# eul2quat

Convert Euler angles to quaternion

## Syntax

``quat = eul2quat(eul)``
``quat = eul2quat(eul,sequence)``

## Description

example

````quat = eul2quat(eul)` converts a given set of Euler angles, `eul`, to the corresponding quaternion, `quat`. The default order for Euler angle rotations is `"ZYX"`.```

example

````quat = eul2quat(eul,sequence)` converts a set of Euler angles into a quaternion. The Euler angles are specified in the axis rotation sequence, `sequence`. The default order for Euler angle rotations is `"ZYX"`.```

## Examples

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```eul = [0 pi/2 0]; qZYX = eul2quat(eul)```
```qZYX = 1×4 0.7071 0 0.7071 0 ```
```eul = [pi/2 0 0]; qZYZ = eul2quat(eul,"ZYZ")```
```qZYZ = 1×4 0.7071 0 0 0.7071 ```

## Input Arguments

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Euler rotation angles in radians, specified as an n-by-3 array of intrinsic Euler rotation angles. Each row represents one Euler angle set in the sequence defined by the `sequence` argument. For example, with the default sequence `"ZYX"`, each row of `eul` is of the form ```[zAngle yAngle xAngle]```.

Example: `[0 0 1.5708]`

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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Unit quaternion, returned as an n-by-4 matrix containing n quaternions. Each quaternion, one per row, is of the form q = [w x y z], with w as the scalar number.

Example: `[0.7071 0.7071 0 0]`

## Version History

Introduced in R2015a

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