Apply forward 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 geometric transformation to an input
(u,v) point.
[X,Y] = transformPointsForward(tform,5,10)
X =
6.6605
Y =
8.9798Specify the x- and y-coordinates vectors of five points to transform.
x = [10 11 15 2 2]; y = [15 32 34 7 10];
Define the inverse and forward mapping functions. Both functions accept and return points in packed (x,y) format.
inversefn = @(c) [c(:,1).^2,sqrt(c(:,2))]; forwardfn = @(c) [sqrt(c(:,1)),c(:,2).^2];
Create a 2-D geometric transform object, tform, that stores the inverse mapping function and the optional forward mapping function.
tform = geometricTransform2d(inversefn,forwardfn)
tform =
geometricTransform2d with properties:
InverseFcn: @(c)[c(:,1).^2,sqrt(c(:,2))]
ForwardFcn: @(c)[sqrt(c(:,1)),c(:,2).^2]
Dimensionality: 2
Apply the inverse geometric transform to the input points.
[u,v] = transformPointsInverse(tform,x,y)
u = 1×5
100 121 225 4 4
v = 1×5
3.8730 5.6569 5.8310 2.6458 3.1623
Apply the forward geometric transform to the transformed points u and v.
[x,y] = transformPointsForward(tform,u,v)
x = 1×5
10 11 15 2 2
y = 1×5
15.0000 32.0000 34.0000 7.0000 10.0000
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
(u,v,w)
point.
[X,Y,Z] = transformPointsForward(tform,2,3,5)
X =
48
Y =
27
Z =
33Specify the x-, y- and the z-coordinate vectors of five points to transform.
x = [3 5 7 9 11]; y = [2 4 6 8 10]; z = [5 9 13 17 21];
Define the inverse and forward mapping functions that accept and return points in packed (x,y,z) format.
inverseFcn = @(c)[c(:,1).^2,c(:,2).^2,c(:,3).^2]; forwardFcn = @(c)[sqrt(c(:,1)),sqrt(c(:,2)),sqrt(c(:,3))];
Create a 3-D geometric transformation object, tform, that stores these inverse and forward mapping functions.
tform = geometricTransform3d(inverseFcn,forwardFcn)
tform =
geometricTransform3d with properties:
InverseFcn: @(c)[c(:,1).^2,c(:,2).^2,c(:,3).^2]
ForwardFcn: @(c)[sqrt(c(:,1)),sqrt(c(:,2)),sqrt(c(:,3))]
Dimensionality: 3
Apply the inverse transformation of this 3-D geometric transformation to the input points.
[u,v,w] = transformPointsInverse(tform,x,y,z)
u = 1×5
9 25 49 81 121
v = 1×5
4 16 36 64 100
w = 1×5
25 81 169 289 441
Apply the forward geometric transform to the transformed points u, v, and w.
[x,y,z] = transformPointsForward(tform,u,v,w)
x = 1×5
3 5 7 9 11
y = 1×5
2 4 6 8 10
z = 1×5
5 9 13 17 21
tform — Geometric transformationGeometric transformation, specified as a geometric transformation object.
For 2-D geometric transformations, tform can be a
rigid2d, affine2d, projective2d, or geometricTransform2d geometric transformation object.
For 3-D geometric transformations, tform can be an
affine3d, rigid3d, or geometricTransform3d geometric transformation object.
u — 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 u matches
the dimensionality of tform.
Data Types: single | double
v — 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 v must match the size of
u.
Data Types: single | double
U — 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 U 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, U has size
l-by-3 and the third column lists
the z-coordinate of the points to transform.
Data Types: single | double
x — 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 x matches
the dimensionality of tform.
Data Types: single | double
y — 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 y matches the size of
x.
Data Types: single | double
z — z-coordinates of points after transformationz-coordinates of points after transformation, returned
as an m-by-n-by-p
numeric array. The size of z matches the size of
x.
Data Types: single | double
X — Coordinates of points after transformationCoordinates of points after transformation, returned as a numeric array.
The size of X matches the size of
U.
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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