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.

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

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

	Rotation (const Matrix4 &m)
	Generates a rotation from a rotation matrix. The 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)
	Constructs a rotation from quaternion parameters x y z w.

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

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

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

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

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

Rotation &	conjugate ()
	Negates the rotation.

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

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

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

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

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 rotations `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)
	Multiplies two rotations with each other (see multiply).

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

Quaternions extend the concept of rotation in three dimensions to rotation in four dimensions. This avoids the problem of a 'gimbal-lock' and allows for the implementation of a 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 37 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 a rotation matrix. The 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 normalizes 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 99 of file mlRotation.h.

◆ getVector()

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

inline

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

Definition at line 96 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 rotations rot1 and rot2.

Returns an interpolated rotation.

Friends And Related Symbol 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 106 of file mlRotation.h.

◆ _vector

Vector3 ml::Rotation::_vector