maspack.matrix
Class RigidTransform2d

java.lang.Object
  maspack.matrix.MatrixObject
      maspack.matrix.AffineTransform2dObject
          maspack.matrix.RigidTransform2d

public class RigidTransform2d

extends AffineTransform2dObject

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   ]
 

Field Summary

Vector2d	p Translation vector associated with this transformation.
RotationMatrix2d	R Rotation matrix associated with this transformation.

Constructor Summary

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

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.AffineTransform2dObject

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

Methods inherited from class maspack.matrix.MatrixObject

determinant, epsilonEquals, equals, equals, frobeniusNorm, get, getColumn, getRow, infinityNorm, isFixedSize, oneNorm, scan, set, set, setColumn, setRow, setSize, toString, toString, toString

Methods inherited from class java.lang.Object

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

Field Detail

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 AffineTransform2dObject

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 AffineTransform2dObject

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)