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# MEulerRotation Class Reference
OpenMaya - API module for common classes

Search for all occurrences

## Detailed Description

Euler Rotation Math.

This class provides methods for working with euler angle rotations. Euler angles are described by rotations in radians around the x, y, and z axes, and the order in which those rotations occur.

Examples:

  hwDecalBumpShader_NV20.cpp, rockingTransform.cpp, rockingTransformCheck.cpp, rockingTransformCheck.h, and rotateManip.cpp.

`#include <MEulerRotation.h>`

List of all members.

## Public Types
enum | RotationOrder { kXYZ, kYZX, kZXY, kXZY, kYXZ, kZYX }
| Valid rotaton orders. More...
## Public Member Functions
| MEulerRotation ()
| The default class constructor.
| MEulerRotation (const MEulerRotation &src)
| The copy constructor.
| MEulerRotation (const MVector &v, RotationOrder ord=kXYZ)
| Class constructor.
| MEulerRotation (double xx, double yy, double zz, RotationOrder ord=kXYZ)
| Class constructor.
| ~MEulerRotation ()
| Class destructor.
MEulerRotation & | operator= (const MEulerRotation &src)
| The assignment operator.
MEulerRotation & | operator= (const MQuaternion &q)
| The assignment operator.
MEulerRotation & | operator= (const MMatrix &m)
| Convert the given 4X4 homogeneous rotation matrix to a euler rotation.
MEulerRotation & | operator= (const MVector &v)
| The assignment operator.
MEulerRotation & | setValue (const MVector &v, RotationOrder ord=kXYZ)
| Sets the euler rotation to the values contained in the vector and with the specified rotation order.
MEulerRotation & | setValue (double xx, double yy, double zz, RotationOrder ord=kXYZ)
| Sets the euler rotation to the x, y, and z rotation components with the specified rotation order.
MQuaternion | asQuaternion () const
| Converts an euler rotation to a quaternion.
MMatrix | asMatrix () const
| Converts an euler rotation to a rotation matrix.
MVector | asVector () const
| Converts an euler rotation to a vector.
double | operator[] (unsigned int i) const
| The index operator.
MEulerRotation | operator+ (const MEulerRotation &other) const
| The euler rotation addition operator.
MEulerRotation & | operator+= (const MEulerRotation &other)
| The in place euler rotation addition operator.
MEulerRotation | operator- (const MEulerRotation &other) const
| The euler rotation subtraction operator.
MEulerRotation & | operator-= (const MEulerRotation &other)
| The in place euler rotation subtraction operator.
MEulerRotation | operator- () const
| The unary minus operator.
MEulerRotation | operator* (const MEulerRotation &other) const
| The euler rotation multiplication operator.
MEulerRotation | operator* (const MQuaternion &other) const
| This quaternion multiplication operator.
MEulerRotation | operator* (double other) const
| This scalar multiplication operator.
MEulerRotation & | operator*= (const MEulerRotation &other)
| The in place euler rotation multiplication operator.
MEulerRotation & | operator*= (const MQuaternion &other)
| The in place quaternion multiplication operator.
MEulerRotation & | operator*= (double other)
| The in place scalar multiplication operator.
bool | operator== (const MEulerRotation &other) const
| The euler rotation equality operator.
bool | operator!= (const MEulerRotation &other) const
| The euler rotation inequality operator.
bool | isEquivalent (const MEulerRotation &other, double tolerance=kEulerRotationEpsilon) const
| This method returns true if this euler rotation is equivalent, within some given tolerance, to the other euler rotation.
bool | isZero (double tolerance=kEulerRotationEpsilon) const
| This method returns true if this euler rotation is zero, within some given tolerance.
MEulerRotation & | incrementalRotateBy (const MVector &axis, double angle)
| Perform an incremental rotation by the specified axis and angle.
MEulerRotation | inverse () const
| Returns the inverse of this euler rotation.
MEulerRotation & | invertIt ()
| Performs an in place inversion of this euler rotation.
MEulerRotation | reorder (RotationOrder ord) const
| Returns the reordering of this euler rotation, such that the euler rotation will have the specified rotation order.
MEulerRotation & | reorderIt (RotationOrder ord)
| Performs an in place reordering of this euler rotation, such that the euler rotation will have the specified rotation order.
MEulerRotation | bound () const
| Returns the result of bounding this rotation to be within +/- PI.
MEulerRotation & | boundIt (const MEulerRotation &src)
| Sets this euler rotation to be the input rotation that has been bound to be within +/- PI.
MEulerRotation & | boundIt ()
| Bounds this rotation to be within +/- PI.
MEulerRotation | alternateSolution () const
| Returns an alternate solution to this rotation.
MEulerRotation & | setToAlternateSolution (const MEulerRotation &src)
| Sets this euler rotation to an alternate solution of the input rotation.
MEulerRotation & | setToAlternateSolution ()
| Sets this euler rotation to an alternate solution of this rotation.
MEulerRotation | closestSolution (const MEulerRotation &dst) const
| Returns the euler rotation that is the closest solution to the "dst" euler rotation.
MEulerRotation & | setToClosestSolution (const MEulerRotation &src, const MEulerRotation &dst)
| Sets this euler rotation to the euler rotation that is the closest solution of the "src" euler rotation to the "dst" euler rotation.
MEulerRotation & | setToClosestSolution (const MEulerRotation &dst)
| Sets this euler rotation to the euler rotation that is the closest solution to the "dst" euler rotation.
MEulerRotation | closestCut (const MEulerRotation &dst) const
| Returns the closest cut of this rotation to "dst".
MEulerRotation & | setToClosestCut (const MEulerRotation &src, const MEulerRotation &dst)
| Sets this rotation to be the closest cut of "src" to "dst".
MEulerRotation & | setToClosestCut (const MEulerRotation &dst)
| Sets this rotation to be the closest cut to "dst".
double & | operator[] (unsigned int i)
| NO SCRIPT SUPPORT.
## Static Public Member Functions
static MEulerRotation | decompose (const MMatrix &matrix, RotationOrder ord)
| Decompose a rotation matrix into the desired euler angles with the specified order.
static MEulerRotation | bound (const MEulerRotation &src)
| NO SCRIPT SUPPORT.
static MEulerRotation | alternateSolution (const MEulerRotation &src)
| NO SCRIPT SUPPORT.
static MEulerRotation | closestSolution (const MEulerRotation &src, const MEulerRotation &dst)
| NO SCRIPT SUPPORT.
static MEulerRotation | closestCut (const MEulerRotation &src, const MEulerRotation &dst)
| NO SCRIPT SUPPORT.
## Public Attributes
double | x
| The x component of the euler rotation in radians. Search for all occurrences
double | y
| The y component of the euler rotation in radians. Search for all occurrences
double | z
| The z component of the euler rotation in radians. Search for all occurrences
RotationOrder | order
| The rotation order of the euler rotation.
## Static Public Attributes Search for all occurrences
static const MEulerRotation | identity
| The euler rotation identity. The rotation order is XYZ.
## Friends
OPENMAYA_EXPORT MEulerRotation | operator* (double scale, const MEulerRotation &other)
| NO SCRIPT SUPPORT.
OPENMAYA_EXPORT std::ostream & | operator<< (std::ostream &os, const MEulerRotation &rotation)
| NO SCRIPT SUPPORT. Search for all occurrences

## Member Enumeration Documentation

enum RotationOrder

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Valid rotaton orders.

Enumerator:

  kXYZ | Search for all occurrences
  kYZX | Search for all occurrences
  kZXY | Search for all occurrences
  kXZY | Search for all occurrences
  kYXZ | Search for all occurrences
  kZYX | Search for all occurrences

## Constructor & Destructor Documentation

MEulerRotation | ( |  | ) |

The default class constructor.

The rotation order is set to XYZ.

MEulerRotation | ( | const MEulerRotation & | src | ) |

The copy constructor.

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

Parameters:

  [in] | src | the euler rotation to copy

MEulerRotation | ( | const MVector & | v,
|  | MEulerRotation::RotationOrder | ord = `kXYZ`
| ) |  |

Class constructor.

Construct an euler rotation from a vector with the given rotation order.

Parameters:

  [in] | v | vector from which to set the x, y, and z rotation components
  [in] | ord | the rotation order; the default rotation order is XYZ

MEulerRotation | ( | double | xx,
|  | double | yy,
|  | double | zz,
|  | MEulerRotation::RotationOrder | ord = `kXYZ`
| ) |  |

Class constructor.

Initializes the euler rotation with the explicit x, y, z, and rotation order values provided as arguments.

Parameters:

  [in] | xx | the x component of the euler rotation
  [in] | yy | the y component of the euler rotation
  [in] | zz | the z component of the euler rotation
  [in] | ord | the rotation order of the euler rotation; the default rotation order is XYZ

## Member Function Documentation

MEulerRotation & operator= | ( | const MEulerRotation & | src | ) |

The assignment operator.

Parameters:

  [in] | src | the source euler rotation

Returns:
  A reference to the euler rotation that has been assigned to the source euler rotation

MEulerRotation & operator= | ( | const MQuaternion & | q | ) |

The assignment operator.

Parameters:

  [in] | q | the source quaternion

Returns:
  A reference to the euler rotation that has been assigned to the quaternion

MEulerRotation & operator= | ( | const MMatrix & | m | ) |

Convert the given 4X4 homogeneous rotation matrix to a euler rotation.

Parameters:

  [in] | m | the matrix to be converted to a euler rotation

Returns:
  A reference to the euler rotation that has been converted from the rotation matrix

MEulerRotation & operator= | ( | const MVector & | v | ) |

The assignment operator.

Parameters:

  [in] | v | the source vector from which the x, y, and z rotation components are set

Returns:
  A reference to the euler rotation that has been assigned to the source vector

MEulerRotation & setValue | ( | const MVector & | v,
|  | MEulerRotation::RotationOrder | ord = `kXYZ`
| ) |  |

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Sets the euler rotation to the values contained in the vector and with the specified rotation order.

Parameters:

  [in] | v | vector from which to set the x, y, and z rotation components
  [in] | ord | the rotation order; the default rotation order is XYZ

Returns:
  A reference to the euler rotation whose value has been set

MEulerRotation & setValue | ( | double | xx,
|  | double | yy,
|  | double | zz,
|  | MEulerRotation::RotationOrder | ord = `kXYZ`
| ) |  |

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Sets the euler rotation to the x, y, and z rotation components with the specified rotation order.

Parameters:

  [in] | xx | the x component of the rotation
  [in] | yy | the y component of the rotation
  [in] | zz | the z component of the rotation
  [in] | ord | the rotation order; the default rotation order is XYZ

Returns:
  A reference to the euler rotation whose value has been set

MQuaternion asQuaternion | ( |  | ) | const

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Converts an euler rotation to a quaternion.

Returns:
  The quaternion that has been casted from the euler rotation

MMatrix asMatrix | ( |  | ) | const

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Converts an euler rotation to a rotation matrix.

Returns:
  The rotation matrix that has been casted from the euler rotation

MVector asVector | ( |  | ) | const

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Converts an euler rotation to a vector.

The rotation order component is dropped.

Returns:
  The vector that has been casted from the euler rotation

double operator[] | ( | unsigned int | i | ) | const

The index operator.

If its argument is 0 it will return the x component of the euler rotation. If its argument is 1 it will return the y component of the euler rotation. If its argument is 2 it will return the z component of the euler rotation.

Parameters:

  [in] | i | value indicating which component to return

Returns:
  The component of the euler rotation corresponding to the index

MEulerRotation operator+ | ( | const MEulerRotation & | other | ) | const

The euler rotation addition operator.

Parameters:

  [in] | other | the euler rotation to be added to this euler rotation

Returns:
  The sum of the two euler rotations

MEulerRotation & operator+= | ( | const MEulerRotation & | other | ) |

The in place euler rotation addition operator.

Parameters:

  [in] | other | the euler rotation to be added with this euler rotation

Returns:
  A reference the euler rotation which has been added to the other euler rotation

MEulerRotation operator- | ( | const MEulerRotation & | other | ) | const

The euler rotation subtraction operator.

Parameters:

  [in] | other | the euler rotation to be subtracted from this euler rotation

Returns:
  The euler rotation that results from the subtraction

MEulerRotation & operator-= | ( | const MEulerRotation & | other | ) |

The in place euler rotation subtraction operator.

Parameters:

  [in] | other | the euler rotation to be subtracted from this euler rotation

Returns:
  A reference the euler rotation which has had the other euler rotation subtracted from it

MEulerRotation operator- | ( |  | ) | const

The unary minus operator.

Negates the value of each of the x, y, and z components of the euler rotation. The order remains the same.

Returns:
  Euler rotation that results from the negation

MEulerRotation operator* | ( | const MEulerRotation & | other | ) | const

The euler rotation multiplication operator.

Parameters:

  [in] | other | the euler rotation to be multiplied with this euler rotation

Returns:
  The product of the two euler rotations

MEulerRotation operator* | ( | const MQuaternion & | other | ) | const

This quaternion multiplication operator.

Parameters:

  [in] | other | the quaternion to be multiplied with this euler rotation

Returns:
  The product of the euler rotation and the quaternion

MEulerRotation operator* | ( | double | other | ) | const

This scalar multiplication operator.

Parameters:

  [in] | other | the scalar value to be multiplied with this euler rotation

Returns:
  The product of the euler rotation and the scalar value

MEulerRotation & operator*= | ( | const MEulerRotation & | other | ) |

The in place euler rotation multiplication operator.

Parameters:

  [in] | other | the euler rotation to be multiplied with this euler rotation

Returns:
  A reference to the euler rotation which has been multiplied with the other euler rotation

MEulerRotation & operator*= | ( | const MQuaternion & | other | ) |

The in place quaternion multiplication operator.

Parameters:

  [in] | other | the quaternion to be multiplied with this euler rotation

Returns:
  A reference to the euler rotation which has been multiplied with the quaternion

MEulerRotation & operator*= | ( | double | other | ) |

The in place scalar multiplication operator.

Parameters:

  [in] | other | the double to be multiplied with this euler rotation

Returns:
  A reference to the euler rotation which has been multiplied with the double

bool operator== | ( | const MEulerRotation & | other | ) | const

The euler rotation equality operator.

Parameters:

  [in] | other | the euler rotation to be compared with this euler rotation

Returns:
  - true the euler rotations are identical
  - false the euler rotations are not identical

bool operator!= | ( | const MEulerRotation & | other | ) | const

The euler rotation inequality operator.

Parameters:

  [in] | other | the euler rotation to be compared with this euler rotation

Returns:
  - true the euler rotations are not identical
  - false the euler rotations are identical

bool isEquivalent | ( | const MEulerRotation & | other,
|  | double | tolerance = `kEulerRotationEpsilon`
| ) |  | const

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This method returns true if this euler rotation is equivalent, within some given tolerance, to the other euler rotation.

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

Parameters:

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

Returns:
  - true the euler rotations are equivalent
  - false the euler rotations are not equivalent

bool isZero | ( | double | tolerance = `kEulerRotationEpsilon` | ) | const

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This method returns true if this euler rotation is zero, within some given tolerance.

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

Parameters:

  [in] | tolerance | the amount of variation allowed for equivalency to zero

Returns:
  - true the rotation is zero
  - false the rotation is not zero

MEulerRotation & incrementalRotateBy | ( | const MVector & | axis,
|  | double | angle
| ) |  |

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Perform an incremental rotation by the specified axis and angle.

The rotation is broken down and performed in smaller steps so that the angles update properly.

Parameters:

  [in] | axis | the axis to rotate around
  [in] | angle | the angle by which to rotate around the axis

Returns:
  A reference to the euler rotation that has been incrementally rotated

MEulerRotation inverse | ( |  | ) | const

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Returns the inverse of this euler rotation.

The rotation order will be reversed.

Returns:
  Euler rotation that is the inverse of this euler rotation

MEulerRotation & invertIt | ( |  | ) |

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Performs an in place inversion of this euler rotation.

The rotation order will be reversed.

Returns:
  A reference to the euler rotation that has been inverted

MEulerRotation reorder | ( | MEulerRotation::RotationOrder | ord | ) | const

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Returns the reordering of this euler rotation, such that the euler rotation will have the specified rotation order.

Parameters:

  [in] | ord | the new rotation order of the euler rotation

Returns:
  Euler rotation that is the reordering of this euler rotation

MEulerRotation & reorderIt | ( | MEulerRotation::RotationOrder | ord | ) |

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Performs an in place reordering of this euler rotation, such that the euler rotation will have the specified rotation order.

Parameters:

  [in] | ord | the new rotation order of the euler rotation

Returns:
  A reference to the euler rotation that has been reordered

MEulerRotation bound | ( |  | ) | const

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Returns the result of bounding this rotation to be within +/- PI.

Bounding a rotation to be within +/- PI is defined to be the result of offsetting the rotation by +/- 2nPI (term by term) such that the offset is within +/- PI.

Returns:
  The euler rotation that results from bounding this euler rotation

MEulerRotation & boundIt | ( | const MEulerRotation & | src | ) |

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Sets this euler rotation to be the input rotation that has been bound to be within +/- PI.

Bounding a rotation to be within +/- PI is defined to be the result of offsetting the rotation by +/- 2nPI (term by term) such that the offset is within +/- PI.

Parameters:

  [in] | src | the input rotation that will be bound

Returns:
  A reference to the euler rotation that has been set to the bound input rotation

MEulerRotation & boundIt | ( |  | ) |

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Bounds this rotation to be within +/- PI.

Bounding a rotation to be within +/- PI is defined to be the result of offsetting the rotation by +/- 2nPI (term by term) such that the offset is within +/- PI.

Returns:
  A reference to the euler rotation that has been bound

MEulerRotation alternateSolution | ( |  | ) | const

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Returns an alternate solution to this rotation.

The resulting rotation will be bound between +/- PI, and the rotation order will remain unchanged.

Returns:
  An alternate solution to this rotation

MEulerRotation & setToAlternateSolution | ( | const MEulerRotation & | src | ) |

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Sets this euler rotation to an alternate solution of the input rotation.

The resulting rotation will be bound between +/- PI, and the rotation order will remain unchanged.

Parameters:

  [in] | src | the rotation to compute an alternate solution to

Returns:
  A reference to the euler rotation that has been set to an alternate solution

MEulerRotation & setToAlternateSolution | ( |  | ) |

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Sets this euler rotation to an alternate solution of this rotation.

The resulting rotation will be bound between +/- PI, and the rotation order will remain unchanged.

Returns:
  A reference to the euler rotation that has been set to an alternate solution

MEulerRotation closestSolution | ( | const MEulerRotation & | dst | ) | const

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Returns the euler rotation that is the closest solution to the "dst" euler rotation.

Parameters:

  [in] | dst | the euler rotation to which the solution should be closest

Returns:
  The closest solution to the "dst" rotation

MEulerRotation & setToClosestSolution | ( | const MEulerRotation & | src,
|  | const MEulerRotation & | dst
| ) |  |

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Sets this euler rotation to the euler rotation that is the closest solution of the "src" euler rotation to the "dst" euler rotation.

Parameters:

  [in] | src | the euler rotation whose closest solution will be calculated
  [in] | dst | the euler rotation to which the solution should be closest

Returns:
  A reference to the euler rotation that has been set to the closest solution

MEulerRotation & setToClosestSolution | ( | const MEulerRotation & | dst | ) |

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Sets this euler rotation to the euler rotation that is the closest solution to the "dst" euler rotation.

Parameters:

  [in] | dst | the euler rotation to which the solution should be closest

Returns:
  A reference to the euler rotation that has been set to the closest solution

MEulerRotation closestCut | ( | const MEulerRotation & | dst | ) | const

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Returns the closest cut of this rotation to "dst".

The closest cut of rotation A to rotation B is defined to be the rotation that is +/- 2nPI to rotation A (term by term) and within +/- PI to rotation B.

Parameters:

  [in] | dst | the range of the closest cut

Returns:
  The closest cut of this rotation

MEulerRotation & setToClosestCut | ( | const MEulerRotation & | src,
|  | const MEulerRotation & | dst
| ) |  |

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Sets this rotation to be the closest cut of "src" to "dst".

The closest cut of rotation A to rotation B is defined to be the rotation that is +/- 2nPI to rotation A (term by term) and within +/- PI to rotation B.

Parameters:

  [in] | src | the euler rotation whose terms will be offset by +/- 2nPI
  [in] | dst | the range of the closest cut

Returns:
  A reference to the euler rotation that has been set to the closest cut

MEulerRotation & setToClosestCut | ( | const MEulerRotation & | dst | ) |

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Sets this rotation to be the closest cut to "dst".

The closest cut of rotation A to rotation B is defined to be the rotation that is +/- 2nPI to rotation A (term by term) and within +/- PI to rotation B.

Parameters:

  [in] | dst | the range of the closest cut

Returns:
  A reference to the euler rotation that has been set to the closest cut

MEulerRotation decompose | ( | const MMatrix & | matrix,
|  | MEulerRotation::RotationOrder | ord
| ) |  | `[static]`

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Decompose a rotation matrix into the desired euler angles with the specified order.

Parameters:

  [in] | matrix | the matrix that will be decomposed into an euler rotation with the specified order
  [in] | ord | the order which the euler rotation will have

Returns:
  The euler rotation that has been decomposed from the rotation matrix

double & operator[] | ( | unsigned int | i | ) |

NO SCRIPT SUPPORT.

The index operator.

If its argument is 0 it will return the x component of the euler rotation. If its argument is 1 it will return the y component of the euler rotation. If its argument is 2 it will return the z component of the euler rotation.

Parameters:

  [in] | i | value indicating which component to return

Returns:
  A reference to the component of the euler rotation corresponding to the index

MEulerRotation bound | ( | const MEulerRotation & | src | ) | `[static]`

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NO SCRIPT SUPPORT.

Returns the euler rotation that bounds the input rotation to be within +/- PI.

Bounding a rotation to be within +/- PI is defined to be the result of offsetting the rotation by +/- 2nPI (term by term) such that the offset is within +/- PI.

Parameters:

  [in] | src | the input rotation

Returns:
  The euler rotation that bounds the input rotation

MEulerRotation alternateSolution | ( | const MEulerRotation & | src | ) | `[static]`

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NO SCRIPT SUPPORT.

Returns the euler rotation that is an alternate solution of the input rotation.

The resulting rotation will be bound between +/- PI, and the rotation order will remain unchanged.

Parameters:

  [in] | src | the rotation to compute an alternate solution to

Returns:
  The alternate solution to the input rotation

MEulerRotation closestSolution | ( | const MEulerRotation & | src,
|  | const MEulerRotation & | dst
| ) |  | `[static]`

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NO SCRIPT SUPPORT.

Returns the euler rotation that is the closest solution of the "src" euler rotation to the "dst" euler rotation.

Parameters:

  [in] | src | the euler rotation whose closest solution will be calculated
  [in] | dst | the euler rotation to which the solution should be closest

Returns:
  The closest solution of "src" to "dst"

MEulerRotation closestCut | ( | const MEulerRotation & | src,
|  | const MEulerRotation & | dst
| ) |  | `[static]`

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NO SCRIPT SUPPORT.

Returns the euler rotation that is the closest cut of "src" to "dst".

The closest cut of rotation A to rotation B is defined to be the rotation that is +/- 2nPI to rotation A (term by term) and within +/- PI to rotation B.

Parameters:

  [in] | src | the euler rotation whose terms will be offset by +/- 2nPI
  [in] | dst | the range of the closest cut

Returns:
  The closest cut of "src" to "dst"

## Friends And Related Function Documentation

OPENMAYA_EXPORT MEulerRotation operator* | ( | double | scale,
|  | const MEulerRotation & | other
| ) |  | `[friend]`

NO SCRIPT SUPPORT.

Parameters:

  [in] | scale | the amount by which the euler rotation should be scaled
  [in] | other | the euler rotation to which the scale should be applied

Returns:
  Euler rotation that is the result of scaling the other euler rotation

OPENMAYA_EXPORT std::ostream& operator<< | ( | std::ostream & | os,
|  | const MEulerRotation & | rotation
| ) |  | `[friend]`

NO SCRIPT SUPPORT.

The format used is [order: order, x: x, y: y, z: z], where x, y, and z are in degrees.

Parameters:

  [in] | os | the ostream to print to
  [in] | rotation | the euler rotation to be printed x

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

MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation
MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation MEulerRotation