#include <itkAffineTransform.h>
Inheritance diagram for itk::AffineTransform< TScalarType, NDimensions >:
This class allows the definition and manipulation of affine transformations of an n-dimensional affine space (and its associated vector space) onto itself. One common use is to define and manipulate Euclidean coordinate transformations in two and three dimensions, but other uses are possible as well.
An affine transformation is defined mathematically as a linear transformation plus a constant offset. If A is a constant n x n matrix and b is a constant n-vector, then y = Ax+b defines an affine transformation from the n-vector x to the n-vector y.
The difference between two points is a vector and transforms linearly, using the matrix only. That is, (y1-y2) = A*(x1-x2).
The AffineTransform class determines whether to transform an object as a point or a vector by examining its type. An object of type Point transforms as a point; an object of type Vector transforms as a vector.
One common use of affine transformations is to define coordinate conversions in two- and three-dimensional space. In this application, x is a two- or three-dimensional vector containing the "source" coordinates of a point, y is a vector containing the "target" coordinates, the matrix A defines the scaling and rotation of the coordinate systems from the source to the target, and b defines the translation of the origin from the source to the target. More generally, A can also define anisotropic scaling and shearing transformations. Any good textbook on computer graphics will discuss coordinate transformations in more detail. Several of the methods in this class are designed for this purpose and use the language appropriate to coordinate conversions.
Any two affine transformations may be composed and the result is another affine transformation. However, the order is important. Given two affine transformations T1 and T2, we will say that "precomposing T1 with T2" yields the transformation which applies T1 to the source, and then applies T2 to that result to obtain the target. Conversely, we will say that "postcomposing T1 with T2" yields the transformation which applies T2 to the source, and then applies T1 to that result to obtain the target. (Whether T1 or T2 comes first lexicographically depends on whether you choose to write mappings from right-to-left or vice versa; we avoid the whole problem by referring to the order of application rather than the textual order.)
There are two template parameters for this class:
ScalarT The type to be used for scalar numeric values. Either float or double.
NDimensions The number of dimensions of the vector space.
This class provides several methods for setting the matrix and vector defining the transform. To support the registration framework, the transform parameters can also be set as an Array<double> of size (NDimension + 1) * NDimension using method SetParameters(). The first (NDimension x NDimension) parameters defines the matrix in column-major order (where the column index) varies the fastest). The last NDimension parameters defines the translation in each dimensions.
This class also supports the specification of a center of rotation (center) and a translation that is applied with respect to that centered rotation. By default the center of rotation is set to the origin.
Definition at line 109 of file itkAffineTransform.h.
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 152 of file itkAffineTransform.h. |
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Standard covariant vector type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 147 of file itkAffineTransform.h. |
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Standard coordinate point type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 140 of file itkAffineTransform.h. |
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Standard vector type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 142 of file itkAffineTransform.h. |
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Standard vnl_vector type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 144 of file itkAffineTransform.h. |
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Standard inverse matrix type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 151 of file itkAffineTransform.h. |
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Jacobian Type Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 138 of file itkAffineTransform.h. |
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Standard matrix type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 150 of file itkAffineTransform.h. |
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 153 of file itkAffineTransform.h. |
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 149 of file itkAffineTransform.h. |
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 143 of file itkAffineTransform.h. |
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 145 of file itkAffineTransform.h. |
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Parameters Type Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 137 of file itkAffineTransform.h. |
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Standard scalar type for this class Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 139 of file itkAffineTransform.h. |
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Standard typedefs Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 114 of file itkAffineTransform.h. |
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Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. Definition at line 154 of file itkAffineTransform.h. |
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Construct an AffineTransform object This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. * |
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Construct an AffineTransform object This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. * |
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Construct an AffineTransform object This method constructs a new AffineTransform object and initializes the matrix and offset parts of the transformation to values specified by the caller. If the arguments are omitted, then the AffineTransform is initialized to an identity transformation in the appropriate number of dimensions. * |
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Destroy an AffineTransform object * |
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Back transform by an affine transformation This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown.
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Back transform by an affine transformation This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown.
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Back transform by an affine transformation This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown.
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Back transform by an affine transformation This method finds the point or vector that maps to a given point or vector under the affine transformation defined by self. If no such point exists, an exception is thrown.
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >. |
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Back transform a point by an affine transform This method finds the point that maps to a given point under the affine transformation defined by self. If no such point exists, an exception is thrown. The returned value is (a pointer to) a brand new point created with new.
Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >. |
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Run-time type information (and related methods). Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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Dimension of the domain space. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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Dimension of the domain space. Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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Dimension of the domain space. Reimplemented in itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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This method computes the distance from self to the identity transformation, using the same metric as the one-argument form of the Metric() method. * |
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Compute distance between two affine transformations This method computes a ``distance'' between two affine transformations. This distance is guaranteed to be a metric, but not any particular metric. (At the moment, the algorithm is to collect all the elements of the matrix and offset into a vector, and compute the euclidean (L2) norm of that vector. Some metric which could be used to estimate the distance between two points transformed by the affine transformation would be more useful, but I don't have time right now to work out the mathematical details.) |
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New macro for creation of through a Smart Pointer Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, itk::CenteredAffineTransform< TScalarType, NDimensions >, itk::FixedCenterOfRotationAffineTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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Print contents of an AffineTransform Reimplemented from itk::MatrixOffsetTransformBase< TScalarType, NDimensions, NDimensions >. Reimplemented in itk::AzimuthElevationToCartesianTransform< TScalarType, NDimensions >, and itk::ScalableAffineTransform< TScalarType, NDimensions >. |
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Compose affine transformation with an elementary rotation This method composes self with a rotation that affects two specified axes, replacing the current value of self. The rotation angle is in radians. The axis of rotation goes through the origin. The transformation is given by y[axis1] = cos(angle)*x[axis1] + sin(angle)*x[axis2] y[axis2] = -sin(angle)*x[axis1] + cos(angle)*x[axis2]. All coordinates other than axis1 and axis2 are unchanged; a rotation of pi/2 radians will carry +axis1 into +axis2. The rotation is precomposed with self if pre is true, and postcomposed otherwise. Note that the rotation is applied centered at the origin. |
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Compose 2D affine transformation with a rotation This method composes self, which must be a 2D affine transformation, with a clockwise rotation through a given angle in radians. The center of rotation is the origin. The rotation is precomposed with self if pre is true, and postcomposed otherwise. Note that the rotation is applied centered at the origin.
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Compose 3D affine transformation with a rotation This method composes self, which must be a 3D affine transformation, with a clockwise rotation around a specified axis. The rotation angle is in radians; the axis of rotation goes through the origin. The rotation is precomposed with self if pre is true, and postcomposed otherwise. Note that the rotation is applied centered at the origin.
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Compose affine transformation with a scaling This method modifies self to magnify the source by a given factor along each axis. If all factors are the same, or only a single factor is given, then the scaling is isotropic; otherwise it is anisotropic. If an odd number of factors are negative, then the parity of the image changes. If any of the factors is zero, then the transformation becomes a projection and is not invertible. The scaling is precomposed with self if pre is true, and postcomposed otherwise. Note that the scaling is applied centered at the origin. |
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Compose affine transformation with a scaling This method modifies self to magnify the source by a given factor along each axis. If all factors are the same, or only a single factor is given, then the scaling is isotropic; otherwise it is anisotropic. If an odd number of factors are negative, then the parity of the image changes. If any of the factors is zero, then the transformation becomes a projection and is not invertible. The scaling is precomposed with self if pre is true, and postcomposed otherwise. Note that the scaling is applied centered at the origin. |
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Compose affine transformation with a shear This method composes self with a shear transformation, replacing the original contents of self. The shear is precomposed with self if pre is true, and postcomposed otherwise. The transformation is given by y[axis1] = x[axis1] + coef*x[axis2] y[axis2] = x[axis2]. Note that the shear is applied centered at the origin. |
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Compose affine transformation with a translation This method modifies self to include a translation of the origin. The translation is precomposed with self if pre is true, and postcomposed otherwise. This updates Translation based on current center. |
1.3.5 written by Dimitri van Heesch,
© 1997-2000