rotm2eul

Convert rotation matrix to Euler angles

Syntax

``eul = rotm2eul(rotm)``
``eul = rotm2eul(rotm,sequence)``
``[eul,eulAlt] = rotm2eul(___)``

Description

````eul = rotm2eul(rotm)` converts a rotation matrix, `rotm`, to the corresponding Euler angles, `eul`. The input rotation matrix must be in the premultiply form for rotations. The default order for Euler angle rotations is `"ZYX"`. ```

example

````eul = rotm2eul(rotm,sequence)` converts a rotation matrix to Euler angles. The Euler angles are specified in the axis rotation sequence, `sequence`. The default order for Euler angle rotations is `"ZYX"`.```

example

````[eul,eulAlt] = rotm2eul(___)` also returns an alternate set of Euler angles that represents the same rotation `eulAlt`.```

Examples

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```rotm = [0 0 1; 0 1 0; -1 0 0]; eulZYX = rotm2eul(rotm)```
```eulZYX = 1×3 0 1.5708 0 ```
```rotm = [0 0 1; 0 1 0; -1 0 0]; eulZYZ = rotm2eul(rotm,'ZYZ')```
```eulZYZ = 1×3 -3.1416 -1.5708 -3.1416 ```

Input Arguments

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Rotation matrix, specified as a 3-by-3-by-n matrix containing n rotation matrices. Each rotation matrix has a size of 3-by-3 and is orthonormal. The input rotation matrix must be in the premultiply form for rotations.

Note

Rotation matrices that are slightly non-orthonormal can give complex outputs. Consider validating your matrix before inputting to the function.

Example: `[0 0 1; 0 1 0; -1 0 0]`

Axis-rotation sequence for the Euler angles, specified as one of these string scalars:

• `"ZYX"` (default)

• `"ZYZ"`

• `"ZXY"`

• `"ZXZ"`

• `"YXY"`

• `"YZX"`

• `"YXZ"`

• `"YZY"`

• `"XYX"`

• `"XYZ"`

• `"XZX"`

• `"XZY"`

Each character indicates the corresponding axis. For example, if the sequence is `"ZYX"`, then the three specified Euler angles are interpreted in order as a rotation around the z-axis, a rotation around the y-axis, and a rotation around the x-axis. When applying this rotation to a point, it will apply the axis rotations in the order x, then y, then z.

Data Types: `string` | `char`

Output Arguments

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Euler rotation angles in radians, returned as an n-by-3 array of Euler rotation angles. Each row represents one Euler angle set.

Example: `[0 0 1.5708]`

Alternate Euler rotation angle solution in radians, returned as an n-by-3 array of Euler rotation angles. Each row represents one Euler angle set.

Example: `[0 0 1.5708]`

Version History

Introduced in R2015a

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