transformPointsInverse

Apply inverse geometric transformation

Syntax

[u,v] = transformPointsInverse(tform,x,y)

[u,v,w] = transformPointsInverse(tform,x,y,z)

U = transformPointsInverse(tform,X)

Description

[u,v] = transformPointsInverse(tform,x,y) applies the inverse transformation of 2-D geometric transformation tform to the points specified by coordinates x and y.

[u,v,w] = transformPointsInverse(tform,x,y,z) applies the inverse transformation of 3-D geometric transformation tform to the points specified by coordinates x, y, and z.

U = transformPointsInverse(tform,X) applies the inverse transformation of tform to the input coordinate matrix X and returns the coordinate matrix U. transformPointsInverse maps the kth point X(k,:) to the point U(k,:).

Examples

Apply Inverse Transformation of 2-D Geometric Transformation

Create an affine2d object that defines the transformation.

theta = 10;

tform = affine2d([cosd(theta) -sind(theta) 0; sind(theta) cosd(theta) 0; 0 0 1])

tform = 

  affine2d with properties:

                 T: [3x3 double]
    Dimensionality: 2

Apply forward transformation of 2-D geometric transformation to an input point.

[X,Y] = transformPointsForward(tform,5,10)

X =

    6.6605


Y =

    8.9798

Apply inverse transformation of 2-D geometric transformation to output point from the previous step to recover the original coordinates.

[U,V] = transformPointsInverse(tform,X,Y)

U =

    5.0000


V =

    10

Transform Packed Coordinates Using Custom 2-D Transformation

Specify the packed (x,y) coordinates of five input points. The packed coordinates are stored in a 5-by-2 matrix, where the x-coordinate of each point is in the first column, and the y-coordinate of each point is in the second column.

XY = [10 15;11 32;15 34;2 7;2 10];

Define the inverse mapping function. The function accepts and returns points in packed (x,y) format.

inversefn = @(c) [c(:,1)+c(:,2),c(:,1)-c(:,2)]

inversefn = function_handle with value:
    @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2)]

Create a 2-D geometric transform object, tform, that stores the inverse mapping function.

tform = geometricTransform2d(inversefn)

tform = 
  geometricTransform2d with properties:

        InverseFcn: @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2)]
        ForwardFcn: []
    Dimensionality: 2

Apply the inverse geometric transform to the input points.

UV = transformPointsInverse(tform,XY)

UV = 5×2

    25    -5
    43   -21
    49   -19
     9    -5
    12    -8

Apply Inverse Transformation of 3-D Geometric Transformation

Create an affine3d object that defines the transformation.

tform = affine3d([3 1 2 0;4 5 8 0;6 2 1 0;0 0 0 1])

tform = 

  affine3d with properties:

                 T: [4×4 double]
    Dimensionality: 3

Apply forward transformation of 3-D geometric transformation to an input point.

[X,Y,Z] = transformPointsForward(tform,2,3,5)

X =

    48


Y =

    27


Z =

    33

Apply inverse transformation of 3-D geometric transformation to output point from the previous step to recover the original coordinates.

[U,V,W] = transformPointsInverse(tform,X,Y,Z)

U =

    2.0000


V =

     3


W =

    5.0000

Transform Packed Coordinates Using Custom 3-D Transformation

Specify the packed (x,y,z) coordinates of five input points. The packed coordinates are stored as a 5-by-3 matrix, where the first, second, and third columns contain the x-, y-, and z- coordinates,respectively.

XYZ = [5 25 20;10 5 25;15 10 5;20 15 10;25 20 15];

Define an inverse mapping function that accepts and returns points in packed (x,y,z) format.

inverseFcn = @(c) [c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2];

Create a 3-D geometric transformation object, tform, that stores this inverse mapping function.

tform = geometricTransform3d(inverseFcn)

tform = 
  geometricTransform3d with properties:

        InverseFcn: @(c)[c(:,1)+c(:,2),c(:,1)-c(:,2),c(:,3).^2]
        ForwardFcn: []
    Dimensionality: 3

Apply the inverse transformation of this 3-D geometric transformation to the input points.

UVW = transformPointsInverse(tform,XYZ)

UVW = 5×3

    30   -20   400
    15     5   625
    25     5    25
    35     5   100
    45     5   225

Input Arguments

tform — Geometric transformation

geometric transformation object

Geometric transformation, specified as a geometric transformation object.

For 2-D geometric transformations, tform can be a rigid2d, affine2d, projective2d, geometricTransform2d, LocalWeightedMeanTransformation2D, PiecewiseLinearTransformation2D, or PolynomialTransformation2D geometric transformation object.

For 3-D geometric transformations, tform can be an affine3d, rigid3d, or geometricTransform3d geometric transformation object.

x — x-coordinates of points to be transformed

m-by-n or m-by-n-by-p numeric array

x-coordinates of points to be transformed, specified as an m-by-n or m-by-n-by-p numeric array. The number of dimensions of x matches the dimensionality of tform.

Data Types: single | double

y — y-coordinates of points to be transformed

m-by-n or m-by-n-by-p numeric array

y-coordinates of points to be transformed, specified as an m-by-n or m-by-n-by-p numeric array. The size of y must match the size of x.

Data Types: single | double

z — z-coordinates of points to be transformed

m-by-n-by-p numeric array

z-coordinates of points to be transformed, specified as an m-by-n-by-p numeric array. z is used only when tform is a 3-D geometric transformation. The size of z must match the size of x.

Data Types: single | double

X — Coordinates of points to be transformed

l-by-2 or l-by-3 numeric array

Coordinates of points to be transformed, specified as an l-by-2 or l-by-3 numeric array. The number of columns of X matches the dimensionality of tform.

The first column lists the x-coordinate of each point to transform, and the second column lists the y-coordinate. If tform represents a 3-D geometric transformation, X has size l-by-3 and the third column lists the z-coordinate of the points to transform.

Data Types: single | double

Output Arguments

u — x-coordinates of points after transformation

m-by-n or m-by-n-by-p numeric array

x-coordinates of points after transformation, returned as an m-by-n or m-by-n-by-p numeric array. The number of dimensions of u matches the dimensionality of tform.

Data Types: single | double

v — y-coordinates of points after transformation

m-by-n or m-by-n-by-p numeric array

y-coordinates of points after transformation, returned as an m-by-n or m-by-n-by-p numeric array. The size of v matches the size of u.

Data Types: single | double

w — z-coordinates of points after transformation

m-by-n-by-p numeric array

z-coordinates of points after transformation, returned as an m-by-n-by-p numeric array. The size of w matches the size of u.

Data Types: single | double

U — Coordinates of points after transformation

numeric array

Coordinates of points after transformation, returned as a numeric array. The size of U matches the size of X.

The first column lists the x-coordinate of each point after transformation, and the second column lists the y-coordinate. If tform represents a 3-D geometric transformation, the third column lists the z-coordinate of the points after transformation.

Data Types: single | double