maspack.matrix

Class AffineTransform2d

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.AffineTransform2dBase

maspack.matrix.AffineTransform2d

All Implemented Interfaces:

DenseMatrix, LinearTransformNd, Matrix

public class AffineTransform2d
extends AffineTransform2dBase

A 3 x 3 matrix which implements general 2D affine transformations. The matrix has the specific form

     [  A   p  ]
 M = [         ]
     [  0   1  ]
 

where A is a 2 x 2 matrix and p is a 2-vector. In homogeneous coordinates, this implements an affine transform of the form
A v + b

Nested Class Summary

Nested classes/interfaces inherited from interface maspack.matrix.Matrix

Matrix.Partition, Matrix.WriteFormat

Field Summary

Fields

Modifier and Type	Field and Description
Matrix2d	A Matrix component.
static AffineTransform2d	IDENTITY Global identity transform.
Vector2d	p Vector component.

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
AffineTransform2d() Creates an AffineTransform2d and initializes it to the identity.
AffineTransform2d(AffineTransform2dBase T) Creates an AffineTransform2d and initializes it from an existing on
AffineTransform2d(Vector2d p, Matrix2d A) Creates an AffineTransform2d and initializes its components to the specified values.

Method Summary

Modifier and Type	Method and Description
AffineTransform2d	copy()
void	fit(java.util.ArrayList<Point2d> p, java.util.ArrayList<Point2d> q) Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q
boolean	invert() Inverts this transform in place.
boolean	invert(AffineTransform2dBase X) Inverts transform X and places the result in this transform.
void	mul(AffineTransform2dBase X) Multiplies this transformation transformation X and places the result in this transformation.
void	mul(AffineTransform2dBase X1, AffineTransform2dBase X2) Multiplies transformation X1 by transformation X2 and places the result in this transformation.
boolean	mulInverse(AffineTransform2dBase X) Multiplies this transformation by the inverse of transformation X and places the result in this transformation.
boolean	mulInverseBoth(AffineTransform2dBase X1, AffineTransform2dBase X2) Multiplies the inverse of transformation X1 by the inverse of transformation X2 and places the result in this transformation.
boolean	mulInverseLeft(AffineTransform2dBase X1, AffineTransform2dBase X2) Multiplies the inverse of transformation X1 by transformation X2 and places the result in this transformation.
boolean	mulInverseRight(AffineTransform2dBase X1, AffineTransform2dBase X2) Multiplies transformation X1 by the inverse of transformation X2 and places the result in this transformation.
void	set(RigidTransform2d X) Sets this affine transform to the rigid body transform described by X.
void	setRandom() Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).

Methods inherited from class maspack.matrix.AffineTransform2dBase

colSize, epsilonEquals, equals, get, get, getColumn, getColumn, getMatrix, getOffset, getRow, getRow, mul, mul, mulInverse, mulInverse, rowSize, set, set, setColumn, setIdentity, setRow

Methods inherited from class maspack.matrix.DenseMatrixBase

add, checkConsistency, set, set, set, set, setCCSValues, setColumn, setCRSValues, setRow, setSubMatrix

Methods inherited from class maspack.matrix.MatrixBase

containsNaN, determinant, epsilonEquals, equals, frobeniusNorm, frobeniusNormSquared, get, getCCSIndices, getCCSIndices, getCCSIndices, getCCSValues, getCCSValues, getCCSValues, getColumn, getCRSIndices, getCRSIndices, getCRSIndices, getCRSValues, getCRSValues, getCRSValues, getDefaultFormat, getRow, getSize, getSubMatrix, hasNaN, idString, infinityNorm, isFixedSize, isSymmetric, isWritable, maxNorm, mul, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, oneNorm, scan, scan, setCRSValues, setDefaultFormat, setSize, toString, toString, toString, trace, write, write, write, write, write, write, write, writeToFile

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface maspack.matrix.Matrix

determinant, epsilonEquals, equals, frobeniusNorm, frobeniusNormSquared, getCCSIndices, getCCSIndices, getCCSIndices, getCCSValues, getCCSValues, getCCSValues, getColumn, getCRSIndices, getCRSIndices, getCRSIndices, getCRSValues, getCRSValues, getCRSValues, getRow, getSize, getSubMatrix, infinityNorm, isFixedSize, isSymmetric, maxNorm, mul, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, oneNorm, scan, setSize, toString, toString, trace, write, write, write

Field Detail

IDENTITY

public static final AffineTransform2d IDENTITY

Global identity transform. Should not be modified.

A

public final Matrix2d A

Matrix component.

p

public final Vector2d p

Vector component.

Constructor Detail

AffineTransform2d

public AffineTransform2d()

Creates an AffineTransform2d and initializes it to the identity.

AffineTransform2d

public AffineTransform2d(Vector2d p,
                         Matrix2d A)

Creates an AffineTransform2d and initializes its components to the specified values.

Parameters:

A - value for the A matrix

p - value for the p vector

AffineTransform2d

public AffineTransform2d(AffineTransform2dBase T)

Creates an AffineTransform2d and initializes it from an existing on

Parameters:

T - initializing transform

Method Detail

mul

public void mul(AffineTransform2dBase X)

Multiplies this transformation transformation X and places the result in this transformation.

Parameters:

X - right-hand transformation

mul

public void mul(AffineTransform2dBase X1,
                AffineTransform2dBase X2)

Multiplies transformation X1 by transformation X2 and places the result in this transformation.

Parameters:

X1 - left-hand transformation

X2 - right-hand transformation

mulInverse

public boolean mulInverse(AffineTransform2dBase X)

Multiplies this transformation by the inverse of transformation X and places the result in this transformation.

Parameters:

X - right-hand transformation

Returns:

false if X is singular

mulInverseRight

public boolean mulInverseRight(AffineTransform2dBase X1,
                               AffineTransform2dBase X2)

Multiplies transformation X1 by the inverse of transformation X2 and places the result in this transformation.

Parameters:

X1 - left-hand transformation

X2 - right-hand transformation

Returns:

false if X2 is singular

mulInverseLeft

public boolean mulInverseLeft(AffineTransform2dBase X1,
                              AffineTransform2dBase X2)

Multiplies the inverse of transformation X1 by transformation X2 and places the result in this transformation.

Parameters:

X1 - left-hand transformation

X2 - right-hand transformation

Returns:

false if X1 is singular

mulInverseBoth

public boolean mulInverseBoth(AffineTransform2dBase X1,
                              AffineTransform2dBase X2)

Multiplies the inverse of transformation X1 by the inverse of transformation X2 and places the result in this transformation.

Parameters:

X1 - left-hand transformation

X2 - right-hand transformation

Returns:

false if either X1 or X2 is singular

invert

public boolean invert()

Inverts this transform in place.

Overrides:

invert in class AffineTransform2dBase

Returns:

false if this transform is singular

invert

public boolean invert(AffineTransform2dBase X)

Inverts transform X and places the result in this transform.

Parameters:

X - transform to invert

Returns:

false if transform X is singular

set

public void set(RigidTransform2d X)

Sets this affine transform to the rigid body transform described by X.

Overrides:

set in class AffineTransform2dBase

Parameters:

X - rigid body transform to copy

fit

public void fit(java.util.ArrayList<Point2d> p,
                java.util.ArrayList<Point2d> q)
         throws ImproperSizeException

Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q

Parameters:

p - set of target 2d points

q - set of input 2d points

Throws:

ImproperSizeException

setRandom

public void setRandom()

Description copied from class: DenseMatrixBase

Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).

Overrides:

setRandom in class DenseMatrixBase

copy

public AffineTransform2d copy()

Specified by:

copy in class AffineTransform2dBase

Returns:

a deep copy of the transform