maspack.matrix

Class AffineTransform3dBase

java.lang.Object

maspack.matrix.MatrixBase

maspack.matrix.DenseMatrixBase

maspack.matrix.AffineTransform3dBase

All Implemented Interfaces:

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

Direct Known Subclasses:

AffineTransform3d, RigidTransform3d, ScaledRigidTransform3d

public abstract class AffineTransform3dBase
extends DenseMatrixBase
implements VectorTransformer3d, java.io.Serializable

Base class for 4 x 4 matrices representing 3D affine transformations. A 3D affine transformation applied to a 3-vector v has the form
A v + b
In homogeneous coordinates, this is represented by a 4 x 4 matrix of the form

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

See Also:

Serialized Form

Nested Class Summary

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

Matrix.Partition, Matrix.WriteFormat

Field Summary

Fields inherited from interface maspack.matrix.Matrix

INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors

Constructor and Description
AffineTransform3dBase()

Method Summary

Modifier and Type	Method and Description
void	addTranslation(double tx, double ty, double tz) Sets the translation component of this affine transform.
void	addTranslation(Vector3d p) Sets the translation component of this affine transform.
AffineTransform3dBase	clone()
int	colSize() Returns the number of columns in this matrix (which is always 4).
abstract AffineTransform3dBase	copy() Creates and returns a copy of this transformer.
boolean	epsilonEquals(AffineTransform3dBase X, double epsilon) Returns true if the elements of this transformation equal those of transform X1within a prescribed tolerance epsilon.
boolean	equals(AffineTransform3dBase X) Returns true if the elements of this transformation exactly equal those of transform X1.
void	get(double[] values) Copies the elements of this matrix into an array of doubles.
double	get(int i, int j) Gets a single element of this matrix.
void	getColumn(int j, double[] values) Copies a column of this matrix into an array of doubles.
void	getColumn(int j, double[] values, int off) Copies a column of this matrix into an array of doubles, starting at a specified offset.
Matrix3dBase	getMatrix() Returns the matrix assiciated with this affine transform.
void	getMatrixComponents(RotationMatrix3d R, Vector3d s, Matrix3d X) Returns the shear, scaling, and rotational components of this AffineTransform.
Vector3d	getOffset() Returns the offset vector assiciated with this affine transform.
void	getRow(int i, double[] values) Copies a row of this matrix into an array of doubles.
void	getRow(int i, double[] values, int off) Copies a row of this matrix into an array of doubles, starting at a specified offset.
void	inverseTransformCovec(Vector3d nr, Vector3d n0) Applies an inverse transform to covector c0 and places the result in cr.
void	inverseTransformPnt(Vector3d pr, Vector3d p0) Applies an inverse transform to point p0 and places the result in pr.
void	inverseTransformVec(Vector3d vr, Vector3d v0) Applies an inverse transform to vector v0 and places the result in vr.
boolean	invert() Inverts this transform in place.
boolean	isAffine() Returns true if this transformer implements a linear affine transform.
boolean	isIdentity() Returns true if this transform equals the identity.
boolean	isRigid() Returns true if this transformer implements a linear rigid transform.
void	mul(RigidTransform3d X2)
void	mul(Vector4d vr) Multiplies the column vector vr by this transform and places the result back in vr.
void	mul(Vector4d vr, Vector4d v1) Multiplies the column vector v1 by this transform and places the result in vr.
void	mulInverse(RigidTransform3d T) Post-multiplies this transformation by the inverse of the rigid transformation T and places the result in this transformation.
boolean	mulInverse(Vector4d vr) Multiplies the column vector vr by the inverse of this transform and places the result back in vr.
boolean	mulInverse(Vector4d vr, Vector4d v1) Multiplies the column vector v1 by the inverse of this transform and places the result in vr.
void	mulInverseLeft(RigidTransform3d T1, AffineTransform3dBase X2) Multiplies the inverse of the rigid transformation T1 by the transformation X2 and places the result in this transformation.
void	mulInverseRight(AffineTransform3dBase X1, RigidTransform3d T2) Multiplies transformation X1 by the inverse of the rigid transformation T2 and places the result in this transformation.
int	rowSize() Returns the number of rows in this matrix (which is always 4).
void	set(AffineTransform3dBase A)
void	set(double[] vals) Sets the elements of this matrix from an array of doubles.
void	set(int i, int j, double value) Sets a single element of this matrix.
void	setColumn(int j, double[] values) Sets a column of this matrix from an array of doubles.
void	setIdentity() Sets the transformation to the identity.
abstract void	setRandom() Sets the elements of this matrix to uniformly distributed random values in the range -0.5 (inclusive) to 0.5 (exclusive).
void	setRotation(AxisAngle axisAng) Sets the matrix component of this affine transform to an explicit rotation.
void	setRotation(Quaternion quat) Sets the matrix component of this affine transform to an explicit rotation.
void	setRotation(RotationMatrix3d R) Sets the matrix component of this affine transform to an explicit rotation.
void	setRow(int i, double[] values) Set a row of this matrix from an array of doubles.
void	setTranslation(double tx, double ty, double tz) Sets the translation component of this affine transform.
void	setTranslation(Vector3d p) Sets the translation component of this affine transform.
void	transformCovec(Vector3d nr, Vector3d n0) Transforms a covector c0 and places the result in cr.
void	transformPnt(Vector3d pr, Vector3d p0) Transforms point p0 and places the result in pr.
void	transformVec(Vector3d vr, Vector3d v0) Transforms vector v0 and places the result in vr.

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.VectorTransformer3d

toString

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

Constructor Detail

AffineTransform3dBase

public AffineTransform3dBase()

Method Detail

getMatrix

public Matrix3dBase getMatrix()

Returns the matrix assiciated with this affine transform.

Returns:

matrix

getOffset

public Vector3d getOffset()

Returns the offset vector assiciated with this affine transform.

Returns:

offset vector

colSize

public int colSize()

Returns the number of columns in this matrix (which is always 4).

Specified by:

colSize in interface LinearTransformNd

Specified by:

colSize in interface Matrix

Specified by:

colSize in class MatrixBase

Returns:

4

rowSize

public int rowSize()

Returns the number of rows in this matrix (which is always 4).

Specified by:

rowSize in interface LinearTransformNd

Specified by:

rowSize in interface Matrix

Specified by:

rowSize in class MatrixBase

Returns:

4

get

public double get(int i,
                  int j)

Gets a single element of this matrix.

Specified by:

get in interface Matrix

Specified by:

get in class MatrixBase

Parameters:

i - element row index

j - element column index

Returns:

element value

get

public void get(double[] values)

Copies the elements of this matrix into an array of doubles. The elements are stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Specified by:

get in interface Matrix

Overrides:

get in class MatrixBase

Parameters:

values - array into which values are copied

getColumn

public void getColumn(int j,
                      double[] values)

Copies a column of this matrix into an array of doubles.

Specified by:

getColumn in interface Matrix

Overrides:

getColumn in class MatrixBase

Parameters:

j - column index

values - array into which the column is copied

getColumn

public void getColumn(int j,
                      double[] values,
                      int off)

Copies a column of this matrix into an array of doubles, starting at a specified offset.

Specified by:

getColumn in interface Matrix

Overrides:

getColumn in class MatrixBase

Parameters:

j - column index

values - array into which the column is copied

off - offset in values where copying should begin

getRow

public void getRow(int i,
                   double[] values)

Copies a row of this matrix into an array of doubles.

Specified by:

getRow in interface Matrix

Overrides:

getRow in class MatrixBase

Parameters:

i - row index

values - array into which the row is copied

getRow

public void getRow(int i,
                   double[] values,
                   int off)

Copies a row of this matrix into an array of doubles, starting at a specified offset.

Specified by:

getRow in interface Matrix

Overrides:

getRow in class MatrixBase

Parameters:

i - row index

values - array into which the row is copied

off - offset in values where copying should begin

set

public void set(AffineTransform3dBase A)

set

public void set(int i,
                int j,
                double value)

Sets a single element of this matrix.

Specified by:

set in interface DenseMatrix

Specified by:

set in class DenseMatrixBase

Parameters:

i - element row index

j - element column index

value - element value

set

public void set(double[] vals)

Sets the elements of this matrix from an array of doubles. The elements in the array should be stored using row-major order, so that element (i,j) is stored at location i*colSize()+j.

Specified by:

set in interface DenseMatrix

Overrides:

set in class DenseMatrixBase

Parameters:

vals - array from which values are copied

setColumn

public void setColumn(int j,
                      double[] values)

Sets a column of this matrix from an array of doubles.

Specified by:

setColumn in interface DenseMatrix

Overrides:

setColumn in class DenseMatrixBase

Parameters:

j - column index

values - array from which column values are copied

setRow

public void setRow(int i,
                   double[] values)

Set a row of this matrix from an array of doubles.

Specified by:

setRow in interface DenseMatrix

Overrides:

setRow in class DenseMatrixBase

Parameters:

i - row index

values - array from which the row is copied

setTranslation

public void setTranslation(Vector3d p)

Sets the translation component of this affine transform.

Parameters:

p - translation vector

addTranslation

public void addTranslation(Vector3d p)

Sets the translation component of this affine transform.

Parameters:

p - translation vector

setTranslation

public void setTranslation(double tx,
                           double ty,
                           double tz)

Sets the translation component of this affine transform.

Parameters:

tx - x-component of translation

ty - y-component of translation

tz - z-component of translation

addTranslation

public void addTranslation(double tx,
                           double ty,
                           double tz)

Sets the translation component of this affine transform.

Parameters:

tx - x-component of translation

ty - y-component of translation

tz - z-component of translation

setRotation

public void setRotation(AxisAngle axisAng)

Sets the matrix component of this affine transform to an explicit rotation.

Parameters:

axisAng - axis-angle describing the rotation

setRotation

public void setRotation(Quaternion quat)

Sets the matrix component of this affine transform to an explicit rotation.

Parameters:

quat - quaternion describing the rotation

setRotation

public void setRotation(RotationMatrix3d R)

Sets the matrix component of this affine transform to an explicit rotation.

Parameters:

R - rotation matrix

setIdentity

public void setIdentity()

Sets the transformation to the identity.

mulInverse

public void mulInverse(RigidTransform3d T)

Post-multiplies this transformation by the inverse of the rigid transformation T and places the result in this transformation.

Parameters:

T - right-hand rigid transformation

mulInverseRight

public void mulInverseRight(AffineTransform3dBase X1,
                            RigidTransform3d T2)

Multiplies transformation X1 by the inverse of the rigid transformation T2 and places the result in this transformation.

Parameters:

X1 - left-hand transformation

T2 - right-hand rigid transformation

mulInverseLeft

public void mulInverseLeft(RigidTransform3d T1,
                           AffineTransform3dBase X2)

Multiplies the inverse of the rigid transformation T1 by the transformation X2 and places the result in this transformation.

Parameters:

T1 - left-hand rigid transformation

X2 - right-hand transformation

mul

public void mul(Vector4d vr,
                Vector4d v1)

Multiplies the column vector v1 by this transform and places the result in vr.

Parameters:

vr - result vector

v1 - vector to multiply

mul

public void mul(Vector4d vr)

Multiplies the column vector vr by this transform and places the result back in vr.

Parameters:

vr - vector to multiply (in place)

mul

public void mul(RigidTransform3d X2)

mulInverse

public boolean mulInverse(Vector4d vr,
                          Vector4d v1)

Multiplies the column vector v1 by the inverse of this transform and places the result in vr.

Parameters:

vr - result vector

v1 - vector to multiply

Returns:

false if this transform is singular

mulInverse

public boolean mulInverse(Vector4d vr)

Multiplies the column vector vr by the inverse of this transform and places the result back in vr.

Parameters:

vr - vector to multiply (in place)

Returns:

false if this transform is singular

invert

public boolean invert()

Inverts this transform in place.

Returns:

false if this transform is singular

epsilonEquals

public boolean epsilonEquals(AffineTransform3dBase X,
                             double epsilon)

Returns true if the elements of this transformation equal those of transform X1within a prescribed tolerance epsilon.

Parameters:

X - transform to compare with

epsilon - comparison tolerance

Returns:

false if the transforms are not equal within the specified tolerance

equals

public boolean equals(AffineTransform3dBase X)

Returns true if the elements of this transformation exactly equal those of transform X1.

Parameters:

X - transform to compare with

Returns:

false if the transforms are not equal

getMatrixComponents

public void getMatrixComponents(RotationMatrix3d R,
                                Vector3d s,
                                Matrix3d X)

Returns the shear, scaling, and rotational components of this AffineTransform. This is done by computing the SVD of the transform:

     M = U S V'
 

The rotation is then set to U, the scale factors are set to the diagonal elements of S, and the shear is set to U'.

Parameters:

R - returns the rotation matrix

s - returns the three scaling factors

X - returns the shearing transform

transformPnt

public void transformPnt(Vector3d pr,
                         Vector3d p0)

Transforms point p0 and places the result in pr.

Specified by:

transformPnt in interface VectorTransformer3d

Parameters:

pr - returns the transformed point

p0 - point to be transformed

transformVec

public void transformVec(Vector3d vr,
                         Vector3d v0)

Transforms vector v0 and places the result in vr.

Specified by:

transformVec in interface VectorTransformer3d

Parameters:

vr - returns the transformed vector

v0 - vector to be transformed

transformCovec

public void transformCovec(Vector3d nr,
                           Vector3d n0)

Transforms a covector c0 and places the result in cr. If a vector is transformed linearly according to

   vr = A v0,
 

then the covector will be transformed according to

         -1 T 
   cr = A     c0,
 

Normal vectors and gradients are generally transformed as covectors. In the case of normals, the application will need to normalize the result if this transformation is not rigid.

Specified by:

transformCovec in interface VectorTransformer3d

Parameters:

nr - returns the transformed covector

n0 - normal to be transformed

inverseTransformPnt

public void inverseTransformPnt(Vector3d pr,
                                Vector3d p0)

Applies an inverse transform to point p0 and places the result in pr.

Specified by:

inverseTransformPnt in interface VectorTransformer3d

Parameters:

pr - returns the transformed point

p0 - point to be transformed

inverseTransformVec

public void inverseTransformVec(Vector3d vr,
                                Vector3d v0)

Applies an inverse transform to vector v0 and places the result in vr.

Specified by:

inverseTransformVec in interface VectorTransformer3d

Parameters:

vr - returns the transformed vector

v0 - vector to be transformed

inverseTransformCovec

public void inverseTransformCovec(Vector3d nr,
                                  Vector3d n0)

Applies an inverse transform to covector c0 and places the result in cr. See VectorTransformer3d.transformCovec(maspack.matrix.Vector3d, maspack.matrix.Vector3d) for more details about covector transformation.

Specified by:

inverseTransformCovec in interface VectorTransformer3d

Parameters:

nr - returns the transformed normal

n0 - normal to be transformed

isAffine

public boolean isAffine()

Returns true if this transformer implements a linear affine transform.

Specified by:

isAffine in interface VectorTransformer3d

isRigid

public boolean isRigid()

Returns true if this transformer implements a linear rigid transform.

Specified by:

isRigid in interface VectorTransformer3d

isIdentity

public boolean isIdentity()

Returns true if this transform equals the identity.

Returns:

true if this transform equals the identity

setRandom

public abstract 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 abstract AffineTransform3dBase copy()

Description copied from interface: VectorTransformer3d

Creates and returns a copy of this transformer.

Specified by:

copy in interface VectorTransformer3d

Returns:

deep copy of transform

clone

public AffineTransform3dBase clone()
                            throws java.lang.CloneNotSupportedException

Overrides:

clone in class java.lang.Object

Throws:

java.lang.CloneNotSupportedException