# transltform2d

2-D translation geometric transformation

## Description

A transltform2d object stores information about a 2-D translation geometric transformation and enables forward and inverse transformations.

## Creation

### Description

tform = transltform2d creates a transltform2d object that performs the identity transformation.

example

tform = transltform2d(Translation) creates a transltform2d 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- and y-directions.

tform = transltform2d(tx,ty) creates a transltform2d object that performs a translation transformation with the specified amounts of translation tx and ty in the x- and y-directions, respectively.

tform = transltform2d(A) creates a transltform2d object and sets the property A as the specified 2-D translation transformation matrix.

tform = transltform2d(tformIn) creates a transltform2d object from another geometric transformation object, tformIn, that represents a valid 2-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

Translation 2-D geometric transformation, specified as an affinetform2d object, rigidtform2d object, simtform2d object, transltform2d object, or projtform2d object.

## Properties

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Forward 2-D translation transformation, specified as a nonsingular 3-by-3 numeric matrix. When you create the object, you can also specify A as a 2-by-3 numeric matrix. In this case, the object concatenates the row vector [0 0 1] to the end of the matrix, forming a 3-by-3 matrix. The default of A is the identity matrix.

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

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

For a translation transformation, A has the form:

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

where tx and ty are the amount of translation in the x- and y-directions, respectively, and correspond to the Translation property.

Data Types: double | single

Amount of translation, specified as a 2-element numeric vector of the form [tx ty].

Data Types: double | single

Dimensionality of the geometric transformation for both input and output points, specified as 2.

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];

Create a transltform2d object that performs the specified translation.

tform = transltform2d(t)
tform =
transltform2d with properties:

Dimensionality: 2
Translation: [10 20.5000]
A: [3x3 double]

Examine the value of the A property.

tform.A
ans = 3×3

1.0000         0   10.0000
0    1.0000   20.5000
0         0    1.0000

## Version History

Introduced in R2022b