transltform3d

3-D translation geometric transformation

Since R2022b

Description

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

Creation

You can create a transltform3d object in these ways:

• imregtform — Estimates a geometric transformation that maps a moving image to a fixed image using similarity optimization.

• fitgeotform3d (Medical Imaging Toolbox) — Estimates a geometric transformation that maps pairs of control points between two images.

• The transltform3d function described here.

Syntax

tform = transltform3d

tform = transltform3d(t)

tform = transltform3d(tx,ty,tz)

tform = transltform3d(translMat)

tform = transltform3d(tformIn)

Description

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

tform = transltform3d(t) creates a transltform3d object that performs a translation transformation based on the specified amount of translation t.

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(translMat) creates a transltform3d object from the specified 3-D translation transformation matrix, translMat.

tform = transltform3d(tformIn) creates a transltform2d object from another geometric transformation object, tformIn, that represents a valid 3-D translation geometric transformation.

Input Arguments

t — Amount of translation

[0 0 0] (default) | 3-element numeric vector

Amount of translation, specified as a 3-element numeric vector of the form [t_x t_y t_z]. These amounts of translation correspond to the values t_x, t_y, and t_z in the translation transformation matrix defined by A.

This argument sets the Translation property.

Data Types: double | single

tx — Amount of translation in x-direction

0 (default) | numeric scalar

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

ty — Amount of translation in y-direction

0 (default) | numeric scalar

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

tz — Amount of translation in z-direction

0 (default) | numeric scalar

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

translMat — Forward 3-D translation transformation

4-by-4 identity matrix (default) | 4-by-4 numeric matrix

Forward 3-D translation transformation, specified as a 4-by-4 numeric matrix. When you create the object, you can also specify translMat 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.

A valid 3-D translation transformation A has the form:

$${\rm A}=\left[\begin{array}{cccc}1& 0& 0& t_x\\ 0& 1& 0& t_y\\ 0& 0& 1& t_z\\ 0& 0& 0& 1\end{array}\right]$$

t_x, t_y, and t_z are the amount of translation in the x-, y-, and z-directions, respectively, and set the Translation property.

This argument sets the A property.

Data Types: double | single

tformIn — Translation 3-D geometric transformation

affinetform3d object | rigidtform3d object | simtform3d object | transltform3d object

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

Output Arguments

tform — Translation 3-D geometric transformation

transltform3d object

Translation 3-D geometric transformation, returned as a transltform3d object.

Properties

A — Forward 3-D translation transformation

4-by-4 identity matrix (default) | 4-by-4 numeric matrix

Forward 3-D translation transformation, specified as a 4-by-4 numeric 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:

$$\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]={\rm A}\times \left[\begin{array}{c}u\\ v\\ w\\ 1\end{array}\right]$$

For a translation transformation, A has the form:

$${\rm A}=\left[\begin{array}{cccc}1& 0& 0& t_x\\ 0& 1& 0& t_y\\ 0& 0& 1& t_z\\ 0& 0& 0& 1\end{array}\right]$$

where t_x, t_y, and t_z are the amount of translation in the x-, y-, and z-directions, respectively, and correspond to the Translation property.

Data Types: double | single

Translation — Amount of translation

[0 0 0] (default) | 3-element numeric vector

Amount of translation, specified as a 3-element numeric vector of the form [t_x t_y t_z].

Data Types: double | single

Dimensionality — Dimensionality of geometric transformation

Read-only: 3 (default)

This property is read-only.

Dimensionality of the geometric transformation for both input and output points, returned as the value 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

Create 3-D Translation Transformation

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: [1.0000         0         0   10.0000
                          0    1.0000         0   20.5000
                          0         0    1.0000   15.0000
                          0         0         0    1.0000]

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

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

• transltform3d supports the generation of C and C++ code (requires MATLAB^® Coder™). For more information, see Code Generation for Image Processing.

• When generating code, you can only specify singular objects. Arrays of objects are not supported.

• Generated code cannot return a transltform3d object. Instead, you can return a numeric array, such as the value of the A property.

Thread-Based Environment

Run code in the background using MATLAB® backgroundPool or accelerate code with Parallel Computing Toolbox™ ThreadPool.

This function fully supports thread-based environments. For more information, see Run MATLAB Functions in Thread-Based Environment.

Version History

Introduced in R2022b