RigidTransform2d (Artisynth API documentation)

java.lang.Object
- maspack.matrix.MatrixBase
- - maspack.matrix.DenseMatrixBase
  - - maspack.matrix.AffineTransform2dBase
    - - maspack.matrix.RigidTransform2d

All Implemented Interfaces:

DenseMatrix, LinearTransformNd, Matrix
```
public class RigidTransform2d
extends AffineTransform2dBase
```
A specialized 3 x 3 matrix that implements a two-dimensional rigid body transformation in homogeneous coordinates.
A rigid body transformation is used to transform a point from one spatial coordinate frame into another. If x0 and x1 denote the point in the orginal frame 0 and target frame 1, respectively, then the transformation is computed according to
```
 x1 = R x0 + p
 
```
where R is a 2 x 2 rotation matrix and p is a translation vector. In homogenous coordinates, this operation can be represented as
```
 [ x1 ]   [ R  p ] [ x0 ]
 [    ] = [      ] [    ]
 [  1 ]   [ 0  1 ] [  1 ]
 
```
The components p and R of the transformation represent the position and orientation of frame 0 with respect to frame 1. In particular, the translation vector p gives the origin position, while the columns of R give the directions of the axes.
If X01 is a transformation from frame 0 to frame 1, and X12 is a transformation from frame 1 to frame 2, then the transformation from frame 0 to frame 2 is given by the product
```
 X02 = X12 X01
 
```
In this way, a transformation can be created by multiplying a series of sub-transformations.
If X01 is a transformation from frame 0 to frame 1, then the inverse transformation X10 is a transformation from frame 1 to frame 0, and is given by
```
       [  T    T   ]
       [ R   -R  p ]
 X10 = [           ]
       [ 0     1   ]
 
```

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
`static RigidTransform2d`	`IDENTITY` Global identity transform.
`Vector2d`	`p` Translation vector associated with this transformation.
`RotationMatrix2d`	`R` Rotation matrix associated with this transformation.

Fields inherited from interface maspack.matrix.Matrix
INDEFINITE, POSITIVE_DEFINITE, SPD, SYMMETRIC

Constructor Summary

Constructors
Constructor and Description
`RigidTransform2d()` Creates a new transformation initialized to the identity.
`RigidTransform2d(double x, double y, double ang)` Creates a new transformation with the specified translation values and rotation angle
`RigidTransform2d(RigidTransform2d X)` Creates a new transformation which is a copy of an existing one.
`RigidTransform2d(Vector2d p, double ang)` Creates a new transformation with the specified translation vector and rotation angle
`RigidTransform2d(Vector2d p, RotationMatrix2d R)` Creates a new transformation with the specified translation vector and rotation matrix.

Method Summary

All Methods Instance Methods Concrete Methods
Modifier and Type	Method and Description
`RigidTransform2d`	`copy()`
`void`	`fit(java.util.ArrayList<Point2d> p, java.util.ArrayList<Point2d> q)`
`void`	`fit(java.util.ArrayList<Point2d> p, java.util.ArrayList<Point2d> q, boolean doScaling)` Sets this rigid 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(RigidTransform2d X)` Inverts transform X and places the result in this transform.
`void`	`mul(RigidTransform2d X)` Post-multiplies this transformation by another and places the result in this transformation.
`void`	`mul(RigidTransform2d X1, RigidTransform2d X2)` Multiplies transformation X1 by X2 and places the result in this transformation.
`void`	`mulInverse(RigidTransform2d X)` Post-multiplies this transformation by the inverse of transformation X and places the result in this transformation.
`boolean`	`mulInverse(Vector3d vr, Vector3d v1)` Multiplies the column vector v1 by the inverse of this transform and places the result in vr.
`void`	`mulInverseBoth(RigidTransform2d X1, RigidTransform2d X2)` Multiplies the inverse of transformation X1 by the inverse of transformation X2 and places the result in this transformation.
`void`	`mulInverseLeft(RigidTransform2d X1, RigidTransform2d X2)` Multiplies the inverse of transformation X1 by transformation X2 and places the result in this transformation.
`void`	`mulInverseRight(RigidTransform2d X1, RigidTransform2d X2)` Multiplies transformation X1 by the inverse of transformation X2 and places the result in this transformation.

Methods inherited from class maspack.matrix.AffineTransform2dBase
colSize, epsilonEquals, equals, get, get, getColumn, getColumn, getMatrix, getOffset, getRow, getRow, mul, mul, mulInverse, rowSize, set, 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, maxNorm, mul, mul, mul, mulAdd, mulAdd, mulAdd, mulTranspose, mulTranspose, mulTranspose, mulTransposeAdd, mulTransposeAdd, mulTransposeAdd, numNonZeroVals, numNonZeroVals, oneNorm, scan, setCRSValues, setDefaultFormat, setSize, toString, toString, toString, trace, 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 RigidTransform2d IDENTITY
```
    Global identity transform. Should not be modified.
  - R
```
public final RotationMatrix2d R
```
    Rotation matrix associated with this transformation.
  - p
```
public final Vector2d p
```
    Translation vector associated with this transformation.
- Constructor Detail
  - RigidTransform2d
```
public RigidTransform2d()
```
    Creates a new transformation initialized to the identity.
  - RigidTransform2d
```
public RigidTransform2d(Vector2d p,
                        RotationMatrix2d R)
```
    Creates a new transformation with the specified translation vector and rotation matrix.
    
    Parameters:
    
    p - translation vector
    
    R - rotation matrix
  - RigidTransform2d
```
public RigidTransform2d(Vector2d p,
                        double ang)
```
    Creates a new transformation with the specified translation vector and rotation angle
    
    Parameters:
    
    p - translation vector
    
    ang - rotation angle (radians)
  - RigidTransform2d
```
public RigidTransform2d(double x,
                        double y,
                        double ang)
```
    Creates a new transformation with the specified translation values and rotation angle
    
    Parameters:
    
    x - translation x component
    
    y - translation y component
    
    ang - rotation angle (radians)
  - RigidTransform2d
```
public RigidTransform2d(RigidTransform2d X)
```
    Creates a new transformation which is a copy of an existing one.
    
    Parameters:
    
    X - transform to copy
- Method Detail
  - mul
```
public void mul(RigidTransform2d X)
```
    Post-multiplies this transformation by another and places the result in this transformation.
    
    Parameters:
    
    X - transformation to multiply by
  - mul
```
public void mul(RigidTransform2d X1,
                RigidTransform2d X2)
```
    Multiplies transformation X1 by X2 and places the result in this transformation.
    
    Parameters:
    
    X1 - first transformation
    
    X2 - second transformation
  - mulInverse
```
public void mulInverse(RigidTransform2d X)
```
    Post-multiplies this transformation by the inverse of transformation X and places the result in this transformation.
    
    Parameters:
    
    X - right-hand transformation
  - mulInverseRight
```
public void mulInverseRight(RigidTransform2d X1,
                            RigidTransform2d 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
  - mulInverseLeft
```
public void mulInverseLeft(RigidTransform2d X1,
                           RigidTransform2d 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
  - mulInverseBoth
```
public void mulInverseBoth(RigidTransform2d X1,
                           RigidTransform2d 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
  - mulInverse
```
public boolean mulInverse(Vector3d vr,
                          Vector3d v1)
```
    Multiplies the column vector v1 by the inverse of this transform and places the result in vr.
    
    Overrides:
    
    mulInverse in class AffineTransform2dBase
    
    Parameters:
    
    vr - result vector
    
    v1 - vector to multiply
    
    Returns:
    
    false if this transform is singular
  - invert
```
public boolean invert()
```
    Inverts this transform in place.
    
    Overrides:
    
    invert in class AffineTransform2dBase
    
    Returns:
    
    true (transform is never singular)
  - invert
```
public boolean invert(RigidTransform2d X)
```
    Inverts transform X and places the result in this transform.
    
    Parameters:
    
    X - transform to invert
    
    Returns:
    
    true (transform is never singular)
  - fit
```
public void fit(java.util.ArrayList<Point2d> p,
                java.util.ArrayList<Point2d> q,
                boolean doScaling)
         throws ImproperSizeException
```
    Sets this rigid 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
    
    doScaling - flag to apply uniform scaling in addition to rigid transform
    
    Throws:
    
    ImproperSizeException
  - fit
```
public void fit(java.util.ArrayList<Point2d> p,
                java.util.ArrayList<Point2d> q)
         throws ImproperSizeException
```
    Throws:
    
    ImproperSizeException
  - copy
```
public RigidTransform2d copy()
```
    Specified by:
    
    copy in class AffineTransform2dBase
    
    Returns:
    
    a deep copy of the transform

Class RigidTransform2d

Nested Class Summary

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

Field Summary

Fields inherited from interface maspack.matrix.Matrix

Constructor Summary

Method Summary

Methods inherited from class maspack.matrix.AffineTransform2dBase

Methods inherited from class maspack.matrix.DenseMatrixBase

Methods inherited from class maspack.matrix.MatrixBase

Methods inherited from class java.lang.Object

Methods inherited from interface maspack.matrix.Matrix

Field Detail

IDENTITY

R

p

Constructor Detail

RigidTransform2d

RigidTransform2d

RigidTransform2d

RigidTransform2d

RigidTransform2d

Method Detail

mul

mul

mulInverse

mulInverseRight

mulInverseLeft

mulInverseBoth

mulInverse

invert

invert

fit

fit

copy