

inline

Quaternion negation (i.e.

unary operator -)

Template Parameters

T	the numeric data type used for arguments and the return value. Can usually be deduced.
QOpt	the option flags (alignment etc.) used for the quaternion arguments. Can be deduced.

Parameters

q	The quaternion to negate

Returns: the negation of q (i.e. -q)

Namespaces

Typedefs

Functions

Detailed Description

Typedef Documentation

§ Quaterniond

§ Quaternionf

Function Documentation

§ computeAngle()

§ computeAngleAndAxis()

§ computeRotationVector()

§ interpolate()

§ makeRotationQuaternion()

§ negate()