# tilt

Tilt angle

Since R2023b

## Syntax

``T = tilt(orientations)``

## Description

example

````T = tilt(orientations)` returns the tilt angles based on the specified `orientations`. See Tilt Angle Definition for more details.```

## Examples

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Define four sets of Euler angles and obtain their corresponding quaternions.

```angles = [0 0 0; 0 0 10; 0 0 170; 0 0 190]; quats = quaternion(angles,"eulerd","ZYX","frame");```

Obtain the tilt angles and convert their units to degrees.

`tiltAngles = rad2deg(tilt(quats))`
```tiltAngles = 4×1 0 10.0000 170.0000 170.0000 ```

## Input Arguments

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Orientations, specified as an N-by-1 vector of `quaternion` objects or as a 3-by-3-by-N array of rotation matrices. N is the total number of orientations.

## Output Arguments

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Tilt angles, in radians, returned as an N-element column vector of scalars in the range [0, pi]. N is the total number of orientations.

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### Tilt Angle Definition

The tilt angle is defined as the angle between the positive-Z direction of the reference frame and the positive-z direction of the body frame. The `orientations` input defines the rotational coordinate transformation from the reference frame to the body frame.

## Version History

Introduced in R2023b