rigidtform2d

2-D rigid geometric transformation

Since R2022b

Description

A rigidtform2d object stores information about a 2-D rigid geometric transformation and enables forward and inverse transformations.

Creation

Syntax

tform = rigidtform2d

tform = rigidtform2d(Translation)

tform = rigidtform2d(RotationAngle,Translation)

tform = rigidtform2d(R,Translation)

tform = rigidtform2d(A)

tform = rigidtform2d(tformIn)

Description

tform = rigidtform2d creates a rigidtform2d object that performs an identity transformation.

tform = rigidtform2d(Translation) creates a rigidtform2d object that performs a rigid transformation consisting only of translation. The specified property Translation indicates the amount of translation in the x- and y-directions.

If you want a transformation that performs only 2-D translation, consider using the transltform2d object.

tform = rigidtform2d(RotationAngle,Translation) creates a rigidtform2d object that performs a rigid transformation based on the specified values of the RotationAngle and Translation properties. These properties indicate the rotation angle and the amount of translation in the x- and y- directions.

tform = rigidtform2d(R,Translation) creates a rigidtform2d object that performs a rigid transformation based on the specified values of the R and Translation properties. These properties indicate the rotation matrix and the amount of translation in the x- and y- directions.

tform = rigidtform2d(A) creates a rigidtform2d object and sets the property A as the specified 2-D rigid transformation matrix.

tform = rigidtform2d(tformIn) creates a rigidtform2d object from another geometric transformation object, tformIn, that represents a valid 2-D rigid geometric transformation.

Input Arguments

tformIn — Rigid 2-D geometric transformation

affinetform2d object | rigidtform2d object | simtform2d object | transltform2d object | projtform2d object

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

Properties

A — Forward 2-D rigid transformation

3-by-3 identity matrix (default) | 3-by-3 numeric matrix

Forward 2-D rigid transformation, specified as a 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 value 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:

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

For a rigid transformation, A has the form:

$${\rm A}=\left[\begin{array}{ccc}cosd(r)& -\mathrm{sind}(r)& t_x\\ \mathrm{sind}(r)& cosd(r)& t_y\\ 0& 0& 1\end{array}\right]$$

where r is the rotation angle and corresponds to the property RotationAngle. t_x and t_y are the amount of translation in the x- and y- directions, respectively, and correspond to the property Translation.

Data Types: double | single

R — Rotation matrix

2-by-2 identity matrix (default) | 2-by-2 numeric matrix

Rotation matrix, specified as a 2-by-2 numeric matrix. The matrix must have the form

 R = [cosd(r) -sind(r); sind(r)  cosd(r)]

where r is the value of the RotationAngle property.

RotationAngle — Rotation angle about origin

0 (default) | numeric scalar

Rotation angle about the origin, in degrees, specified as a numeric scalar. The rotation angle corresponds to the value r in the transformation matrix defined by A, and in the rotation matrix defined by R.

Data Types: double | single

Translation — Amount of translation

[0 0] (default) | 2-element numeric vector

Amount of translation, specified as a 2-element numeric vector of the form [t_x t_y]. These amounts of translation correspond to the values t_x and t_y in the rigid transformation matrix defined by A.

Data Types: double | single

Dimensionality — Dimensionality of geometric transformation

2 (default)

This property is read-only.

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

Create 2-D Rigid Transformation

Specify a rotation angle and an amount of translation.

theta = 30;
translation = [10 20.5];

Create a rigidtform2d object that performs the specified rotation and translation.

tform = rigidtform2d(theta,translation)

tform = 
  rigidtform2d with properties:

    Dimensionality: 2
     RotationAngle: 30
       Translation: [10 20.5000]
                 R: [2x2 double]

                 A: [0.8660   -0.5000   10.0000
                     0.5000    0.8660   20.5000
                          0         0    1.0000]

Examine the value of the A property.

tform.A

ans = 3×3

    0.8660   -0.5000   10.0000
    0.5000    0.8660   20.5000
         0         0    1.0000

Extended Capabilities

C/C++ Code Generation

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

Usage notes and limitations:

• rigidtform2d supports the generation of 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.

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

R2022b: Recommended over rigid2d

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. The rigidtform2d object stores information about 2-D rigid geometric transformations in a format consistent with the premultiply convention.

The rigid2d object is not recommended because it uses the postmultiply convention. Although there are no plans to remove the rigid2d object at this time, you can streamline your geometric transformation workflows by switching to the rigidtform2d object. For more information, see Migrate Geometric Transformations to Premultiply Convention.