Apply inverse 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: 2Apply forward transformation of 2-D geometric transformation to an input point.
[X,Y] = transformPointsForward(tform,5,10)
X =
6.6605
Y =
8.9798Apply 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: 3Apply forward transformation of 3-D geometric transformation to an input point.
[X,Y,Z] = transformPointsForward(tform,2,3,5)
X =
48
Y =
27
Z =
33Apply 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 =
5.0000Specify 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
tform — Geometric transformationGeometric 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 transformedx-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 transformedy-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
X — Coordinates of points to be transformedCoordinates 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
u — x-coordinates of points after transformationx-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 transformationy-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 transformationz-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 transformationCoordinates 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
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