maspack.matrix

Class AffineTransform3d

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.AffineTransform3dBase

maspack.matrix.AffineTransform3d

All Implemented Interfaces:

java.io.Serializable, DenseMatrix, LinearTransformNd, Matrix, VectorTransformer3d

public class AffineTransform3d
extends AffineTransform3dBase

A 4 x 4 matrix which implements general 3D affine transformations. The matrix has the specific form

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

where A is a 3 x 3 matrix and p is a 3-vector. In homogeneous coordinates, this implements an affine transform of the form
A v + b

In this class, the fields A and p are exposed, and users can manipulate them as desired. This allows us to minimize the number of methds in the AffineTransform3d class itself.

See Also:

Serialized Form

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
Matrix3d	A Matrix component.
static AffineTransform3d	IDENTITY Global identity transform.
static int	MATRIX_3X4_STRING Specifies a string representation of this transformation as a 3 x 4 matrix (i.e., with the 4th row ommitted).
static int	MATRIX_4X4_STRING Specifies a string representation of this transformation as a 4 x 4 matrix.
Vector3d	p Vector component.

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
AffineTransform3d() Creates an AffineTransform3d and initializes it to the identity.
AffineTransform3d(AffineTransform3dBase X)
AffineTransform3d(double[] m) Constructs using an array representing the 3x4 matrix [A|p] given in row-major format
AffineTransform3d(double m00, double m01, double m02, double px, double m10, double m11, double m12, double py, double m20, double m21, double m22, double pz)
AffineTransform3d(Matrix3d A, Vector3d p) Creates an AffineTransform3d and initializes its components to the specified values.

Method Summary

Modifier and Type	Method and Description
void	applyScaling(double sx, double sy, double sz) Scales the columns of A by the specified amounts.
AffineTransform3d	copy() Creates and returns a copy of this transformer.
static AffineTransform3d	createScaling(double s) Creates an AffineTransform3d which performs uniform scaling along all axes.
static AffineTransform3d	createScaling(double sx, double sy, double sz) Creates an AffineTransform3d which performs scaling along the x, y, and z axes.
void	factorA(RotationMatrix3d R, Vector3d scale, Vector3d shear) Factors the A matrix of this transformation into rotation, scale, and shear components, so that
void	fit(java.util.ArrayList<Point3d> p, java.util.ArrayList<Point3d> q) Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q
Vector3d	fitOrthogonal(java.util.ArrayList<Point3d> p, java.util.ArrayList<Point3d> q) Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q, where X has orthogonal columns, corresponding to a rigid transform with three scale factors (one for each dimension)
Vector3d	fitOrthogonal(java.util.ArrayList<Point3d> p, java.util.ArrayList<Point3d> q, double threshold) Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q, where X has orthogonal columns, corresponding to a rigid transform with three scale factors (one for each dimension).
void	fitRigid(java.util.ArrayList<Point3d> p, java.util.ArrayList<Point3d> q, boolean scale) Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q, where X is a rigid transformation with a single scale factor
boolean	invert() Inverts this transform in place.
boolean	invert(AffineTransform3dBase X) Inverts transform X and places the result in this transform.
void	mul(AffineTransform3dBase X) Multiplies this transformation transformation X and places the result in this transformation.
void	mul(AffineTransform3dBase X1, AffineTransform3dBase X2) Multiplies transformation X1 by transformation X2 and places the result in this transformation.
boolean	mulInverse(AffineTransform3dBase X) Multiplies this transformation by the inverse of transformation X and places the result in this transformation.
boolean	mulInverseBoth(AffineTransform3dBase X1, AffineTransform3dBase X2) Multiplies the inverse of transformation X1 by the inverse of transformation X2 and places the result in this transformation.
boolean	mulInverseLeft(AffineTransform3dBase X1, AffineTransform3dBase X2) Multiplies the inverse of transformation X1 by transformation X2 and places the result in this transformation.
boolean	mulInverseRight(AffineTransform3dBase X1, AffineTransform3dBase X2) Multiplies transformation X1 by the inverse of transformation X2 and places the result in this transformation.
void	set(RigidTransform3d X) Sets this affine transform to the rigid body transform described by X.
void	setA(RotationMatrix3d R, Vector3d scale, Vector3d shear) Sets the A matrix of this transformation from rotation, scale, and shear components, so that
void	setRandom() Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).
void	setScaling(double sx, double sy, double sz) Sets A to diagonal scaling matrix.
java.lang.String	toString() Returns a string representation of this transformation as a 4 x 4 matrix.
java.lang.String	toString(NumberFormat numberFmt, int outputCode) Returns a specified string representation of this transformation, with each number formatted according to the a supplied numeric format.
java.lang.String	toString(java.lang.String numberFmtStr) Returns a string representation of this transformation as a 4 x 4 matrix, with each number formatted according to a supplied numeric format.
java.lang.String	toString(java.lang.String numberFmtStr, int outputCode) Returns a specified string representation of this transformation, with each number formatted according to the a supplied numeric format.

Methods inherited from class maspack.matrix.AffineTransform3dBase

addTranslation, addTranslation, clone, colSize, epsilonEquals, equals, get, get, getColumn, getColumn, getMatrix, getMatrixComponents, getOffset, getRow, getRow, inverseTransformCovec, inverseTransformPnt, inverseTransformVec, isAffine, isIdentity, isRigid, mul, mul, mul, mulInverse, mulInverse, mulInverse, mulInverseLeft, mulInverseRight, rowSize, set, set, set, setColumn, setIdentity, setRotation, setRotation, setRotation, setRow, setTranslation, setTranslation, transformCovec, transformPnt, transformVec

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, 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, trace, write, write, write

Field Detail

IDENTITY

public static final AffineTransform3d IDENTITY

Global identity transform. Should not be modified.

MATRIX_3X4_STRING

public static final int MATRIX_3X4_STRING

Specifies a string representation of this transformation as a 3 x 4 matrix (i.e., with the 4th row ommitted).

See Also:

Constant Field Values

MATRIX_4X4_STRING

public static final int MATRIX_4X4_STRING

Specifies a string representation of this transformation as a 4 x 4 matrix.

See Also:

Constant Field Values

A

public final Matrix3d A

Matrix component.

p

public final Vector3d p

Vector component.

Constructor Detail

AffineTransform3d

public AffineTransform3d()

Creates an AffineTransform3d and initializes it to the identity.

AffineTransform3d

public AffineTransform3d(Matrix3d A,
                         Vector3d p)

Creates an AffineTransform3d and initializes its components to the specified values.

Parameters:

A - value for the A matrix

p - value for the p vector

AffineTransform3d

public AffineTransform3d(AffineTransform3dBase X)

AffineTransform3d

public AffineTransform3d(double m00,
                         double m01,
                         double m02,
                         double px,
                         double m10,
                         double m11,
                         double m12,
                         double py,
                         double m20,
                         double m21,
                         double m22,
                         double pz)

AffineTransform3d

public AffineTransform3d(double[] m)

Constructs using an array representing the 3x4 matrix [A|p] given in row-major format

Method Detail

mul

public void mul(AffineTransform3dBase X)

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

Parameters:

X - right-hand transformation

mul

public void mul(AffineTransform3dBase X1,
                AffineTransform3dBase 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(AffineTransform3dBase 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(AffineTransform3dBase X1,
                               AffineTransform3dBase 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(AffineTransform3dBase X1,
                              AffineTransform3dBase 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(AffineTransform3dBase X1,
                              AffineTransform3dBase 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 AffineTransform3dBase

Returns:

false if this transform is singular

invert

public boolean invert(AffineTransform3dBase 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(RigidTransform3d X)

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

Parameters:

X - rigid body transform to copy

setScaling

public void setScaling(double sx,
                       double sy,
                       double sz)

Sets A to diagonal scaling matrix.

Parameters:

sx - x scale factor

sy - y scale factor

sz - z scale factor

applyScaling

public void applyScaling(double sx,
                         double sy,
                         double sz)

Scales the columns of A by the specified amounts. This is equivalent to post-multiplying A by a diagonal matrix. Note that the resulting scaling effect will be in addition to any previous scaling effect.

Parameters:

sx - x scale factor

sy - y scale factor

sz - z scale factor

factorA

public void factorA(RotationMatrix3d R,
                    Vector3d scale,
                    Vector3d shear)

Factors the A matrix of this transformation into rotation, scale, and shear components, so that

 A = R S X
 

where R is a right-handed rotation matrix, S is a diagonal scaling matrix, and X is a shear matrix of the form

     [ 1   xy  xz ]
 X = [ 0   1   yz ]
     [ 0   0   1  ]
 

Parameters:

R - if non-null, returns the rotation matrix

scale - if non-null, returns the diagonal components of S

shear - if non-null, returns the components xy, xz, yz of X

setA

public void setA(RotationMatrix3d R,
                 Vector3d scale,
                 Vector3d shear)

Sets the A matrix of this transformation from rotation, scale, and shear components, so that

 A = R S X
 

where R is a right-handed rotation matrix, S is a diagonal scaling matrix, and X is a shear matrix of the form

     [ 1  xy  xz ]
 X = [ 0   1  yz ]
     [ 0   0  1  ]
 

Parameters:

R - the rotation matrix

scale - diagonal components of S

shear - components xy, xz, yz of X

createScaling

public static AffineTransform3d createScaling(double sx,
                                              double sy,
                                              double sz)

Creates an AffineTransform3d which performs scaling along the x, y, and z axes.

Parameters:

sx - x scale factor

sy - y scale factor

sz - z scale factor

createScaling

public static AffineTransform3d createScaling(double s)

Creates an AffineTransform3d which performs uniform scaling along all axes.

Parameters:

s - scale factor

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).

Specified by:

setRandom in class AffineTransform3dBase

copy

public AffineTransform3d copy()

Description copied from interface: VectorTransformer3d

Creates and returns a copy of this transformer.

Specified by:

copy in interface VectorTransformer3d

Specified by:

copy in class AffineTransform3dBase

Returns:

deep copy of transform

fit

public void fit(java.util.ArrayList<Point3d> p,
                java.util.ArrayList<Point3d> 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 3d points

q - set of input 3d points

Throws:

ImproperSizeException

fitRigid

public void fitRigid(java.util.ArrayList<Point3d> p,
                     java.util.ArrayList<Point3d> q,
                     boolean scale)
              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, where X is a rigid transformation with a single scale factor

Parameters:

p - set of target 3d points

q - set of input 3d points

scale - allow scaling

Throws:

ImproperSizeException

fitOrthogonal

public Vector3d fitOrthogonal(java.util.ArrayList<Point3d> p,
                              java.util.ArrayList<Point3d> q,
                              double threshold)

Sets this affine transform to one that provides the best fit of q to p in the least-squares sense: p ~ X q, where X has orthogonal columns, corresponding to a rigid transform with three scale factors (one for each dimension). Uses an iterative procedure, stops when the scale factors change less than a given threshold

Parameters:

p - set of target 3d points

q - set of input 3d points

threshold - algorithm stops when ||s_{i} - s_{i-1}||/||s_{i-1}|| < threshold

Returns:

3-vector containing the scale factors

fitOrthogonal

public Vector3d fitOrthogonal(java.util.ArrayList<Point3d> p,
                              java.util.ArrayList<Point3d> 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, where X has orthogonal columns, corresponding to a rigid transform with three scale factors (one for each dimension)

Parameters:

p - set of target 3d points

q - set of input 3d points

Returns:

a 3-vector containing the scale factors

Throws:

ImproperSizeException

toString

public java.lang.String toString()

Returns a string representation of this transformation as a 4 x 4 matrix.

Overrides:

toString in class MatrixBase

Returns:

String representation of this matrix

See Also:

MatrixBase.toString(String)

toString

public java.lang.String toString(java.lang.String numberFmtStr)

Returns a string representation of this transformation as a 4 x 4 matrix, with each number formatted according to a supplied numeric format.

Specified by:

toString in interface Matrix

Specified by:

toString in interface VectorTransformer3d

Overrides:

toString in class MatrixBase

Parameters:

numberFmtStr - numeric format string (see NumberFormat)

Returns:

String representation of this vector

See Also:

NumberFormat

toString

public java.lang.String toString(java.lang.String numberFmtStr,
                                 int outputCode)

Returns a specified string representation of this transformation, with each number formatted according to the a supplied numeric format.

Parameters:

numberFmtStr - numeric format string (see NumberFormat)

outputCode - desired representation, which should be either MATRIX_4X4_STRING, or MATRIX_3X4_STRING

toString

public java.lang.String toString(NumberFormat numberFmt,
                                 int outputCode)

Returns a specified string representation of this transformation, with each number formatted according to the a supplied numeric format.

Parameters:

numberFmt - numeric format

outputCode - desired representation, which should be either MATRIX_4X4_STRING, or MATRIX_3X4_STRING