transformPointsInverse

Apply inverse geometric transformation

Description

example

[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

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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

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

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

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

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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-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-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-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

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

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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

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

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

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