Class to handle Rotations (internally the rotation is stored as a quaternion) More...

#include <mlRotation.h>

Public Member Functions
	Rotation ()
	Rotation initialized to identity rotation.
	Rotation (const Vector3 &axis, MLdouble angle)
	Generate from axis and angle, the angle is given in radian.
	Rotation (const Vector3 &fromVec, const Vector3 &toVec)
	Generate rotation from fromVec to toVec.
	Rotation (const Matrix4 &m)
	Generate rotation from rotation matrix (result is invalid, if the matrix is not a rotation matrix)
	Rotation (const Rotation &)
	Copy constructor.
	Rotation (MLdouble x, MLdouble y, MLdouble z, MLdouble w)
	Construct rotation from quaternion parameters x y z w (these parameters are NOT axis and angle, read more on quaternions to use this constructor)
Matrix4	getMatrix () const
	Convert the Rotation to a Rotation Matrix.
void	getRotation (Vector3 &axis, MLdouble &angle) const
	Convert the Rotation to an axis axis and and angle angle (in radian).
void	setRotation (const Vector3 &axis, MLdouble angle)
	Build a rotation from and axis axis and an angle angle (in radian).
Rotation	multiply (const Rotation &rotation) const
	Multiplies (concatenates) this rotation with rotation and returns the new rotation.
Vector3	rotate (const Vector3 &vec) const
	Rotate the given vector, return the result vector.
Rotation &	conjugate ()
	Negates the rotation.
Rotation &	operator*= (const Rotation &rotation)
	Multiply two rotations with each other (see multiply)
Rotation &	operator= (const Rotation &rotation)
	Assignment operator.
Static Public Member Functions
static Matrix4	slerp (const Matrix4 &m1, const Matrix4 &m2, MLdouble t)
	spherical linear interpolation at t between matrices m1 and m2.
static Rotation	slerp (const Rotation &rot1, const Rotation &rot2, MLdouble t)
	spherical linear interpolation at t between rotation rot1 and rot2.
Protected Attributes
Vector3	_vector
	The x,y,z part of the quaternion.
MLdouble	_scalar
	The w part of the quaternion.
Friends
ML_LINEAR_ALGEBRA_EXPORT friend Rotation	operator* (const Rotation &a, const Rotation &b)
	Multiply two rotations with each other (see multiply)

Detailed Description

Class to handle Rotations (internally the rotation is stored as a quaternion)

See "Advanced Animation and Rendering Techniques", Watt, Addison+Wesley, page 360ff for an introduction on quaternions. For technical details, see: http://skal.planet-d.net/demo/matrixfaq.htm#Q47 The implementation of this class is based on the code examples in the FAQ.

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 such as Longitude, Latitude and Rotation angles. A Quaternion is defined using four floating point values |x y z w|. These are calculated from the combination of the three coordinates of the rotation axis and the rotation angle.

Definition at line 34 of file mlRotation.h.

Constructor & Destructor Documentation

ml::Rotation::Rotation ( )

Rotation initialized to identity rotation.

ml::Rotation::Rotation	(	const Vector3 &	axis,
		MLdouble	angle
	)

Generate from axis and angle, the angle is given in radian.

ml::Rotation::Rotation	(	const Vector3 &	fromVec,
		const Vector3 &	toVec
	)

Generate rotation from fromVec to toVec.

ml::Rotation::Rotation ( const Matrix4 & m )

Generate rotation from rotation matrix (result is invalid, if the matrix is not a rotation matrix)

ml::Rotation::Rotation ( const Rotation & )

Copy constructor.

ml::Rotation::Rotation	(	MLdouble	x,
		MLdouble	y,
		MLdouble	z,
		MLdouble	w
	)

Construct rotation from quaternion parameters x y z w (these parameters are NOT axis and angle, read more on quaternions to use this constructor)

Member Function Documentation

Rotation& ml::Rotation::conjugate ( )

Negates the rotation.

Matrix4 ml::Rotation::getMatrix ( ) const

Convert the Rotation to a Rotation Matrix.

void ml::Rotation::getRotation	(	Vector3 &	axis,
		MLdouble &	angle
	)		const

Convert the Rotation to an axis axis and and angle angle (in radian).

Rotation ml::Rotation::multiply ( const Rotation & rotation ) const

Multiplies (concatenates) this rotation with rotation and returns the new rotation.

Rotation& ml::Rotation::operator*= ( const Rotation & rotation )

Multiply two rotations with each other (see multiply)

Rotation& ml::Rotation::operator= ( const Rotation & rotation )

Assignment operator.

Vector3 ml::Rotation::rotate ( const Vector3 & vec ) const

Rotate the given vector, return the result vector.

void ml::Rotation::setRotation	(	const Vector3 &	axis,
		MLdouble	angle
	)

Build a rotation from and axis axis and an angle angle (in radian).

static Matrix4 ml::Rotation::slerp	(	const Matrix4 &	m1,
		const Matrix4 &	m2,
		MLdouble	t
	)		`[static]`

spherical linear interpolation at t between matrices m1 and m2.

returns an interpolated rotation matrix

static Rotation ml::Rotation::slerp	(	const Rotation &	rot1,
		const Rotation &	rot2,
		MLdouble	t
	)		`[static]`

spherical linear interpolation at t between rotation rot1 and rot2.

returns an interpolated rotation

Friends And Related Function Documentation

ML_LINEAR_ALGEBRA_EXPORT friend Rotation operator*	(	const Rotation &	a,
		const Rotation &	b
	)		`[friend]`

Multiply two rotations with each other (see multiply)

Member Data Documentation

MLdouble ml::Rotation::_scalar [protected]

The w part of the quaternion.

Definition at line 96 of file mlRotation.h.

Vector3 ml::Rotation::_vector [protected]

The x,y,z part of the quaternion.

Definition at line 93 of file mlRotation.h.

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

MeVis/Foundation/Sources/MLLinearAlgebra/mlRotation.h

Public Member Functions

Static Public Member Functions

Protected Attributes

Friends

Detailed Description

Constructor & Destructor Documentation

Member Function Documentation

Friends And Related Function Documentation

Member Data Documentation