# rotvecd

Convert quaternion to rotation vector (degrees)

## Syntax

``rotationVector = rotvecd(quat)``

## Description

example

````rotationVector = rotvecd(quat)` converts the quaternion array, `quat`, to an N-by-3 matrix of equivalent rotation vectors in degrees. The elements of `quat` are normalized before conversion.```

## Examples

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Convert a random quaternion scalar to a rotation vector in degrees.

```quat = quaternion(randn(1,4)); rotvecd(quat)```
```ans = 1×3 96.6345 -119.0274 45.4312 ```

## Input Arguments

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Quaternion to convert, specified as scalar, vector, matrix, or multidimensional array of quaternions.

Data Types: `quaternion`

## Output Arguments

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Rotation vector representation, returned as an N-by-3 matrix of rotation vectors, where each row represents the [x y z] angles of the rotation vectors in degrees. The ith row of `rotationVector` corresponds to the element `quat(i)`.

The data type of the rotation vector is the same as the underlying data type of `quat`.

Data Types: `single` | `double`

## Algorithms

All rotations in 3-D can be represented by four elements: a three-element axis of rotation and a rotation angle. If the rotation axis is constrained to be unit length, the rotation angle can be distributed over the vector elements to reduce the representation to three elements.

Recall that a quaternion can be represented in axis-angle form

`$q=\mathrm{cos}\left(\theta }{2}\right)+\mathrm{sin}\left(\theta }{2}\right)\left(\text{xi}+y\text{j}+z\text{k}\right),$`

where θ is the angle of rotation in degrees, and [x,y,z] represent the axis of rotation.

Given a quaternion of the form

`$q=a+bi+cj+dk\text{\hspace{0.17em}},$`

you can solve for the rotation angle using the axis-angle form of quaternions:

`$\theta =2{\mathrm{cos}}^{-1}\left(a\right).$`

Assuming a normalized axis, you can rewrite the quaternion as a rotation vector without loss of information by distributing θ over the parts b, c, and d. The rotation vector representation of q is

`${q}_{\text{rv}}=\frac{\theta }{\mathrm{sin}\left(\theta }{2}\right)}\left[b,c,d\right].$`

## Extended Capabilities

### Topics

Introduced in R2018b