RigidTransform2D

java.lang.Object
- vona.math.RigidTransform2D

```
public class RigidTransform2D
extends java.lang.Object
```
A rigid 2D real double-precision transform.

This class is intended to be mutable but to enforce that the represented transform is always rigid. The fields x and y give the translation, and may be modified freely. The rotation is internally represented three different ways for performance: sine s, cosine c, and an un-normalized CCW rotation angle in radians t. Keeping these consistent with each other means that the rotation can only be read and written through the methods setRotation(double) and getRotation(), respectively.

This class is designed primarily for speed of most operations. Arguments are not checked, but the only invalid arguments would be null pointers. Synchronization is not provided. A little memory (two extra doubles) are sacrificed relative to a minimal representation, and the setRotation(double) method is relatively slow, as it must call Math.cos() and Math.sin(). All other operations perform only simple algebra, though slightly more bookeeping is required for the multiple representation of rotation.

Points are transform(java.awt.geom.Point2D.Double)ed in the usual way: first they are rotated about the origin of their original coordinate system, and then the translation vector (x, y) is added.

Copyright (C) 2004 Marsette A. Vona, III

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.

Author:

Marsette (Marty) A. Vona, III

Field Summary

Fields
Modifier and Type	Field and Description
`protected double`	`c` Cosine of the rotation angle `t`.
`private static java.lang.String`	`cvsid` CVS id.
`static double`	`DEFAULT_RANDOM_TRANSLATION_MAGNITUDE` Default random transformation translation magnitude.
`protected double`	`s` Sine of the rotation angle `t`.
`protected double`	`t` The CCW rotation angle in radians.
`double`	`x` The x component of translation.
`double`	`y` The y component of translation.

Constructor Summary

Constructors
Constructor and Description
`RigidTransform2D()` Create a new rigid transform initialized to identity.
`RigidTransform2D(double t)` Create a new rigid transform initialized to a given rotation and no translation.
`RigidTransform2D(double x, double y)` Create a new rigid transform initialized to a given translation and no rotation.
`RigidTransform2D(double x, double y, double t)` Create a new rigid transform initialized to a given translation and rotation.
`RigidTransform2D(RigidTransform2D o)` Create a new rigid transform initialized from another.

Method Summary

Methods
Modifier and Type	Method and Description
`RigidTransform2D`	`append(RigidTransform2D o)` `this = o*this`
`boolean`	`closeToIdentity()` Covers `closeToIdentity(double)` but uses default epsilon of `VonaMath.epsilonEquals(double, double)`.
`boolean`	`closeToIdentity(double epsilon)` Check whether this transform is within epsilon of an identity transform.
`RigidTransform2D`	`copyFrom(RigidTransform2D o)` `this = o`
`RigidTransform2D`	`dup()` Clone.
`protected void`	`formatField(double value, java.text.NumberFormat nf, int fieldWidth, java.lang.StringBuffer buf)` Format a field for `matrixToString(NumberFormat, int)`.
`double`	`getRotation()` Get the rotation of this transform.
`RigidTransform2D`	`invert()` `this = this'`
`static void`	`main(java.lang.String[] argv)` Test driver.
`java.lang.String`	`matrixToString(int fieldWidth)` Covers `matrixToString(NumberFormat, int)`, uses no NumberFormat.
`java.lang.String`	`matrixToString(java.text.NumberFormat nf, int fieldWidth)` Convert to a matrix as a multi-line string.
`RigidTransform2D`	`prepend(RigidTransform2D o)` `this = this*o`
`RigidTransform2D`	`reset()` Set the identity transform.
`static boolean`	`selfTest(int trials, double maxTranslationMagnitude)` Run a randomized self-test.
`RigidTransform2D`	`setIdentity()` Convenience cover of `reset()`.
`RigidTransform2D`	`setRandom()` Covers `setRandom(double)` but uses [-`DEFAULT_RANDOM_TRANSLATION_MAGNITUDE`,-`DEFAULT_RANDOM_TRANSLATION_MAGNITUDE`] for translation range.
`RigidTransform2D`	`setRandom(double maxTranslationMagnitude)` Covers `setRandom(double, double)` but uses [-Math.PI,Math.PI] for rotation range.
`RigidTransform2D`	`setRandom(double maxTranslationMagnitude, double maxRotationMagnitude)` Covers `setRandom(double, double, double)` but uses same range for x and y.
`RigidTransform2D`	`setRandom(double maxXMagnitude, double maxYMagnitude, double maxRotationMagnitude)` Covers `setRandom(double, double, double, double, double, double)` but uses symmetric ranges.
`RigidTransform2D`	`setRandom(double minX, double maxX, double minY, double maxY, double minRotation, double maxRotation)` Set to a random transformation.
`RigidTransform2D`	`setRotation(double t)` Set the rotation of this transform.
`java.lang.String`	`toString()` Covers `toString(NumberFormat)`, uses no NumberFormat.
`java.lang.String`	`toString(java.text.NumberFormat nf)` Convert to a human-readable string.
`double[]`	`transform(double[] p)` Same function as `transform(Point2D.Double)` but represents point as a double array {x, y}.
`float[]`	`transform(float[] p)` Same function as `transform(Point2D.Double)` but represents point as a float array {x, y}.
`java.awt.geom.Point2D.Double`	`transform(java.awt.geom.Point2D.Double p)` Transform a point.
`RigidTransform2D`	`unappend(RigidTransform2D o)` `this = o^(-1)*this`
`RigidTransform2D`	`unprepend(RigidTransform2D o)` `this = this*o^(-1)`

Methods inherited from class java.lang.Object
clone, equals, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

- Field Detail
  - cvsid
```
private static final java.lang.String cvsid
```
    CVS id.
    
    See Also:
    Constant Field Values
  - DEFAULT_RANDOM_TRANSLATION_MAGNITUDE
```
public static final double DEFAULT_RANDOM_TRANSLATION_MAGNITUDE
```
    Default random transformation translation magnitude.
    
    See Also:
    Constant Field Values
  - c
```
protected double c
```
    Cosine of the rotation angle t.
  - s
```
protected double s
```
    Sine of the rotation angle t.
  - t
```
protected double t
```
    The CCW rotation angle in radians.
  - x
```
public double x
```
    The x component of translation.
  - y
```
public double y
```
    The y component of translation.
- Constructor Detail
  - RigidTransform2D
```
public RigidTransform2D()
```
    Create a new rigid transform initialized to identity.
  - RigidTransform2D
```
public RigidTransform2D(RigidTransform2D o)
```
    Create a new rigid transform initialized from another.
    
    Parameters:
    o - the transform to copy, not null
  - RigidTransform2D
```
public RigidTransform2D(double t)
```
    Create a new rigid transform initialized to a given rotation and no translation.
    
    Parameters:
    t - the CCW rotation in radians
  - RigidTransform2D
```
public RigidTransform2D(double x,
                double y)
```
    Create a new rigid transform initialized to a given translation and no rotation.
    
    Parameters:
    x - the x component of the translation
    y - the y component of the translation
  - RigidTransform2D
```
public RigidTransform2D(double x,
                double y,
                double t)
```
    Create a new rigid transform initialized to a given translation and rotation.
    
    Parameters:
    x - the x component of the translation
    y - the y component of the translation
    t - the CCW rotation in radians
- Method Detail
  - setRotation
```
public RigidTransform2D setRotation(double t)
```
    Set the rotation of this transform.
    
    This is the only relatively slow method in this class, as it must call Math.cos() and Math.sin().
    
    Parameters:
    t - the CCW rotation in radians
    
    Returns:
    a reference to this
  - getRotation
```
public double getRotation()
```
    Get the rotation of this transform.
    
    Returns:
    the CCW rotation in radians
  - append
```
public RigidTransform2D append(RigidTransform2D o)
```
    this = o*this
    
    Parameters:
    o - the other transform
    
    Returns:
    a reference to this
  - unappend
```
public RigidTransform2D unappend(RigidTransform2D o)
```
    this = o^(-1)*this
    
    Parameters:
    o - the other transform
    
    Returns:
    a reference to this
  - prepend
```
public RigidTransform2D prepend(RigidTransform2D o)
```
    this = this*o
    
    Parameters:
    o - the other transform
    
    Returns:
    a reference to this
  - unprepend
```
public RigidTransform2D unprepend(RigidTransform2D o)
```
    this = this*o^(-1)
    
    Parameters:
    o - the other transform
    
    Returns:
    a reference to this
  - invert
```
public RigidTransform2D invert()
```
    this = this'
    
    Returns:
    a reference to this
  - reset
```
public RigidTransform2D reset()
```
    Set the identity transform.
    
    Returns:
    a reference to this
  - setIdentity
```
public RigidTransform2D setIdentity()
```
    Convenience cover of reset().
  - copyFrom
```
public RigidTransform2D copyFrom(RigidTransform2D o)
```
    this = o
    
    Parameters:
    o - the other transform
    
    Returns:
    a reference to this
  - dup
```
public RigidTransform2D dup()
```
    Clone.
    
    Returns:
    an independent copy of this
  - transform
```
public java.awt.geom.Point2D.Double transform(java.awt.geom.Point2D.Double p)
```
    Transform a point.
    
    The point is transformed in the usual way: first it is rotated about the origin of its original coordinate system, and then the translation vector (x, y) is added.
    
    This corresponds to a left-multiply by the transform matrix if p is taken to be a homogenous column vector (x, y, 1)'.
    
    Parameters:
    p - the point to transform
    
    Returns:
    a reference to p
  - transform
```
public double[] transform(double[] p)
```
    Same function as transform(Point2D.Double) but represents point as a double array {x, y}.
  - transform
```
public float[] transform(float[] p)
```
    Same function as transform(Point2D.Double) but represents point as a float array {x, y}.
  - setRandom
```
public RigidTransform2D setRandom(double minX,
                         double maxX,
                         double minY,
                         double maxY,
                         double minRotation,
                         double maxRotation)
```
    Set to a random transformation.
    
    Parameters:
    minX - the minimum x translation
    maxX - the maximum x translation
    minY - the minimum y translation
    maxY - the maximum y translation
    minRotation - the minimum rotation in radians
    maxRotation - the maximum rotation in radians
  - setRandom
```
public RigidTransform2D setRandom(double maxXMagnitude,
                         double maxYMagnitude,
                         double maxRotationMagnitude)
```
    Covers setRandom(double, double, double, double, double, double) but uses symmetric ranges.
  - setRandom
```
public RigidTransform2D setRandom(double maxTranslationMagnitude,
                         double maxRotationMagnitude)
```
    Covers setRandom(double, double, double) but uses same range for x and y.
  - setRandom
```
public RigidTransform2D setRandom(double maxTranslationMagnitude)
```
    Covers setRandom(double, double) but uses [-Math.PI,Math.PI] for rotation range.
  - setRandom
```
public RigidTransform2D setRandom()
```
    Covers setRandom(double) but uses [-DEFAULT_RANDOM_TRANSLATION_MAGNITUDE,-DEFAULT_RANDOM_TRANSLATION_MAGNITUDE] for translation range.
    for rotation range.
  - closeToIdentity
```
public boolean closeToIdentity(double epsilon)
```
    Check whether this transform is within epsilon of an identity transform.
    
    Parameters:
    epsilon - the fudge factor
  - closeToIdentity
```
public boolean closeToIdentity()
```
    Covers closeToIdentity(double) but uses default epsilon of VonaMath.epsilonEquals(double, double).
  - selfTest
```
public static boolean selfTest(int trials,
               double maxTranslationMagnitude)
```
    Run a randomized self-test.
    
    Parameters:
    trials - number of trials
    maxTranslationMagnitude - the maximum translation magnitude for the random transforms
    
    Returns:
    true iff all trials pass
  - main
```
public static void main(java.lang.String[] argv)
```
    Test driver.
    
    Command line:
```
 RigidTransform2D [numTrials [maxTranslationMagnitude]]

 
```
  - toString
```
public java.lang.String toString(java.text.NumberFormat nf)
```
    Convert to a human-readable string.
    
    Parameters:
    nf - optional NumberFormat, may be null
  - toString
```
public java.lang.String toString()
```
    Covers toString(NumberFormat), uses no NumberFormat.
    
    Overrides:
    
    toString in class java.lang.Object
  - matrixToString
```
public java.lang.String matrixToString(java.text.NumberFormat nf,
                              int fieldWidth)
```
    Convert to a matrix as a multi-line string.
    
    Parameters:
    nf - optional NumberFormat, may be null
    fieldWidth - matrix column width
  - matrixToString
```
public java.lang.String matrixToString(int fieldWidth)
```
    Covers matrixToString(NumberFormat, int), uses no NumberFormat.
  - formatField
```
protected void formatField(double value,
               java.text.NumberFormat nf,
               int fieldWidth,
               java.lang.StringBuffer buf)
```
    Format a field for matrixToString(NumberFormat, int).
    
    Parameters:
    value - the field value
    nf - the optional NumberFormat, may be null
    fieldWidth - the field width
    buf - output is written here

Class RigidTransform2D

Field Summary

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Field Detail

cvsid

DEFAULT_RANDOM_TRANSLATION_MAGNITUDE

c

s

t

x

y

Constructor Detail

RigidTransform2D

RigidTransform2D

RigidTransform2D

RigidTransform2D

RigidTransform2D

Method Detail

setRotation

getRotation

append

unappend

prepend

unprepend

invert

reset

setIdentity

copyFrom

dup

transform

transform

transform

setRandom

setRandom

setRandom

setRandom

setRandom

closeToIdentity

closeToIdentity

selfTest

main

toString

toString

matrixToString

matrixToString

formatField