# rigid3d

3-D rigid geometric transformation

## Description

A `rigid3d` object stores information about a 3-D rigid geometric transformation and enables forward and inverse transformations.

## Creation

### Syntax

``tform = rigid3d``
``tform = rigid3d(t)``
``tform = rigid3d(rot,trans)``

### Description

````tform = rigid3d` creates a default `rigid3d` object that corresponds to an identity transformation.```
````tform = rigid3d(t)` creates a `rigid3d` object based on a specified forward rigid transformation matrix, `t`. The `t` input sets the `T` property.```

example

````tform = rigid3d(rot,trans)` creates a `rigid3d` object based on the rotation, `rot`, and translation, `trans`, components of the transformation. `rot` sets the `Rotation` property. `trans` sets the `Translation` property.```

## Properties

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Forward rigid transformation, specified as a 4-by-4 numeric matrix. This matrix must be a homogeneous transformation matrix that satisfies the post-multiply convention given by:

`$\left[\begin{array}{cccc}x& y& z& 1\end{array}\right]=\left[\begin{array}{cccc}u& v& w& 1\end{array}\right]*T$`

`T` has the form

`$\begin{array}{ccccc}\left[{r}_{11}& {r}_{12}& {r}_{13}& 0;& ...\\ {r}_{21}& {r}_{22}& {r}_{23}& 0;& ...\\ {r}_{31}& {r}_{32}& {r}_{33}& 0;& ...\\ {t}_{x}& {t}_{y}& {t}_{z}& 1\right];& \end{array}$`

Data Types: `single` | `double`

Dimensionality of the geometric transformation, specified as a positive integer.

Rotation component of the transformation, specified as a 3-by-3 numeric matrix. This rotation matrix satisfies the post-multiply convention given by

`$\left[\begin{array}{ccc}x& y& z\end{array}\right]=\left[\begin{array}{ccc}u& v& w\end{array}\right]*R$`

Data Types: `single` | `double`

Translation component of the transformation, specified as a 3-element numeric row vector. This translation vector satisfies the convention given by

`$\left[\begin{array}{ccc}x& y& z\end{array}\right]=\left[\begin{array}{ccc}u& v& w\end{array}\right]+t$`

Data Types: `single` | `double`

## Object Functions

 `invert` Invert geometric transformation `outputLimits` Find output spatial limits given input spatial limits `transformPointsForward` Apply forward geometric transformation `transformPointsInverse` Apply inverse geometric transformation

## Examples

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Specify an angle of rotation in degrees and create a 3-by-3 rotation matrix.

```theta = 30; rot = [ cosd(theta) sind(theta) 0; ... -sind(theta) cosd(theta) 0; ... 0 0 1];```

Specify the amount of horizontal, vertical, and depthwise translation, respectively.

`trans = [2 3 4];`

Create a `rigid3d` object that performs the rotation and translation.

`tform = rigid3d(rot,trans)`
```tform = rigid3d with properties: Rotation: [3x3 double] Translation: [2 3 4] ```

## Version History

Introduced in R2020a