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simtform2d

2-D similarity geometric transformation

    Description

    A simtform2d object stores information about a 2-D similarity geometric transformation and enables forward and inverse transformations.

    Creation

    You can create a simtform2d object in these ways:

    • fitgeotform2d — Estimate a geometric transformation that maps pairs of control points between two images.

    • The simtform2d function described here.

    Description

    tform = simtform2d creates a simtform2d object that performs the identity transformation.

    tform = simtform2d(Scale,RotationAngle,Translation) creates a simtform2d object that performs a similarity transformation based on the specified values of the Scale, RotationAngle, and Translation properties. These properties specify the scale factor, rotation angle, and the amount of translation in the x- and y-directions, respectively.

    example

    tform = simtform2d(Scale,R,Translation) creates a simtform2d object that performs a similarity transformation based on the specified values of the Scale, R, and Translation properties. These properties indicate the scale factor, rotation matrix, and the amounts of translation in the x- and y-directions.

    tform = simtform2d(A) creates a simtform2d object and sets the property A as the specified 2-D similarity transformation matrix.

    tform = simtform2d(tformIn) creates a simtform2d object from another geometric transformation object, tformIn, that represents a valid 2-D similarity geometric transformation.

    Input Arguments

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    Similarity 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 similarity 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:

    [xy1]=Α×[uv1]

    For a similarity transformation, A has the form:

    Α=[s×cosd(r)s×sind(r)txs×sind(r)s×cosd(r)ty001]

    where s is the scale factor and corresponds to the Scale property. r is the rotation angle and corresponds to the RotationAngle property. 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

    Scale factor, specified as a nonzero number. The scale factor corresponds to the value s in the similarity transformation matrix defined by property A.

    Data Types: double | single

    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.

    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

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

    Data Types: double | single

    This property is read-only.

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

    Data Types: double

    Object Functions

    invertInvert geometric transformation
    outputLimitsFind output spatial limits given input spatial limits
    transformPointsForwardApply forward geometric transformation
    transformPointsInverseApply inverse geometric transformation

    Examples

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    Specify the scale factor, rotation angle, and the amount of translation.

    scaleFactor = 3;
    theta = 30;
    translation = [10 20.5];

    Create a simtform2d object that performs the specified scaling, rotation, and translation.

    tform = simtform2d(scaleFactor,theta,translation)
    tform = 
      simtform2d with properties:
    
        Dimensionality: 2
                 Scale: 3
         RotationAngle: 30
           Translation: [10 20.5000]
                     R: [2x2 double]
                     A: [3x3 double]
    
    

    Examine the value of the A property.

    tform.A
    ans = 3×3
    
        2.5981   -1.5000   10.0000
        1.5000    2.5981   20.5000
             0         0    1.0000
    
    

    Extended Capabilities

    Version History

    Introduced in R2022b