transformPointsForward
Apply forward geometric transformation
Syntax
Description
Examples
Apply Forward Transformation of 2-D Geometric Transformation
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 forward geometric transformation to an input point.
u = 5; v = 10; [x,y] = transformPointsForward(tform,u,v)
x = 7.5000
y = 14
Transform Coordinate Arrays Using Custom 2-D Transformation
Specify 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
Apply Forward Transformation of 3-D Geometric Transformation
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.
u = 1; v = 1; w = 1.01; [x,y,z] = transformPointsForward(tform,u,v,w)
x = 11
y = 21.5000
z = 16.0100
Transform Coordinate Arrays Using Custom 3-D Transformation
Specify 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
Input Arguments
tform
— Geometric transformation
geometric transformation object
Geometric transformation, specified as a geometric transformation object listed in the table.
Geometric Transformation Object | Description |
---|---|
2-D Linear Geometric Transformations | |
transltform2d | Translation transformation |
rigidtform2d | Rigid transformation: translation and rotation |
simtform2d | Similarity transformation: translation, rotation, and isotropic scaling |
affinetform2d | Affine transformation: translation, rotation, anisotropic scaling, reflection, and shearing |
projtform2d | Projective transformation |
3-D Linear Geometric Transformations | |
transltform3d | Translation transformation |
rigidtform3d | Rigid transformation: translation and rotation |
simtform3d | Similarity transformation: translation, rotation, and isotropic scaling |
affinetform3d | Affine transformation: translation, rotation, anisotropic scaling, reflection, and shearing |
Nonlinear Geometric Transformations | |
geometricTransform2d | Custom 2-D geometric transformation using point-wise mapping functions |
geometricTransform3d | Custom 3-D geometric transformation using point-wise mapping functions |
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 Version History.
u
— 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 u
matches
the dimensionality of tform
.
Data Types: single
| double
v
— 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 v
must match the size of
u
.
Data Types: single
| double
U
— 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 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
Output Arguments
x
— 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 x
matches
the dimensionality of tform
.
Data Types: single
| double
y
— 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 y
matches the size of
x
.
Data Types: single
| double
z
— 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 z
matches the size of
x
.
Data Types: single
| double
X
— Coordinates of points after transformation
numeric array
Coordinates 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
Version History
Introduced in R2013aR2022b: Supports new geometric transformation objects
Starting in R2022b, most Image Processing Toolbox™ functions create and perform geometric transformations using the
premultiply convention. Accordingly, you can now specify tform
as a geometric transformation object that uses the premultiply convention, such as
an affinetform2d
object.
Before, for linear geometric transformations, you specified
tform
as a geometric transformation object that uses a
postmultiply convention, such as an affine2d
object. Although
transformPointsForward
still accepts objects that use the
postmultiply convention, these objects are not recommended. For more information,
see Migrate Geometric Transformations to Premultiply Convention.
There is no change to the support for nonlinear geometric transformations.
See Also
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