# eul2tform

Convert Euler angles to homogeneous transformation

## Syntax

``tform = eul2tform(eul)``
``tform = eul2tform(eul,sequence)``

## Description

````tform = eul2tform(eul)` converts a set of Euler angles, `eul`, into a homogeneous transformation matrix, `tform`. When using the transformation matrix, premultiply it with the coordinates to be transformed (as opposed to postmultiplying). The default order for Euler angle rotations is `"ZYX"`.```

example

````tform = eul2tform(eul,sequence)` converts Euler angles to a homogeneous transformation. The Euler angles are specified in the axis rotation sequence, `sequence`. The default order for Euler angle rotations is `"ZYX"`.```

example

## Examples

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```eul = [0 pi/2 0]; tformZYX = eul2tform(eul)```
```tformZYX = 4×4 0.0000 0 1.0000 0 0 1.0000 0 0 -1.0000 0 0.0000 0 0 0 0 1.0000 ```
```eul = [0 pi/2 pi/2]; tformZYZ = eul2tform(eul,'ZYZ')```
```tformZYZ = 4×4 0.0000 -0.0000 1.0000 0 1.0000 0.0000 0 0 -0.0000 1.0000 0.0000 0 0 0 0 1.0000 ```

## 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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Homogeneous transformation matrix, specified by a 4-by-4-by-n array of n homogeneous transformation matrices. When using the transformation matrix, premultiply it with the coordinates to be rotated (as opposed to postmultiplying).

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

## Version History

Introduced in R2015a

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