MQuaternion Class Reference

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Detailed Description

Quaternion math.

This class provides methods for working with Quaternions. Quaternions can be used to specify orientations and rotations of 3-D objects relative to a starting reference, similar to the way that cartesian vectors can be used to specify positions and translations of 3-D objects relative to an origin. Quaternions represent orientations as a single rotation, just as rectangular co-ordinates represent position as a single vector.

Examples:

customAttrManip.cpp, hwReflectBumpShader_NV20.h, hwRefractReflectShader_NV20.cpp, and rockingTransform.cpp.

#include <MQuaternion.h>

List of all members.

Public Member Functions
	MQuaternion ()
	The default class constructor.
	MQuaternion (const MQuaternion &src)
	The copy constructor.
	MQuaternion (double xx, double yy, double zz, double ww)
	Class constructor.
	MQuaternion (const double q[4])
	Class constructor.
	MQuaternion (const MVector &a, const MVector &b)
	Class constructor.
	MQuaternion (const MVector &a, const MVector &b, double angleFactor)
	Class constructor.
	MQuaternion (double angle, const MVector &axisb)
	This constructor creates a new quaternion whose rotation is expressed by a pivot axis and a rotation (in radians) about that axis.
	~MQuaternion ()
	Class destructor.
MQuaternion &	operator= (const MQuaternion &src)
	The assignment operator.
MQuaternion &	operator= (const MMatrix &matrix)
	Convert the given 4X4 homogeneous rotation matrix to a quaternion of unit length.
MQuaternion &	operator= (const MEulerRotation &matrix)
	Convert the given euler rotation to a quaternion.
MMatrix	asMatrix () const
	Converts a quaternion to a 4X4 homogeneous rotation matrix.
MEulerRotation	asEulerRotation () const
	Converts a quaternion to an euler rotation.
MQuaternion &	setAxisAngle (const MVector &axis, double theta)
	Sets this quaternion to be the rotation as expressed by a pivot axis and a rotation theta (in radians) about that axis.
bool	getAxisAngle (MVector &axis, double &theta) const
	Converts this quaternion into a user understandable representation.
MQuaternion &	setToXAxis (double theta)
	Sets this quaternion to be the rotation about the X axis of theta (in radians).
MQuaternion &	setToYAxis (double theta)
	Sets this quaternion to be the rotation about the Y axis of theta (in radians).
MQuaternion &	setToZAxis (double theta)
	Sets this quaternion to be the rotation about the Z axis of theta (in radians).
MStatus	get (double dest[4]) const
	Extracts the x, y, z, and w components of the quaternion and places them in elements 0, 1, 2, and 3 of the double array passed.
double	operator[] (unsigned int i) const
	The index operator.
MQuaternion	operator+ (const MQuaternion &other) const
	The quaternion addition operator.
MQuaternion	operator* (const MQuaternion &other) const
	This quaternion multiplication operator.
MQuaternion &	operator*= (const MQuaternion &rhs)
	The in place quaternion multiplication operator.
MQuaternion	operator- (const MQuaternion &other) const
	The quaternion subtraction operator.
MQuaternion	operator- () const
	The unary minus operator.
MQuaternion &	negateIt ()
	Performs an in place negation of the quaternion.
bool	operator== (const MQuaternion &other) const
	The quaternion equality operator.
bool	operator!= (const MQuaternion &other) const
	The quaternion inequality operator.
bool	isEquivalent (const MQuaternion &other, double tolerance=kQuaternionEpsilon) const
	This method returns true if this quaternion is equal, within some given tolerance, to the other quaternion.
MQuaternion &	scaleIt (double scale)
	Performs an in place scaling of the quaternion.
MQuaternion	normal () const
	Returns the normal of this quaternion.
MQuaternion &	normalizeIt ()
	Performs an in place normalization of this quaternion.
MQuaternion	conjugate () const
	Returns the conjugate of this quaternion.
MQuaternion &	conjugateIt ()
	Performs an in place conjugation of this quaternion.
MQuaternion	inverse () const
	Returns the inverse of this quaternion.
MQuaternion &	invertIt ()
	Performs an in place inversion of this quaternion.
MQuaternion	log () const
	Returns the natural log of a quaternion.
MQuaternion	exp () const
	Exponentiates a quaternion that has a scalar part of zero.
double &	operator[] (unsigned int i)
	NO SCRIPT SUPPORT.
	operator MMatrix () const
	NO SCRIPT SUPPORT.
Public Attributes
double	x
	The quaternion's imaginary x component. Search for all occurrences
double	y
	The quaternion's imaginary y component. Search for all occurrences
double	z
	The quaternion's imaginary z component. Search for all occurrences
double	w
	The quaternion's real component.
Static Public Attributes Search for all occurrences
static const MQuaternion	identity
	The multiplicative identity.
Friends
OPENMAYA_EXPORT MQuaternion	operator* (double scale, const MQuaternion &other)
	NO SCRIPT SUPPORT.
OPENMAYA_EXPORT MQuaternion	slerp (const MQuaternion &p, const MQuaternion &q, double t)
	Spherical linear interpolation (abbreviated as slerp) of unit quaternions.
OPENMAYA_EXPORT MQuaternion	slerp (const MQuaternion &p, const MQuaternion &q, double t, short spin)
	NO SCRIPT SUPPORT.
OPENMAYA_EXPORT MQuaternion	squad (const MQuaternion &p, const MQuaternion &a, const MQuaternion &b, const MQuaternion &q, double t)
	NO SCRIPT SUPPORT.
OPENMAYA_EXPORT MQuaternion	squad (const MQuaternion &p, const MQuaternion &a, const MQuaternion &b, const MQuaternion &q, double t, short spin)
	NO SCRIPT SUPPORT.
OPENMAYA_EXPORT MQuaternion	squadPt (const MQuaternion &q0, const MQuaternion &q1, const MQuaternion &q2)
	NO SCRIPT SUPPORT.
OPENMAYA_EXPORT std::ostream &	operator<< (std::ostream &os, const MQuaternion &q)
	NO SCRIPT SUPPORT. Search for all occurrences

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Constructor & Destructor Documentation

MQuaternion

(

)

The default class constructor.

Initializes the quaternion to the multiplicative identity.

MQuaternion

(

const MQuaternion &

src

)

The copy constructor.

Creates a new quaternion and initializes it to the same values as the given quaternion.

Parameters:

[in]

src

the quaternion object to copy

MQuaternion	(	double	xx,
		double	yy,
		double	zz,
		double	ww
	)

Class constructor.

Initializes the quaternion with the explicit x, y, z, and w values provided as arguments.

Parameters:

[in]	xx	the x component of the quaternion
[in]	yy	the y component of the quaternion
[in]	zz	the z component of the quaternion.
[in]	ww	the w component of the quaternion.

MQuaternion

(

const double

q[4]

)

Class constructor.

Initializes the quaternion with the explicit x, y, z, and w values provided in the given double array.

Parameters:

[in]

q

the 4 element array containing the initial x, y, z, and w values

MQuaternion	(	const MVector &	a,
		const MVector &	b
	)

Class constructor.

Creates a new quaternion that will rotate vector a into vector b about their mutually perpendicular axis.

Parameters:

[in]	a	vector to rotate from
[in]	b	vector to rotate to

MQuaternion	(	const MVector &	a,
		const MVector &	b,
		double	angleFactor
	)

Class constructor.

Creates a new quaternion that will rotate vector a into vector b about their mutually perpendicular axis by a given factor.

Parameters:

[in]	a	vector to rotate from
[in]	b	vector to rotate to
[in]	angleFactor	the factor by which the rotation should be multiplied; a factor of 1.0 is equivalent to a rotation of vector a into vector b

MQuaternion	(	double	angle,
		const MVector &	axis
	)

This constructor creates a new quaternion whose rotation is expressed by a pivot axis and a rotation (in radians) about that axis.

If the length of the axis is too small the quaternion returned will be the identity quaternion.

Parameters:

[in]	angle	the amount of rotation around the axis
[in]	axis	the axis about which the rotation occurs

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Member Function Documentation

MQuaternion & operator=

(

const MQuaternion &

src

)

The assignment operator.

Parameters:

[in]

src

the source quaternion

Returns:

A reference to the quaternion that has been assigned to the source quaternion

MQuaternion & operator=

(

const MMatrix &

matrix

)

Convert the given 4X4 homogeneous rotation matrix to a quaternion of unit length.

This methods always returns a quaternion of unit length if it is given a proper orthogonal matrix. A proper othogonal matrix is one such that the determinant of the matrix is one. (If the determinant were -1, this would imply that the orthogonal matrix is also producing a reflection, in addition to a rotation.)

Parameters:

[in]

matrix

the matrix to be converted to a quaternion

Returns:

A reference to the quaternion that has been converted from the rotation matrix

MQuaternion & operator=

(

const MEulerRotation &

euler

)

Convert the given euler rotation to a quaternion.

Parameters:

[in]

euler

the euler rotation to be converted to a quaternion

Returns:

A reference to the quaternion that has been converted from the euler rotation

MMatrix asMatrix

(

)

const

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Converts a quaternion to a 4X4 homogeneous rotation matrix.

The construction of the matrix assumes that the vectors are going to be multiplied on the left side of the matrix. If the quaternion's length has degenerated, this method will still produce a well behaved matrix.

ReturnValue

• the matrix converted from a quaternion

Examples:

rockingTransform.cpp.

MEulerRotation asEulerRotation

(

)

const

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Converts a quaternion to an euler rotation.

ReturnValue

• the euler rotation converted from a quaternion

MQuaternion & setAxisAngle	(	const MVector &	axis,
		double	theta
	)

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Sets this quaternion to be the rotation as expressed by a pivot axis and a rotation theta (in radians) about that axis.

If the axis is too small the quaternion returned will be the identity quaternion.

Parameters:

[in]	axis	the axis about which to rotate
[in]	theta	the angle of rotation about the axis in radians

Returns:

A reference to the quaternion that has had its axis and angle set

bool getAxisAngle	(	MVector &	axis,
		double &	theta
	)		const

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Converts this quaternion into a user understandable representation.

That is, the quaternion is represented as a pivot vector 'axis' and a rotation 'theta' (in radians) about that pivot vector.

If the identity unit quaternion is attempted to be converted to the pivot axis and angle representation it will be set to a zero degree rotation about the axis that was passed in. (Note that any axis will do, since an infinity of axis with rotation of zero satisfy the identity rotation.) If the axis is zero length, then an arbitrary axis will be chosen (z-axis).

Parameters:

[out]	axis	the axis about which the rotation occurs
[out]	theta	the angle of rotation about the axis in radians

Returns:

• true angle != 0
• false angle == 0 (uses arbitrary axis, if given axis not valid)

Examples:

hwRefractReflectShader_NV20.cpp.

MQuaternion & setToXAxis

(

double

theta

)

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Sets this quaternion to be the rotation about the X axis of theta (in radians).

If the length of the axis is too small the quaternion returned will be the identity quaternion.

Parameters:

[in]

theta

the angle of rotation about the X axis in radians

Returns:

A reference to the quaternion that has been set to rotate about the X axis by the given amount

Examples:

rockingTransform.cpp.

MQuaternion & setToYAxis

(

double

theta

)

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Sets this quaternion to be the rotation about the Y axis of theta (in radians).

If the length of the axis is too small the quaternion returned will be the identity quaternion.

Parameters:

[in]

theta

the angle of rotation about the Y axis in radians

Returns:

A reference to the quaternion that has been set to rotate about the Y axis by the given amount

MQuaternion & setToZAxis

(

double

theta

)

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Sets this quaternion to be the rotation about the Z axis of theta (in radians).

If the length of the axis is too small the quaternion returned will be the identity quaternion.

Parameters:

[in]

theta

the angle of rotation about the Z axis in radians

Returns:

A reference to the quaternion that has been set to rotate about the Z axis by the given amount

MStatus get

(

double

dest[4]

)

const

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Extracts the x, y, z, and w components of the quaternion and places them in elements 0, 1, 2, and 3 of the double array passed.

Parameters:

[out]

dest

the array of 4 doubles into which the results are placed.

Returns:

MS::kSuccess if dest is a non-zero pointer and MS::kFailure otherwise

double operator[]

(

unsigned int

i

)

const

The index operator.

If its argument is 0 it will return the x component of the quaternion. If its argument is 1 it will return the y component of the quaternion. If its argument is 2 it will return the z component of the quaternion. If its argument is 3 it will return the w component of the quaternion.

Parameters:

[in]

i

value indicating which component to return

Returns:

The component of the quaternion corresponding to the index

MQuaternion operator+

(

const MQuaternion &

other

)

const

The quaternion addition operator.

Parameters:

[in]

other

the quaternion to be added to this quaternion

Returns:

The sum of the two quaternions

MQuaternion operator*

(

const MQuaternion &

other

)

const

This quaternion multiplication operator.

Quaternions in Maya multiply on the right (post-multiply) the same as matrices. Many popular quaternion papers (Shoemake) use pre-multiplication where quaternions pre-multiply on the left so you must be aware of this when using quaternions.

In general, if p and q are quaternions, pq != qp, i.e., multiplication does not commute!

Parameters:

[in]

other

the quaternion to be multiplied with this quaternion

Returns:

The product of the two quaternions

MQuaternion & operator*=

(

const MQuaternion &

other

)

The in place quaternion multiplication operator.

Quaternions in Maya multiply on the right (post-multiply) the same as matrices.

Parameters:

[in]

other

the quaternion to be multiplied with this quaternion

Returns:

A reference to this quaternion which has been multiplied with the other quaternion

MQuaternion operator-

(

const MQuaternion &

other

)

const

The quaternion subtraction operator.

Parameters:

[in]

other

the quaternion to be subtracted from this quaternion

Returns:

The quaternion that results from the subtraction

MQuaternion operator-

(

)

const

The unary minus operator.

Negates the value of each of the x, y, z, and w components of the quaternion.

Returns:

Quaternion that results from the negation

MQuaternion & negateIt

(

)

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Performs an in place negation of the quaternion.

The result is a quaternion whose x, y, z, and w values have been negated.

Returns:

A reference to the quaternion that has been negated

bool operator==

(

const MQuaternion &

other

)

const

The quaternion equality operator.

This returns true if all four of the x, y, z, and w components are identical.

Parameters:

[in]

other

the quaternion to be compared with this quaternion

Returns:

• true the quaternions are identical
• false the quaternions are not identical

bool operator!=

(

const MQuaternion &

other

)

const

The quaternion inequality operator.

This returns false if all four of the x, y, z, and w components are identical.

Parameters:

[in]

other

the quaternion to be compared with this quaternion

Returns:

• true the quaternions are not identical
• false the quaternions are identical

bool isEquivalent	(	const MQuaternion &	other,
		double	tolerance = kQuaternionEpsilon
	)		const

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This method returns true if this quaternion is equal, within some given tolerance, to the other quaternion.

'tolerance' defaults to kQuaternionEpsilon which is 1.0e-10

Parameters:

[in]	other	the quaternion to be compared with this quaternion
[in]	tolerance	the amount of variation allowed for equivalency

Returns:

• true the quaternions are equivalent
• false the quaternions are not equivalent

MQuaternion & scaleIt

(

double

scale

)

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Performs an in place scaling of the quaternion.

The result is a quaternion whose x, y, z, and w values have been scaled by the specified amount.

Parameters:

[in]

scale

the amount by which the quaternion should be scaled

Returns:

A reference to the quaternion that has been scaled

MQuaternion normal

(

)

const

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Returns the normal of this quaternion.

The result is a quaternion of unit length.

If the quaternion is zero or has a very small length it will instead be set to the multiplicative identity.

Returns:

Quaternion that is the normal of this quaternion

MQuaternion & normalizeIt

(

)

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Performs an in place normalization of this quaternion.

The result is a quaternion of unit length.

If the quaternion is zero or has a very small length it will instead be set to the multiplicative identity.

Returns:

A reference to the quaternion that has been normalized

MQuaternion conjugate

(

)

const

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Returns the conjugate of this quaternion.

The result is a quaternion whose x, y, and z values have been negated.

Returns:

Quaternion that is the conjugate of this quaternion

MQuaternion & conjugateIt

(

)

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Performs an in place conjugation of this quaternion.

The result is a quaternion whose x, y, and z values have been negated.

Returns:

A reference to the quaternion that has been conjugated

MQuaternion inverse

(

)

const

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Returns the inverse of this quaternion.

Returns:

Quaternion that is the inverse of this quaternion

MQuaternion & invertIt

(

)

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Performs an in place inversion of this quaternion.

Returns:

A reference to the quaternion that has been inverted

MQuaternion log

(

)

const

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Returns the natural log of a quaternion.

The precondition for using this method is that the quaternion must be normalized.

Note that the log of a unit quaternion is not necessarily a unit quaternion.

Returns:

Quaternion that is the log of this quaternion

MQuaternion exp

(

)

const

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Exponentiates a quaternion that has a scalar part of zero.

The precondition for using this method is that w is zero.

Returns:

Quaternion that is the result of exponentiating this quaternion

double & operator[]

(

unsigned int

i

)

NO SCRIPT SUPPORT.

The index operator.

If its argument is 0 it will return the x component of the quaternion. If its argument is 1 it will return the y component of the quaternion. If its argument is 2 it will return the z component of the quaternion. If its argument is 3 it will return the w component of the quaternion.

Parameters:

[in]

i

value indicating which component to return

Returns:

A reference to the component of the quaternion corresponding to the index

operator MMatrix

(

)

const

NO SCRIPT SUPPORT.

Casts a quaternion to a matrix.

Returns:

A matrix that is casted from a quaternion

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Friends And Related Function Documentation

OPENMAYA_EXPORT MQuaternion operator*	(	double	scale,
		const MQuaternion &	other
	)		[friend]

NO SCRIPT SUPPORT.

Parameters:

[in]	scale	the amount by which the quaternion should be scaled
[in]	other	the quaternion to which the scale should be applied

Returns:

Quaternion that is the result of scaling the other quaternion

OPENMAYA_EXPORT MQuaternion slerp	(	const MQuaternion &	p,
		const MQuaternion &	q,
		double	t
	)		[friend]

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Spherical linear interpolation (abbreviated as slerp) of unit quaternions.

As t goes from 0 to 1, the quaternion returned goes from p to q. The interpolation always takes shortest path (in quaternion space) from p to q.

Parameters:

[in]	p	quaternion to rotate from
[in]	q	quaternion to rotate to
[in]	t	interpolation value

Returns:

Quaternion that has been interpolated from p to q

OPENMAYA_EXPORT MQuaternion slerp	(	const MQuaternion &	p,
		const MQuaternion &	q,
		double	t,
		short	spin
	)		[friend]

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NO SCRIPT SUPPORT.

As t goes from 0 to 1, the quaternion returned goes from p to q. The spin parameter determines how many complete revolutions around the axis will occur as p goes to q. Negative spins will take the "long way" around the great sphere when rotating. (-1 can be used to interpolate using the "long" path on the quaternion sphere without any extra spins.)

Parameters:

[in]	p	quaternion to rotate from
[in]	q	quaternion to rotate to
[in]	t	interpolation value
[in]	spin	the number of complete revolutions around the axis

Returns:

Quaternion that has been interpolated from p to q

OPENMAYA_EXPORT MQuaternion squad	(	const MQuaternion &	p,
		const MQuaternion &	a,
		const MQuaternion &	b,
		const MQuaternion &	q,
		double	t
	)		[friend]

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NO SCRIPT SUPPORT.

Need to use squadPoint or some other suitable method for finding a and b

Parameters:

[in]	p	quaternion to rotate from
[in]	a	intermediate squad point
[in]	b	intermediate squad point
[in]	q	quaternion to rotate to
[in]	t	interpolation value

Returns:

Quaternion that has been interpolated from p to q

OPENMAYA_EXPORT MQuaternion squad	(	const MQuaternion &	p,
		const MQuaternion &	a,
		const MQuaternion &	b,
		const MQuaternion &	q,
		double	t,
		short	spin
	)		[friend]

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NO SCRIPT SUPPORT.

Need to use squadPoint or some other suitable method for finding a and b

Parameters:

[in]	p	quaternion to rotate from
[in]	a	intermediate squad point
[in]	b	intermediate squad point
[in]	q	quaternion to rotate to
[in]	t	interpolation value
[in]	spin	number of full spins

Returns:

Quaternion that has been interpolated from p to q

OPENMAYA_EXPORT MQuaternion squadPt	(	const MQuaternion &	q0,
		const MQuaternion &	q1,
		const MQuaternion &	q2
	)		[friend]

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NO SCRIPT SUPPORT.

This method uses the average of the tangents of arcs to adjacent points. Therefore, to squad from p to q we need to find a and b in the following manner:

Given: unit quaternion control points we wish to interpolate (q0, q1,..., p-1, p, q, q+1,..., qN)

Want: a, b such that squad(p, a, b, q, t) generates a C1 continuous cubic curve from p to q as we vary t from 0 to 1.

Calculation: a = squadPoint(p-1, p, q); b = squadPoint(p, q, q+1);

Notes: We only need to compute one squadPoint for each segment (except at endpoints) since the next 'a' value is simply our current 'b' value (ie. a(i) = b(i-1) or b(i) = a(i+1)).

Parameters:

[in]	q0	quaternion from which the squad is computed
[in]	q1	quaternion from which the squad is computed
[in]	q2	quaternion from which the squad is computed

Returns:

Unit quaternion resulting from the squad computation

OPENMAYA_EXPORT std::ostream& operator<<	(	std::ostream &	os,
		const MQuaternion &	q
	)		[friend]

NO SCRIPT SUPPORT.

The format used is [x: x, y: y, z: z, w: w].

Parameters:

[in]	os	the ostream to print to
[in]	q	the quaternion to be printed

Returns:

The ostream reference, os, provided as the first parameter.