rigid2d

(Not recommended) 2-D rigid geometric transformation using postmultiply convention

rigid2d is not recommended. Use the rigidtform2d object instead. For more information, see Compatibility Considerations.

Description

A rigid2d object stores information about a 2-D rigid geometric transformation and enables forward and inverse transformations.

Creation

Syntax

tform = rigid2d

tform = rigid2d(t)

tform = rigid2d(rot,trans)

Description

tform = rigid2d creates a default rigid2d object that corresponds to an identity transformation.

tform = rigid2d(t) sets the T property as the specified 2-D rigid transformation matrix t.

tform = rigid2d(rot,trans) sets the Rotation and Translation properties as the specified rotation matrix rot and translation vector trans, respectively.

Properties

T — Forward rigid transformation

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

Forward rigid transformation, specified as a 3-by-3 numeric matrix. The matrix T satisfies the postmultiply convention given by:

[x y 1] = [u v 1] * Rotation + Translation

Data Types: single | double

Rotation — Rotation component of transformation

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

Rotation component of the transformation, specified as a 2-by-2 numeric matrix.

Data Types: single | double

Translation — Translation component of transformation

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

Translation component of the transformation, specified as a 2-element numeric row vector.

Data Types: single | double

Dimensionality — Dimensionality of geometric transformation

2 (default)

This property is read-only.

Dimensionality of the geometric transformation, specified as the number 2.

Object Functions

invert	Invert geometric transformation
isTranslation	Determine if geometric transformation is pure translation
outputLimits	Find output spatial limits given input spatial limits
transformPointsForward	Apply forward geometric transformation
transformPointsInverse	Apply inverse geometric transformation

Examples

Create Rigid 2-D Object with Defined Translation and Rotation

Specify an angle of rotation in degrees and create a 2-by-2 rotation matrix.

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

Specify the amount of horizontal and vertical translation, respectively.

trans = [2 3];

Create a rigid2d object that performs the rotation and translation.

tform = rigid2d(rot,trans)

tform = 
  rigid2d with properties:

       Rotation: [2x2 double]
    Translation: [2 3]

Version History

Introduced in R2020b

R2022b: Not recommended

Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the premultiply convention. Accordingly, 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, which supports the premultiply convention. For more information, see Migrate Geometric Transformations to Premultiply Convention.

To update your code:

• Change instances of the function name rigid2d to rigidtform2d.

• Specify the transformation matrix as the transpose of the matrix T or Rotation. T is either the value of the T property of the rigid2d object or the transformation matrix used to create the rigid2d object. Rotation is either the value of the Rotation property of the rigid2d object or the rotation matrix used to create the rigid2d object.

Discouraged Usage	Recommended Replacement
This example creates a rigid2d object from transformation matrix T in the postmultiply convention. T = [1 0 0; 0 1 0; 5 10 1]; tformPost = rigid2d(T);	This example creates a rigidtform2d object from the transpose of the transformation matrix T. T = [1 0 0; 0 1 0; 5 10 1]; tform = rigidtform2d(T'); This example starts with a rigid2d object called tformPost and creates a rigidtform2d object from the transpose of the T property of tformPost. T = tformPost.T; tform = rigidtform2d(T');
This example creates a rigid2d object from a rotation matrix rot in the postmultiply convention and a translation trans. theta = 45; rot = [cosd(theta) sind(theta); -sind(theta) cosd(theta)]; trans = [5 10]; tformPost = rigid2d(rot,trans);	This example creates a rigidtform2d object from the transpose of the rotation matrix rot and a translation trans. theta = 45; rot = [cosd(theta) sind(theta); -sind(theta) cosd(theta)]; trans = [5 10]; tform = rigidtform2d(rot',trans); You can simplify your code by specifying the angle of rotation directly. tform = rigidtform2d(theta,trans);