Last Modified: March 15, 2017

Converts a 3-by-3 matrix of direction cosines into Euler angles.

A 3-by-3 direction cosine matrix.

If **rotation type** is Passive and Intrinsic or Passive and Extrinsic, the matrix maps points in the old coordinate frame to points in the new coordinate frame. If **rotation type** is Active, the matrix maps the coordinates of the original points to the coordinates of the rotated points. Each element must be in the range of [-1, 1].

Order of the axes to rotate the coordinates around.

Name | Value | Description |
---|---|---|

X-Y-Z | 0 | The first, second, and third rotations are about the x-, y-, and z-axes, respectively. |

X-Z-Y | 1 | The first, second, and third rotations are about the x-, z-, and y-axes, respectively. |

Y-X-Z | 2 | The first, second, and third rotations are about the y-, x-, and z-axes, respectively. |

Y-Z-X | 3 | The first, second, and third rotations are about the y-, z-, and x-axes, respectively. |

Z-X-Y | 4 | The first, second, and third rotations are about the z-, x-, and y-axes, respectively. |

Z-Y-X | 5 | The first, second, and third rotations are about the z-, y-, and x-axes, respectively. |

X-Y-X | 6 | The first, second, and third rotations are about the x-, y-, and x-axes, respectively. |

X-Z-X | 7 | The first, second, and third rotations are about the x-, z-, and x-axes, respectively. |

Y-X-Y | 8 | The first, second, and third rotations are about the y-, x-, and y-axes, respectively. |

Y-Z-Y | 9 | The first, second, and third rotations are about the y-, z-, and y-axes, respectively. |

Z-X-Z | 10 | The first, second, and third rotations are about the z-, x-, and z-axes, respectively. |

Z-Y-Z | 11 | The first, second, and third rotations are about the z-, y-, and z-axes, respectively. |

**Default: **Z-X-Z

Type of rotation to perform.

Name | Value | Description |
---|---|---|

Passive and Intrinsic | 0 | The rotation occurs about the axes of a rotating coordinate system, which is initially aligned with the fixed one, and modifies its orientation after each elemental rotation. The coordinate system rotates, while the coordinate is fixed. |

Passive and Extrinsic | 1 | The rotation occurs about the axes of a fixed coordinate system. The coordinate system rotates, while the coordinate is fixed. |

Active | 2 | The rotation occurs about the axes of the same coordinate system. The coordinate system is fixed, while the coordinate rotates. |

**Default: **Passive and Intrinsic

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

Euler angles in radians.

Rotation angle about the first axis in radians.

Rotation angle about the second axis in radians.

Rotation angle about the third axis in radians.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

Direction cosines and Euler angles are two different ways of expressing a rotation. The following equations describe how this node converts direction cosines into Euler angles when **rotation order** is the default Z-X-Z and **rotation type** is the default Passive and Intrinsic:

$\{\begin{array}{c}\theta =\mathrm{arccos}\left({R}_{33}\right)\\ \varphi =\mathrm{atan2}({R}_{31},\text{\hspace{0.17em}}{-R}_{32}\text{\hspace{0.17em}})\\ \psi =\mathrm{atan2}({R}_{13},\text{\hspace{0.17em}}{R}_{23}\text{\hspace{0.17em}})\end{array}$

where

- θ, ϕ, and ψ are the output
**Euler angles** -
*R*_{i}_{j}is the element at the*i*^{th}row and*j*^{th}column of the input**direction cosines**matrix

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices