# 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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Define a 3-by-3 geometric transformation matrix. This example specifies a matrix for an affine transformation consisting of vertical shear and horizontal stretch.

A = [1.5 0 0; 0.8 1 0; 0 0 1];

Create an affinetform2d object from the transformation matrix.

tform = affinetform2d(A);

Apply the inverse geometric transformation to a point.

x = 7.5;
y = 14;
[u,v] = transformPointsInverse(tform,x,y)
u = 5
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

Define a rigid geometric transformation consisting only of translation.

t = [10 20.5 15];
tform = transltform3d(t);

Apply the forward geometric transformation to an input point.

x = 11;
y = 21.5;
z = 16.01;
[u,v,w] = transformPointsInverse(tform,x,y,z)
u = 1
v = 1
w = 1.0100

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 listed in the table.

Geometric Transformation ObjectDescription
2-D Linear Geometric Transformations
transltform2dTranslation transformation
rigidtform2dRigid transformation: translation and rotation
simtform2dSimilarity transformation: translation, rotation, and isotropic scaling
affinetform2dAffine transformation: translation, rotation, nonisotropic scaling, reflection, and shearing
projtform2dProjective transformation
3-D Linear Geometric Transformations
transltform3dTranslation transformation
rigidtform3dRigid transformation: translation and rotation
simtform3dSimilarity transformation: translation, rotation, and isotropic scaling
affinetform3dAffine transformation: translation, rotation, nonisotropic scaling, reflection, and shearing
Nonlinear Geometric Transformations
geometricTransform2dCustom 2-D geometric transformation using point-wise mapping functions
geometricTransform3dCustom 3-D geometric transformation using point-wise mapping functions
LocalWeightedMeanTransformation2D2-D local weighted means transformation
PiecewiseLinearTransformation2D2-D piecewise linear transformation
PolynomialTransformation2D2-D polynomial transformation

Note

You can also specify tform as an object of type rigid2d, rigid3d, affine2d, affine3d, or projective2d. However, these objects are not recommended. For more information, see Compatibility Considerations.

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

## Version History

Introduced in R2013a

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