de.lmu.ifi.dbs.elki.math.linearalgebra

Class AffineTransformation

java.lang.Object

de.lmu.ifi.dbs.elki.math.linearalgebra.AffineTransformation

public class AffineTransformation
extends Object

Affine transformations implemented using homogeneous coordinates. The use of homogeneous coordinates allows the combination of multiple affine transformations (rotations, translations, scaling) into a single matrix operation (of dimensionality dim+1), and also the construction of an inverse transformation.

Field Summary

Fields

Modifier and Type	Field and Description
private int	dim the dimensionality of the transformation
private Matrix	inv the inverse transformation
private Matrix	trans The transformation matrix of dim+1 x dim+1 for homogeneous coordinates

Constructor Summary

Constructors

Constructor and Description
AffineTransformation(int dim) Constructor for an identity transformation.
AffineTransformation(int dim, Matrix trans, Matrix inv) Trivial constructor with all fields, mostly for cloning

Method Summary

Methods

Modifier and Type	Method and Description
void	addAxisReflection(int axis) Add a reflection along the given axis.
void	addMatrix(Matrix m) Add a matrix operation to the matrix.
void	addRotation(int axis1, int axis2, double angle) Convenience function to apply a rotation in 2 dimensions.
void	addScaling(double scale) Simple linear (symmetric) scaling.
void	addTranslation(Vector v) Add a translation operation to the matrix
Vector	apply(Vector v) Apply the transformation onto a vector
Vector	applyInverse(Vector v) Apply the inverse transformation onto a vector
Vector	applyRelative(Vector v) Apply the transformation onto a vector
Vector	applyRelativeInverse(Vector v) Apply the inverse transformation onto a vector
AffineTransformation	clone() Return a clone of the affine transformation
int	getDimensionality() Query dimensionality of the transformation.
Matrix	getInverse() Get a copy of the inverse matrix
Matrix	getTransformation() Get a copy of the transformation matrix
Vector	homogeneRelativeVector(Vector v) Transform a relative vector into homogeneous coordinates.
Vector	homogeneVector(Vector v) Transform an absolute vector into homogeneous coordinates.
static AffineTransformation	reorderAxesTransformation(int dim, int[] axes) Generate a transformation that reorders axes in the given way.
Vector	unhomogeneRelativeVector(Vector v) Project an homogeneous vector back into the original space.
Vector	unhomogeneVector(Vector v) Project an homogeneous vector back into the original space.
private void	updateInverse() Compute the inverse transformation matrix

Methods inherited from class java.lang.Object

equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Field Detail

dim

private int dim

the dimensionality of the transformation

trans

private Matrix trans

The transformation matrix of dim+1 x dim+1 for homogeneous coordinates

inv

private Matrix inv

the inverse transformation

Constructor Detail

AffineTransformation

public AffineTransformation(int dim)

Constructor for an identity transformation.

Parameters:

dim - dimensionality

AffineTransformation

public AffineTransformation(int dim,
                    Matrix trans,
                    Matrix inv)

Trivial constructor with all fields, mostly for cloning

Parameters:

dim - dimensionality

trans - transformation matrix

inv - inverse matrix

Method Detail

reorderAxesTransformation

public static AffineTransformation reorderAxesTransformation(int dim,
                                             int[] axes)

Generate a transformation that reorders axes in the given way. The list of axes to be used should not contain duplicates, or the resulting matrix will not be invertible. It does not have to be complete however, in particular an empty list will result in the identity transform: unmentioned axes will be appended in their original order.

Parameters:

dim - Dimensionality of vector space (resulting Matrix will be dim+1 x dim+1)

axes - (Partial) list of axes

Returns:

new transformation to do the requested reordering

clone

public AffineTransformation clone()

Return a clone of the affine transformation

Overrides:

clone in class Object

Returns:

cloned affine transformation

getDimensionality

public int getDimensionality()

Query dimensionality of the transformation.

Returns:

dimensionality

addTranslation

public void addTranslation(Vector v)

Add a translation operation to the matrix

Parameters:

v - translation vector

addMatrix

public void addMatrix(Matrix m)

Add a matrix operation to the matrix. Be careful to use only invertible matrices if you want an invertible affine transformation.

Parameters:

m - matrix (should be invertible)

addRotation

public void addRotation(int axis1,
               int axis2,
               double angle)

Convenience function to apply a rotation in 2 dimensions.

Parameters:

axis1 - first dimension

axis2 - second dimension

angle - rotation angle in radians.

addAxisReflection

public void addAxisReflection(int axis)

Add a reflection along the given axis.

Parameters:

axis - Axis number to do the reflection at.

addScaling

public void addScaling(double scale)

Simple linear (symmetric) scaling.

Parameters:

scale - Scaling factor

getTransformation

public Matrix getTransformation()

Get a copy of the transformation matrix

Returns:

copy of the transformation matrix

getInverse

public Matrix getInverse()

Get a copy of the inverse matrix

Returns:

a copy of the inverse transformation matrix

updateInverse

private void updateInverse()

Compute the inverse transformation matrix

homogeneVector

public Vector homogeneVector(Vector v)

Transform an absolute vector into homogeneous coordinates.

Parameters:

v - initial vector

Returns:

vector of dim+1, with new column having the value 1.0

homogeneRelativeVector

public Vector homogeneRelativeVector(Vector v)

Transform a relative vector into homogeneous coordinates.

Parameters:

v - initial vector

Returns:

vector of dim+1, with new column having the value 0.0

unhomogeneVector

public Vector unhomogeneVector(Vector v)

Project an homogeneous vector back into the original space.

Parameters:

v - Matrix of 1 x dim+1 containing the homogeneous vector

Returns:

vector of dimension dim

unhomogeneRelativeVector

public Vector unhomogeneRelativeVector(Vector v)

Project an homogeneous vector back into the original space.

Parameters:

v - Matrix of 1 x dim+1 containing the homogeneous vector

Returns:

vector of dimension dim

apply

public Vector apply(Vector v)

Apply the transformation onto a vector

Parameters:

v - vector of dimensionality dim

Returns:

transformed vector of dimensionality dim

applyInverse

public Vector applyInverse(Vector v)

Apply the inverse transformation onto a vector

Parameters:

v - vector of dimensionality dim

Returns:

transformed vector of dimensionality dim

applyRelative

public Vector applyRelative(Vector v)

Apply the transformation onto a vector

Parameters:

v - vector of dimensionality dim

Returns:

transformed vector of dimensionality dim

applyRelativeInverse

public Vector applyRelativeInverse(Vector v)

Apply the inverse transformation onto a vector

Parameters:

v - vector of dimensionality dim

Returns:

transformed vector of dimensionality dim