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

#include <mlRotation.h>

Public Member Functions
	Rotation ()
	Initializes this rotation to the identity rotation. More...

	Rotation (const Vector3 &axis, MLdouble angle)
	Generates a rotation from axis and angle, the angle is given in radians. More...

	Rotation (const Vector3 &fromVec, const Vector3 &toVec)
	Generates a rotation from fromVec to toVec. More...

	Rotation (const Matrix4 &m)
	Generates a rotation from rotation matrix (result is invalid, if the matrix is not a rotation matrix). More...

	Rotation (const Rotation &)
	Copy constructor. More...

	Rotation (MLdouble x, MLdouble y, MLdouble z, MLdouble w)
	Constructs a rotation from quaternion parameters x y z w. More...

Matrix4	getMatrix () const
	Converts the rotation to a rotation matrix and returns the matrix. More...

void	getRotation (Vector3 &axis, MLdouble &angle) const
	Converts the rotation to an axis axis and and angle angle (in radians). More...

void	setRotation (const Vector3 &axis, MLdouble angle)
	Builds a rotation from an axis axis and an angle angle (in radians). More...

Rotation	multiply (const Rotation &rotation) const
	Multiplies (concatenates) this rotation with rotation and returns the new rotation. More...

Vector3	rotate (const Vector3 &vec) const
	Rotates the given vector and returns the result vector. More...

Rotation &	conjugate ()
	Negates the rotation. More...

Rotation &	operator*= (const Rotation &rotation)
	Multiplies two rotations with each other (see multiply). More...

Rotation &	operator= (const Rotation &rotation)
	Assignment operator. More...

const Vector3 &	getVector () const
	Returns the vector part (x/y/z). More...

MLdouble	getScalar () const
	Returns the scalar part (w). More...

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. More...

static Rotation	slerp (const Rotation &rot1, const Rotation &rot2, MLdouble t)
	Spherical linear interpolation at t between rotation rot1 and rot2. More...

Protected Attributes
Vector3	_vector
	The x,y,z part of the quaternion. More...

MLdouble	_scalar
	The w part of the quaternion. More...

Friends
ML_LINEAR_ALGEBRA_EXPORT friend Rotation	operator* (const Rotation &a, const Rotation &b)
	Multiplies two rotations with each other (see multiply). More...

Detailed Description

Class to handle Rotations (internally the rotation is stored as a unit 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 39 of file mlRotation.h.

Constructor & Destructor Documentation

◆ Rotation() [1/6]

ml::Rotation::Rotation ( )

Initializes this rotation to the identity rotation.

◆ Rotation() [2/6]

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

Generates a rotation from axis and angle, the angle is given in radians.

◆ Rotation() [3/6]

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

Generates a rotation from fromVec to toVec.

◆ Rotation() [4/6]

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

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

◆ Rotation() [5/6]

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

Copy constructor.

◆ Rotation() [6/6]

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

Constructs a rotation from quaternion parameters x y z w.

These parameters are NOT axis and angle, read more on quaternions to use this constructor! It accepts any quaternion and normalized it to a unit quaternion.

Member Function Documentation

◆ conjugate()

Rotation& ml::Rotation::conjugate ( )

Negates the rotation.

◆ getMatrix()

Matrix4 ml::Rotation::getMatrix ( ) const

Converts the rotation to a rotation matrix and returns the matrix.

◆ getRotation()

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

Converts the rotation to an axis axis and and angle angle (in radians).

◆ getScalar()

MLdouble ml::Rotation::getScalar ( ) const

inline

Returns the scalar part (w).

Definition at line 100 of file mlRotation.h.

◆ getVector()

const Vector3& ml::Rotation::getVector ( ) const

inline

Returns the vector part (x/y/z).

Definition at line 98 of file mlRotation.h.

◆ multiply()

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

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

◆ operator*=()

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

Multiplies two rotations with each other (see multiply).

◆ operator=()

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

Assignment operator.

◆ rotate()

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

Rotates the given vector and returns the result vector.

◆ setRotation()

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

Builds a rotation from an axis axis and an angle angle (in radians).

◆ slerp() [1/2]

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.

◆ slerp() [2/2]

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

◆ operator*

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

friend

Multiplies two rotations with each other (see multiply).

Member Data Documentation

◆ _scalar

MLdouble ml::Rotation::_scalar

protected

The w part of the quaternion.

Definition at line 107 of file mlRotation.h.

◆ _vector

Vector3 ml::Rotation::_vector