Physsim::Quat Class Reference

Quaternion class used for orientation. More...

#include <Quat.h>

Inheritance diagram for Physsim::Quat:

List of all members.

Public Member Functions
	Quat ()
	Default constructor.
	Quat (Real x, Real y, Real z, Real w)
	Constructs a quaternion from four Real values.
	Quat (boost::shared_array< const Real > q)
	Constructs a quaternion from a Real array of length 4.
	Quat (const Quat &q)
	Copy constructor.
	Quat (const VectorN &v)
	Constructs a quaternion from a vector.
	Quat (const Matrix3 *m)
	Constructs a quaternion from a rotation matrix.
	Quat (const Matrix4 *m)
	Constructs a quaternion from a transformation matrix.
	Quat (const AAngle *a)
	Constructs a quaternion from an axis-angle object.
void	conjugate ()
	Negates the value of each of the x, y, and z coordinates in place.
bool	epsilon_equals (const Quat &q, Real epsilon)
	Determines whether this quaternion is equal to another within the given tolerance.
void	slerp (const Quat &q, Real alpha)
	Performs spherical linear interpolation between this and q.
void	inverse ()
	Computes the inverse orientation represented by this quaternion in place.
void	normalize ()
	Normalizes this quaternion in place.
void	set (const VectorN &v)
void	set (const AAngle *a)
	Sets this to that represented by an axis-angle representation.
void	set (const Matrix3 *m)
	Sets this quaternion to that represented by a rotation matrix.
void	set (const Matrix4 *m)
	Sets this quaternion to that represented by the rotation component of a transformation matrix.
Quat	operator- (const Quat &q) const
	Subtracts a quaternion from this.
void	operator-= (const Quat &q)
	Subtracts one quaternion from another.
Quat	operator+ (const Quat &q) const
	Adds this quaternion to another and returns the result in a new quaternion.
void	operator+= (const Quat &q)
	Adds this quaon to another and stores the result in this.
void	operator= (const Quat &q)
	Copy operator.
Quat	operator * (const Quat &q) const
	Multiplies this by q and returns the result.
Quat	operator * (Real scalar) const
	Multiplies a quaternion by a scalar.
void	operator *= (const Quat &q)
	Multiplies this by q and stores the result in this.
void	operator *= (Real scalar)
	Multiplies a quaternion by a scalar and stores the result in this.
Real	magnitude () const
	Calculates the magnitude of a quaternion.
Static Public Member Functions
static Quat	zero ()
	Constructs a zero quaternion.
static Quat	conjugate (const Quat &q)
	Negates the value of each of the x, y, and z coordinates of the given quaternion.
static bool	epsilon_equals (const Quat &q1, const Quat &q2, Real epsilon)
	Determines whether to quaternions are equal to within the given tolerance.
static Quat	slerp (const Quat &q1, const Quat &q2, Real alpha)
	Performs spherical linear interpolation between this and q.
static Quat	inverse (const Quat &q)
	Computes the inverse orientation of a quaternion.
static Quat	normalize (const Quat &q)
	Computes the normalized quaternion of q.
static Quat	deriv (const Quat &q, const Vector3 &w)
	Computes the derivative of a quaternion given current orientation and angular velocity.
static Vector3	to_omega (const Quat &q, const Quat &qd)
	Computes the angular velocity of a body given the current quaternion orientation and the quaternion velocity.
Public Attributes
Real	_x
	First quaternion component.
Real	_y
	Second quaternion component.
Real	_z
	Third quaterion component.
Real	_w
	Fourth quaternion component.

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Detailed Description

Quaternion class used for orientation.

This class is used to represent orientation via unit quaternions. Note, however, that the user is responsible for normalizing the quaternions; normalization is not automatic.

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Constructor & Destructor Documentation

Quat::Quat

(

)

Default constructor.

Quaternion constructed as [0,0,0] 1

Quat::Quat	(	Real	x,
		Real	y,
		Real	z,
		Real	w
	)

Constructs a quaternion from four Real values.

Parameters:

	x	the first component of the vector
	y	the second component of the vector
	z	the third component of the vector
	w	the scalar component of the quaternion

Quat::Quat

(

const VectorN &

v

)

Constructs a quaternion from a vector.

Parameters:

v

a four-dimensional vector (components 0..2 are the vector component, component 3 is the angular component)

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Member Function Documentation

Quat Quat::conjugate

(

const Quat &

q

)

[static]

Negates the value of each of the x, y, and z coordinates of the given quaternion.

Parameters:

q

the quaternion from which the conjugate is to be computed

void Quat::slerp	(	const Quat &	q,
		Real	alpha
	)

Performs spherical linear interpolation between this and q.

Sets the orientation represented by this quaternion to a linear interpolated orientation between this and q. If alpha is 0, then *this is unaltered. If alpha is 1, then *this is set to q.

Parameters:

	q	the "final" orientation
	alpha	interpolation value (0 <= alpha <= 1)

Quat Quat::slerp	(	const Quat &	q1,
		const Quat &	q2,
		Real	alpha
	)			[static]

Performs spherical linear interpolation between this and q.

Calculates the orientation of determined by linear interpolation between q1 and q2. If alpha is 0, then q1 is returned. If alpha is 1, then q2 is returned.

Parameters:

	q1	the "initial" orientation
	q2	the "final" orientation
	alpha	interpolation value (0 <= alpha <= 1)

Returns:

the orientation linearly interpolated between q1 and q2

void Quat::set

(

const VectorN &

v

)

Parameters:

v

a four-dimensional vector (components 0..2 are the vector component, component 3 is the angular component)

Quat Quat::deriv	(	const Quat &	q,
		const Vector3 &	w
	)			[static]

Computes the derivative of a quaternion given current orientation and angular velocity.

Note that the derivative is not generally a unit quaternion.

Parameters:

	q	the current orientation
	w	the angular velocity

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

• /home/drumwrig/Physsim/include/Physsim/Quat.h
• /home/drumwrig/Physsim/src/Quat.cpp

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