# transltform3d

3-D translation geometric transformation

## Description

A `transltform3d` object stores information about a 3-D translation geometric transformation and enables forward and inverse transformations.

## Creation

### Syntax

``tform = transltform3d``
``tform = transltform3d(Translation)``
``tform = transltform3d(tx,ty,tz)``
``tform = transltform3d(A)``
``tform = transltform3d(tformIn)``

### Description

````tform = transltform3d` creates a `transltform3d` object that performs the identity transformation.```

example

````tform = transltform3d(Translation)` creates a `transltform3d` object that performs a translation transformation based on the specified value of the `Translation` property. This property specifies the amount of translation in the x-, y-, and z-directions.```
````tform = transltform3d(tx,ty,tz)` creates a `transltform3d` object that performs a translation transformation with the specified amounts of translation `tx`, `ty`, and `tz` in the x-, y-, and z-directions, respectively.```
````tform = transltform3d(A)` creates a `transltform3d` object and sets the property `A` as the specified 3-D translation transformation matrix.```
````tform = transltform3d(tformIn)` creates a `transltform2d` object from another geometric transformation object, `tformIn`, that represents a valid 3-D translation geometric transformation.```

### Input Arguments

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Amount of translation in the x-direction, specified as a numeric scalar. This value sets the first element of the `Translation` property.

Amount of translation in the y-direction, specified as a numeric scalar. This value sets the second element of the `Translation` property.

Amount of translation in the z-direction, specified as a numeric scalar. This value sets the third element of the `Translation` property.

Translation 3-D geometric transformation, specified as an `affinetform3d` object, `rigidtform3d` object, `simtform3d` object, or `transltform3d` object.

## Properties

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Forward 3-D translation transformation, specified as a nonsingular 4-by-4 numeric matrix. When you create the object, you can also specify `A` as a 3-by-4 numeric matrix. In this case, the object concatenates the row vector `[0 0 0 1]` to the end of the matrix, forming a 4-by-4 matrix. The default of `A` is the identity matrix.

The matrix `A` transforms the point (u, v, w) in the input coordinate space to the point (x, y, z) in the output coordinate space using the convention:

`$\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]=Α×\left[\begin{array}{c}u\\ v\\ w\\ 1\end{array}\right]$`

For a translation transformation, `A` has the form:

`$Α=\left[\begin{array}{cccc}1& 0& 0& {t}_{x}\\ 0& 1& 0& {t}_{y}\\ 0& 0& 1& {t}_{z}\\ 0& 0& 0& 1\end{array}\right]$`

where tx, ty, and tz are the amount of translation in the x-, y-, and z-directions, respectively.

Data Types: `double` | `single`

Amount of translation, specified as a 3-element numeric vector of the form [tx ty tz].

Data Types: `double` | `single`

Dimensionality of the geometric transformation for both input and output points, specified as `3`.

Data Types: `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 the amount of translation.

`t = [10 20.5 15];`

Create a `transltform3d` object that performs the specified translation.

`tform = transltform3d(t)`
```tform = transltform3d with properties: Dimensionality: 3 Translation: [10 20.5000 15] A: [4x4 double] ```

Examine the value of the `A` property.

`tform.A`
```ans = 4×4 1.0000 0 0 10.0000 0 1.0000 0 20.5000 0 0 1.0000 15.0000 0 0 0 1.0000 ```

## Version History

Introduced in R2022b