# MTransformationMatrix Class Reference [OpenMaya - API module for common classes]

`#include <MTransformationMatrix.h>`

Collaboration diagram for MTransformationMatrix: [legend]

## Detailed Description

Transformation matrix.

An MTransformationMatrix allows the manipulation of the individual transformation components (eg scale, rotation, shear, etc) of a four by four transformation matrix.

The transformation in the node is represented as a 4x4 transformation matrix. This class allows access to the whole matrix, or the individual components (eg scale, rotation, shear, etc) of the transformation. This breakdown provides animators fine control over the animation of these parameters. Therefore, it is necessary to describe the order in which these attributes are applied to build the final matrix attribute.

A transformation matrix is composed of the following components:

• Scale pivot point point around which scales are performed [Sp]
• Scale scaling about x, y, z axes [S]
• Shear shearing in xy, xz, yx [Sh]
• Scale pivot translation translation introduced to preserve existing scale transformations when moving pivot. This is used to prevent the object from moving when the objects pivot point is not at the origin and a non-unit scale is applied to the object [St].
• Rotate pivot point point about which rotations are performed [Rp]
• Rotation orientation rotation to orient local rotation space [Ro]
• Rotation rotation [R]
• Rotate pivot translation translation introduced to preserve exisitng rotate transformations when moving pivot. This is used to prevent the object from moving when the objects pivot point is not at the origin and the pivot is moved. [Rt]
• Translate translation in x, y, z axes [T]
Note that the default RotationOrder is kXYZ.

The matrices are post-multiplied in Maya. For example, to transform a point P from object-space to world-space (P') you would need to post-multiply by the worldMatrix. (P' = P x WM)

The transformation matrix is then constructed as follows:

```     -1                       -1
[Sp]x[S]x[Sh]x[Sp]x[St]x[Rp]x[Ro]x[R]x[Rp]x[Rt]x[T]
```

where 'x' denotes matrix multiplication and '-1' denotes matrix inversion

```     Sp = |  1    0    0    0 |     St = |  1    0    0    0 |
|  0    1    0    0 |          |  0    1    0    0 |
|  0    0    1    0 |          |  0    0    1    0 |
| spx  spy  spz   1 |          | sptx spty sptz  1 |

S  = |  sx   0    0    0 |     Sh = |  1    0    0    0 |
|  0    sy   0    0 |          | shxy  1    0    0 |
|  0    0    sz   0 |          | shxz shyz  1    0 |
|  0    0    0    1 |          |  0    0    0    1 |

Rp = |  1    0    0    0 |     Rt = |  1    0    0    0 |
|  0    1    0    0 |          |  0    1    0    0 |
|  0    0    1    0 |          |  0    0    1    0 |
| rpx  rpy  rpz   1 |          | rptx rpty rptz  1 |

Ro = AX * AY * AZ

AX = |  1    0    0    0 |     AY = |  cy   0   -sy   0 |
|  0    cx   sx   0 |          |  0    1    0    0 |
|  0   -sx   cx   0 |          |  sy   0    cy   0 |
|  0    0    0    1 |          |  0    0    0    1 |

AZ = |  cz   sz   0    0 |     sx = sin(rax), cx = cos(rax)
| -sz   cz   0    0 |     sy = sin(ray), cx = cos(ray)
|  0    0    1    0 |     sz = sin(raz), cz = cos(raz)
|  0    0    0    1 |

R  = RX * RY * RZ  (Note: order is determined by rotateOrder)

RX = |  1    0    0    0 |     RY = |  cy   0   -sy   0 |
|  0    cx   sx   0 |          |  0    1    0    0 |
|  0   -sx   cx   0 |          |  sy   0    cy   0 |
|  0    0    0    1 |          |  0    0    0    1 |

RZ = |  cz   sz   0    0 |     sx = sin(rx), cx = cos(rx)
| -sz   cz   0    0 |     sy = sin(ry), cx = cos(ry)
|  0    0    1    0 |     sz = sin(rz), cz = cos(rz)
|  0    0    0    1 |

T  = |  1    0    0    0 |
|  0    1    0    0 |
|  0    0    1    0 |
|  tx   ty   tz   1 |
```
Examples:

## Public Types

enum  RotationOrder {
kInvalid, kXYZ, kYZX, kZXY,
kXZY, kYXZ, kZYX, kLast
}
Order of rotation. More...

## Public Member Functions

~MTransformationMatrix ()
MTransformationMatrix ()
MTransformationMatrix (const MTransformationMatrix &src)
MTransformationMatrix (const MMatrix &src)
MTransformationMatrixoperator= (const MTransformationMatrix &src)
MTransformationMatrixoperator= (const MMatrix &src)
MMatrix asMatrix () const
MMatrix asMatrix (double percent) const
MMatrix asMatrixInverse () const
MMatrix asScaleMatrix () const
MMatrix asRotateMatrix () const
MStatus getScale (double scale, MSpace::Space space) const
MStatus setScale (const double scale, MSpace::Space space)
MStatus addScale (const double scale, MSpace::Space space)
MQuaternion rotation () const
MTransformationMatrixrotateTo (const MQuaternion &q)
MTransformationMatrixrotateBy (const MQuaternion &q, MSpace::Space space, MStatus *ReturnStatus=NULL)
MEulerRotation eulerRotation () const
MTransformationMatrixrotateTo (const MEulerRotation &e)
MTransformationMatrixrotateBy (const MEulerRotation &e, MSpace::Space space, MStatus *ReturnStatus=NULL)
MStatus getRotationQuaternion (double &x, double &y, double &z, double &w) const
MStatus setRotationQuaternion (double x, double y, double z, double w)
MStatus addRotationQuaternion (double x, double y, double z, double w, MSpace::Space)
MStatus getRotation (double, RotationOrder &order) const
MStatus setRotation (const double rotation, RotationOrder order)
MStatus addRotation (const double rotation, RotationOrder order, MSpace::Space)
RotationOrder rotationOrder (MStatus *ReturnStatus=NULL) const
MStatus reorderRotation (RotationOrder &order)
MStatus setToRotationAxis (const MVector &axis, double rotation)
MQuaternion rotationOrientation () const
MTransformationMatrixsetRotationOrientation (const MQuaternion &q)
MVector getTranslation (MSpace::Space, MStatus *ReturnStatus=NULL) const
MStatus setTranslation (const MVector &vector, MSpace::Space)
MStatus addTranslation (const MVector &vector, MSpace::Space)
MStatus setShear (const double shear, MSpace::Space space)
MStatus getShear (double shear, MSpace::Space space) const
MStatus addShear (const double shear, MSpace::Space space)
MPoint scalePivot (MSpace::Space, MStatus *ReturnStatus=NULL) const
MStatus setScalePivot (const MPoint &, MSpace::Space, bool balance)
MVector scalePivotTranslation (MSpace::Space, MStatus *ReturnStatus=NULL) const
MStatus setScalePivotTranslation (const MVector &vector, MSpace::Space)
MPoint rotatePivot (MSpace::Space, MStatus *ReturnStatus=NULL) const
MStatus setRotatePivot (const MPoint &point, MSpace::Space, bool balance)
MVector rotatePivotTranslation (MSpace::Space space, MStatus *ReturnStatus=NULL) const
MStatus setRotatePivotTranslation (const MVector &vector, MSpace::Space space)
bool isEquivalent (const MTransformationMatrix &other, double tolerance=1.0e-10) const
bool operator== (const MTransformationMatrix &other) const
bool operator!= (const MTransformationMatrix &other) const
MStatus getRotation (double, RotationOrder &order, MSpace::Space) const
This method is obsolete.
MStatus setRotation (const double rotation, RotationOrder order, MSpace::Space)
This method is obsolete.
MStatus getRotationQuaternion (double &x, double &y, double &z, double &w, MSpace::Space) const
This method is obsolete.
MStatus setRotationQuaternion (double x, double y, double z, double w, MSpace::Space)
This method is obsolete.
MVector translation (MSpace::Space, MStatus *ReturnStatus=NULL) const
This method is obsolete.

## Member Enumeration Documentation

Order of rotation.

Enumerator:
 kInvalid kXYZ kYZX kZXY kXZY kYXZ kZYX kLast

## Constructor & Destructor Documentation

 MTransformationMatrix::~MTransformationMatrix ( )

Class Destructor.

 MTransformationMatrix::MTransformationMatrix ( )

Class Constructor.

 MTransformationMatrix::MTransformationMatrix ( const MTransformationMatrix & src )

Class Copy Constructor.

Parameters:
 [in] src transform matrix to be copied

 MTransformationMatrix::MTransformationMatrix ( const MMatrix & src )

Class Constructor.

Parameters:
 [in] src matrix to be copied

## Member Function Documentation

 MTransformationMatrix & MTransformationMatrix::operator= ( const MTransformationMatrix & src )

Copy operator.

Parameters:
 [in] src transform matrix to be copied

 MTransformationMatrix & MTransformationMatrix::operator= ( const MMatrix & src )

Copy operator.

Parameters:
 [in] src matrix to be copied
Returns:
This transformation matrix

 MMatrix MTransformationMatrix::asMatrix ( ) const

Returns the four by four matrix that describes this transformation

Returns:
The matrix
Examples:

 MMatrix MTransformationMatrix::asMatrix ( double percent ) const

Returns a matrix that represents the specified percentage of this transformation matrix.

Parameters:
 [in] percent percent of the transformation to return
Returns:
The percentage matrix

 MMatrix MTransformationMatrix::asMatrixInverse ( ) const

Returns the inverse of the four by four matrix that describes this transformation.

Returns:
The matrix

 MMatrix MTransformationMatrix::asScaleMatrix ( ) const

Returns scale space matrix. The scale space matrix takes points from object space to the space immediately following scale and shear transformations.

Returns:
The scale space matrix

 MMatrix MTransformationMatrix::asRotateMatrix ( ) const

Returns rotate space matrix. The rotate space matrix takes points from object space to the space immediately following the scale/shear/rotation transformations.

Returns:
The rotate space matrix
Examples:

 MStatus MTransformationMatrix::getScale ( double scale, MSpace::Space space ) const

Get the scale component of the transformation matrix.

Parameters:
 [out] scale storage for the scale component [in] space transform space in which to get the scale
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::setScale ( const double scale, MSpace::Space space )

Set the scale component of the transformation matrix.

Parameters:
 [in] scale new scale component [in] space transform space in which to perform the scale
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::addScale ( const double scale, MSpace::Space space )

Add to the scale component by scaling relative to the existing transformation.

Parameters:
 [in] scale relative value to scale by [in] space transform space in which to perform the scale
Returns:
Return status
Status Codes:

 MQuaternion MTransformationMatrix::rotation ( ) const

Returns the rotation component of the transformation matrix as a quaternion. The rotation is returned in MSpace::kTransform space.

Returns:
Quaternion that is the rotation component of the transformation matrix

 MTransformationMatrix & MTransformationMatrix::rotateTo ( const MQuaternion & q )

Sets the rotation component of the transformation matrix using a quaternion. The rotation is performed in MSpace::kTransform space.

Parameters:
 [in] q the quaternion to which the rotation component of the transformation matrix should be set
Returns:
A reference to the resulting transformation matrix

 MTransformationMatrix & MTransformationMatrix::rotateBy ( const MQuaternion & q, MSpace::Space space, MStatus * ReturnStatus = `NULL` )

Adds to the rotation component of the rotation matrix by rotating relative to the existing transformation using a quaternion. The only valid transformation spaces for this method are MSpace::kTransform and MSpace::kPreTransform/MSpacekObject. All other spaces are treated as being equivalent to MSpace::kTransform.

Parameters:
 [in] q the quaternion that indicates how much the transformation matrix will be rotated by [in] space the space in which the rotation is performed [out] ReturnStatus return status
Returns:
A reference to the resulting transformation matrix
Status Codes:

 MEulerRotation MTransformationMatrix::eulerRotation ( ) const

Returns the rotation component of the transformation matrix as an euler rotation.

Returns:
Euler rotation that is the rotation component of the transformation matrix

 MTransformationMatrix & MTransformationMatrix::rotateTo ( const MEulerRotation & e )

Sets the rotation component of the transformation matrix using an euler rotation. The rotation is performed in MSpace::kTransform space.

Parameters:
 [in] e the euler rotation to which the rotation component of the transformation matrix should be set
Returns:
A reference to the resulting transformation matrix

 MTransformationMatrix & MTransformationMatrix::rotateBy ( const MEulerRotation & e, MSpace::Space space, MStatus * ReturnStatus = `NULL` )

Adds to the rotation component of the rotation matrix by rotating relative to the existing transformation using an euler rotation. The only valid transformation spaces for this method are MSpace::kTransform and MSpace::kPreTransform/MSpacekObject. All other spaces are treated as being equivalent to MSpace::kTransform.

Parameters:
 [in] e the euler rotation that indicates how much the transformation matrix will be rotated by [in] space the space in which the rotation is performed [out] ReturnStatus return status
Returns:
A reference to the resulting transformation matrix
Status Codes:

 MStatus MTransformationMatrix::getRotationQuaternion ( double & x, double & y, double & z, double & w ) const

Get the rotation component of the transformation matrix as a quaternion. The rotation is retrieved in MSpace::kTransform space.

Parameters:
 [out] x storage for the x component of the quaternion [out] y storage for the y component of the quaternion [out] z storage for the z component of the quaternion [out] w storage for the w component of the quaternion
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::setRotationQuaternion ( double x, double y, double z, double w )

Set the rotation component of the transformation matrix using a quaternion. The rotation is set in MSpace::kTransform space.

Parameters:
 [in] x x component of new quaternion [in] y y component of new quaternion [in] z z component of new quaternion [in] w w component of new quaternion
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::addRotationQuaternion ( double x, double y, double z, double w, MSpace::Space space )

Add to the rotation component by rotating relative to the existing transformation. Rotation is a quaternion. The only valid transformation spaces for this method are MSpace::kTransform and MSpace::kPreTransform. All other spaces are treated as being equivalent to MSpace::kTransform.

Parameters:
 [in] x x component of quaternion [in] y y component of quaternion [in] z z component of quaternion [in] w w component of quaternion
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::getRotation ( double rot, MTransformationMatrix::RotationOrder & order ) const

Get the rotation component of the transformation matrix in radians. The rotation is retrieved in MSpace::kTransform space.

Parameters:
 [out] rot storage for the rotation in radians [in] order storage for the rotation order
Returns:
Return status
Status Codes:
Examples:

 MStatus MTransformationMatrix::setRotation ( const double rot, MTransformationMatrix::RotationOrder order )

Set the rotation component of the transformation matrix. The rotation is set in MSpace::kTransform space.

Parameters:
 [in] rot new rotation component in radians [in] order order in which to apply rotations
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::addRotation ( const double rot, MTransformationMatrix::RotationOrder order, MSpace::Space space )

Add to the rotation component by rotating relative to the existing transformation. The only valid transformation spaces for this method are MSpace::kTransform and MSpace::kPreTransform. All other spaces are treated as being equivalent to MSpace::kTransform.

Parameters:
 [in] rot relative value to rotate by [in] space transform space in which to perform the rotation
Returns:
Return status
Status Codes:

 MTransformationMatrix::RotationOrder MTransformationMatrix::rotationOrder ( MStatus * ReturnStatus = `NULL` ) const

Returns the rotation order for the transform matrix. That is the order in which the Euler angles are applied to create the end rotation.

Parameters:
 [out] ReturnStatus return status
Returns:
Rotation order
Status Codes:

 MStatus MTransformationMatrix::reorderRotation ( RotationOrder & order )

Reorders the x, y, and z components of the rotation of this transform. The overall rotation will remain the same. This operation is not unique, so spin information will be lost.

Parameters:
 [in] order new order of the rotations
Returns:
Return status
Status Codes:
Examples:

 MStatus MTransformationMatrix::setToRotationAxis ( const MVector & axis, double rotation )

Sets the rotation given an axis and a rotation about it.

Parameters:
 [in] axis axis to rotate about [in] rotation rotation in radians
Returns:
Return status
Status Codes:
Examples:

 MQuaternion MTransformationMatrix::rotationOrientation ( ) const

Returns the rotation orientation for the transformation matrix. The rotation orientation is the rotation that orients the local rotation space. The rotation is returned in MSpace::kTransform space.

Returns:
Rotation orientation

 MTransformationMatrix & MTransformationMatrix::setRotationOrientation ( const MQuaternion & q )

Sets the rotation orientation for the transformation matrix. The rotation orientation is the rotation that orients the local rotation space. The rotation is set in MSpace::kTransform space.

Returns:
Rotation orientation

 MVector MTransformationMatrix::getTranslation ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

Returns the translation component of the translation as a vector in centimeters.

Parameters:
 [in] space space in which to perform the translation [out] ReturnStatus return status
Returns:
Translation vector in centimeters
Status Codes:
Examples:

 MStatus MTransformationMatrix::setTranslation ( const MVector & vector, MSpace::Space space )

Set the translation component of the transformation matrix in centimeters.

Parameters:
 [in] vector new translation component in centimeters. [in] space transform space in which to perform the translation
Returns:
Return status
Status Codes:
Examples:

 MStatus MTransformationMatrix::addTranslation ( const MVector & vector, MSpace::Space space )

Add to the translation component by translating relative to the existing transformation.

Parameters:
 [in] vector relative value to translate by [in] space transform space in which to perform the scale
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::setShear ( const double shear, MSpace::Space space )

Set the shear component of the transformation matrix. The shear values represent (xy, xz, yx).

Parameters:
 [in] shear new shear component [in] space transform space in which to perform the shear
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::getShear ( double shear, MSpace::Space space ) const

Get the shear component of the transformation matrix.

Parameters:
 [out] shear Shear. [in] space Transform space in which to get the shear.
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::addShear ( const double shear, MSpace::Space space )

Add to the shear component by shearing relative to the existing transformation.

Parameters:
 [in] shear relative value to shear by [in] space transform space in which to perform the shear
Returns:
Return status
Status Codes:

 MPoint MTransformationMatrix::scalePivot ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

Returns the pivot around which the scale is applied.

Parameters:
 [in] space space in which to get the pivot [out] ReturnStatus return status
Returns:
Scale pivot point
Status Codes:

 MStatus MTransformationMatrix::setScalePivot ( const MPoint & point, MSpace::Space space, bool balance )

Set the pivot around which the scale is applied.

If balance if true, then the overall transformation matrix will not change and a compensating transformation will be added to the scale transformation to achieve this.

Parameters:
 [in] point new scale pivot [in] space transform space in which to set the scale pivot [in] balance whether to balance the matrix
Returns:
Return status
Status Codes:

 MVector MTransformationMatrix::scalePivotTranslation ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

Returns the scale pivot translation. This is the translation that is used to compensate for the movement of the scale pivot.

Parameters:
 [in] space space in which to get the pivot [out] ReturnStatus return status
Returns:
Scale pivot translation
Status Codes:

 MStatus MTransformationMatrix::setScalePivotTranslation ( const MVector & vector, MSpace::Space space )

Set the pivot translation. This component is used to preserve existing scale transformations when moving pivot. This method will only be useful to advanced users.

Parameters:
 [in] vector new scale pivot translation [in] space transform space in which to set the scale translation
Returns:
Return status
Status Codes:

 MPoint MTransformationMatrix::rotatePivot ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

Returns the pivot around which the rotation is applied.

Parameters:
 [in] space space in which to get the pivot [out] ReturnStatus return status
Returns:
Rotation pivot point
Status Codes:

 MStatus MTransformationMatrix::setRotatePivot ( const MPoint & point, MSpace::Space space, bool balance )

Set the pivot around which the rotation is applied.

If balance if true, then the overall transformation matrix will not change and a compensating transformation will be added to the rotation transformation to achieve this.

Parameters:
 [in] point new rotation pivot [in] space transform space in which to set the pivot [in] balance whether to balance the matrix
Returns:
Return status
Status Codes:

 MVector MTransformationMatrix::rotatePivotTranslation ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

Returns the rotation pivot translation. This is the translation that is used to compensate for the movement of the rotation pivot.

Parameters:
 [in] space space in which to get the pivot translation [out] ReturnStatus return status
Returns:
Scale pivot translation
Status Codes:

 MStatus MTransformationMatrix::setRotatePivotTranslation ( const MVector & vector, MSpace::Space space )

Set the pivot translation. This component is used to preserve existing transformations when moving pivot. This method will only be useful to advanced users.

Parameters:
 [in] vector new rotation pivot translation [in] space transform space in which to set the rotation translation
Returns:
Return status
Status Codes:

 bool MTransformationMatrix::isEquivalent ( const MTransformationMatrix & other, double tol = `1.0e-10` ) const

Returns true if this transform matrix is equivalent to the one passed in within a certain tolerance.

Parameters:
 [in] other transform matrix to test against [in] tol tolerance to test using
Returns:
True if equivalent

 bool MTransformationMatrix::operator== ( const MTransformationMatrix & other ) const

Equality operator.

Parameters:
 [in] other transform matrix to test against
Returns:
True if equal

 bool MTransformationMatrix::operator!= ( const MTransformationMatrix & other ) const

Inequality operator.

Parameters:
 [in] other transform matrix to test against
Returns:
True if not equal

 MStatus MTransformationMatrix::getRotation ( double rot, MTransformationMatrix::RotationOrder & order, MSpace::Space space ) const

This method is obsolete.

Deprecated:
Use the other MTransformationMatrix::getRotation method instead.
This method will be removed in a future Maya release. The transformation space argument was always treated as MSpace::kTransform regardless of the actual argument.

Get the rotation component in radians of the transformation matrix.

Parameters:
 [out] rot storage for the rotation in radians [out] order storage for the rotation order [in] space transform space in which to get the rotation
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::setRotation ( const double rot, MTransformationMatrix::RotationOrder order, MSpace::Space space )

This method is obsolete.

Deprecated:
Use the other MTransformationMatrix::setRotation method instead.
The transformation space argument was always treated as MSpace::kTransform regardless of the actual argument.

Set the rotation component of the transformation matrix.

Parameters:
 [in] rot new rotation component [in] order order in which to apply rotations [in] space transform space in which to perform the rotation
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::getRotationQuaternion ( double & x, double & y, double & z, double & w, MSpace::Space space ) const

This method is obsolete.

Deprecated:
Use the other MTransformationMatrix::getRotationQuaternion method instead.
The transformation space argument was always treated as MSpace::kTransform regardless of the actual argument.

Get the rotation component of the transformation matrix as a quaternion.

Parameters:
 [out] x storage for the x component of the quaternion [out] y storage for the y component of the quaternion [out] z storage for the z component of the quaternion [out] w storage for the w component of the quaternion [in] space transform space in which to get the rotation
Returns:
Return status
Status Codes:

 MStatus MTransformationMatrix::setRotationQuaternion ( double x, double y, double z, double w, MSpace::Space space )

This method is obsolete.

Deprecated:
Use the other MTransformationMatrix::setRotationQuaternion method instead.
The transformation space argument was always treated as MSpace::kTransform regardless of the actual argument.

Set the rotation component of the transformation matrix using a quaternion.

Parameters:
 [in] x x component of new quaternion [in] y y component of new quaternion [in] z z component of new quaternion [in] w w component of new quaternion [in] space transform space in which to perform the rotation
Returns:
Return status
Status Codes:

 MVector MTransformationMatrix::translation ( MSpace::Space space, MStatus * ReturnStatus = `NULL` ) const

This method is obsolete.

Deprecated:
Use MTransformationMatrix::getTranslation instead.
Returns the translation component of the translation as a vector in centimeters.

Parameters:
 [in] space space in which to perform the translation [out] ReturnStatus return status
Returns:
Translation vector in centimeters
Status Codes:
Examples:

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