AffineTransform2D

Documentation of 'math.geom2d.AffineTransform2D' Java class AffineTransform2D

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java.lang.Object
- math.geom2d.AffineTransform2D

All Implemented Interfaces:

java.lang.Cloneable, GeometricObject2D, Bijection2D, Transform2D
```
public class AffineTransform2D
extends java.lang.Object
implements Bijection2D, GeometricObject2D, java.lang.Cloneable
```
Base class for generic affine transforms in the plane. They include rotations, translations, shears, similarities, and combinations of these. Such transformations can be constructed by using coefficients specification, or by creating specialized instances, by using static methods.

Constructor Summary

Constructors
Constructor and Description
`AffineTransform2D()` Creates a new AffineTransform2D, initialized with Identity.
`AffineTransform2D(java.awt.geom.AffineTransform transform)` Creates a new transform from a java AWT transform.
`AffineTransform2D(AffineTransform2D trans)` Deprecated. not necessary to clone immutable objects (0.11.2)
`AffineTransform2D(double[] coefs)` Creates a new Affine Transform by directly specifying the coefficients, in the order m00, m01, m02, m10, m11, m12 (different order of java.awt.geom.AffineTransform).
`AffineTransform2D(double xx, double yx, double tx, double xy, double yy, double ty)`

Method Summary

All Methods Static Methods Instance Methods Concrete Methods Deprecated Methods
Modifier and Type	Method and Description
`double[][]`	`affineMatrix()` Returns the 3x3 square matrix representing the transform.
`boolean`	`almostEquals(GeometricObject2D obj, double eps)` Checks if the two objects are similar up to a given threshold value.
`java.awt.geom.AffineTransform`	`asAwtTransform()` Returns this transform as an instance of java AWT AffineTransform.
`AffineTransform2D`	`chain(AffineTransform2D that)` Returns the affine transform created by applying first this affine transform, then the affine transform given by `that`.
`AffineTransform2D`	`clone()` Deprecated. immutable objects do not need to be cloned (0.11.2)
`double[]`	`coefficients()` Returns coefficients of the transform in a linear array of 6 double.
`AffineTransform2D`	`concatenate(AffineTransform2D that)` Returns the affine transform created by applying first the affine transform given by `that`, then this affine transform.
`static AffineTransform2D`	`create(AffineTransform2D trans)` Creates a new affine transform by copying coefficients.
`static AffineTransform2D`	`create(double[] coefs)` Creates an affine transform defined by an array of coefficients.
`static AffineTransform2D`	`create(double xx, double yx, double tx, double xy, double yy, double ty)`
`static AffineTransform2D`	`createGlideReflection(LinearShape2D line, double distance)` Create a glide reflection, composed of a reflection by the given line, and a translation in the direction of the line by a distance given by second parameter.
`static AffineTransform2D`	`createHomothecy(Point2D center, double k)` Deprecated. replaced by scaling (0.11.1)
`static AffineTransform2D`	`createIdentity()`
`static AffineTransform2D`	`createLineReflection(LinearShape2D line)` Creates a reflection by the given line.
`static AffineTransform2D`	`createPointReflection(Point2D center)` Returns a center reflection around a point.
`static AffineTransform2D`	`createQuadrantRotation(double x0, double y0, int numQuadrant)` Creates a rotation composed of the given number of rotations by 90 degrees around the point given by (x0,y0).
`static AffineTransform2D`	`createQuadrantRotation(int numQuadrant)` Creates a rotation composed of the given number of rotations by 90 degrees around the origin.
`static AffineTransform2D`	`createQuadrantRotation(Point2D center, int numQuadrant)` Creates a rotation composed of the given number of rotations by 90 degrees around the given point.
`static AffineTransform2D`	`createRotation(double angle)` Creates a rotation around the origin, with angle in radians.
`static AffineTransform2D`	`createRotation(double cx, double cy, double angle)` Creates a rotation around the specified point, with angle in radians.
`static AffineTransform2D`	`createRotation(Point2D center, double angle)` Creates a rotation around the specified point, with angle in radians.
`static AffineTransform2D`	`createScaling(double sx, double sy)` Creates a scaling by the given coefficients, centered on the origin.
`static AffineTransform2D`	`createScaling(Point2D center, double sx, double sy)` Creates a scaling by the given coefficients, centered on the point given by (x0,y0).
`static AffineTransform2D`	`createShear(double shx, double shy)` Creates a Shear transform, using the classical Java notation.
`static AffineTransform2D`	`createTransform(java.awt.geom.AffineTransform transform)` Creates a new transform from a java AWT transform.
`static AffineTransform2D`	`createTranslation(double dx, double dy)` Return a translation by the given vector.
`static AffineTransform2D`	`createTranslation(Vector2D vect)` Return a translation by the given vector.
`boolean`	`equals(java.lang.Object obj)`
`AffineTransform2D`	`invert()` Returns the inverse transform.
`boolean`	`isDirect()` Tests if this affine transform is direct, i.e.
`static boolean`	`isDirect(AffineTransform2D trans)` Checks if the transform is direct, i.e.
`boolean`	`isIdentity()` Tests is this affine transform is equal to the identity transform.
`static boolean`	`isIdentity(AffineTransform2D trans)` Checks if the given transform is the identity transform.
`boolean`	`isIsometry()` Tests if this affine transform is an isometry, i.e.
`static boolean`	`isIsometry(AffineTransform2D trans)` Checks if the transform is an isometry, i.e.
`boolean`	`isMotion()` Tests if this affine transform is a motion, i.e.
`static boolean`	`isMotion(AffineTransform2D trans)` Checks if the transform is a motion, i.e.
`boolean`	`isSimilarity()` Tests if this affine transform is a similarity.
`static boolean`	`isSimilarity(AffineTransform2D trans)` Checks if the transform is an similarity, i.e.
`AffineTransform2D`	`preConcatenate(AffineTransform2D that)` Return the affine transform created by applying first this affine transform, then the affine transform given by `that`.
`java.lang.String`	`toString()` Displays the coefficients of the transform, row by row.
`Point2D`	`transform(Point2D p)` Computes the coordinates of the transformed point.
`Point2D[]`	`transform(Point2D[] src, Point2D[] dst)` Transforms an array of points, and returns the transformed points.

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

- Constructor Detail
  - AffineTransform2D
```
public AffineTransform2D()
```
    Creates a new AffineTransform2D, initialized with Identity.
  - AffineTransform2D
```
@Deprecated
public AffineTransform2D(AffineTransform2D trans)
```
    Deprecated. not necessary to clone immutable objects (0.11.2)
    
    Constructor by copy of an existing transform
  - AffineTransform2D
```
public AffineTransform2D(java.awt.geom.AffineTransform transform)
```
    Creates a new transform from a java AWT transform.
  - AffineTransform2D
```
public AffineTransform2D(double[] coefs)
```
    Creates a new Affine Transform by directly specifying the coefficients, in the order m00, m01, m02, m10, m11, m12 (different order of java.awt.geom.AffineTransform).
  - AffineTransform2D
```
public AffineTransform2D(double xx,
                         double yx,
                         double tx,
                         double xy,
                         double yy,
                         double ty)
```
- Method Detail
  - createIdentity
```
public static AffineTransform2D createIdentity()
```
    Since:
    
    0.8.1
  - create
```
public static AffineTransform2D create(AffineTransform2D trans)
```
    Creates a new affine transform by copying coefficients.
    
    Since:
    
    0.8.1
  - create
```
public static AffineTransform2D create(double[] coefs)
```
    Creates an affine transform defined by an array of coefficients. The input array must have either 4 or 6 coefficients.
    
    Since:
    
    0.8.1
  - create
```
public static AffineTransform2D create(double xx,
                                       double yx,
                                       double tx,
                                       double xy,
                                       double yy,
                                       double ty)
```
    Since:
    
    0.8.1
  - createGlideReflection
```
public static AffineTransform2D createGlideReflection(LinearShape2D line,
                                                      double distance)
```
    Create a glide reflection, composed of a reflection by the given line, and a translation in the direction of the line by a distance given by second parameter.
  - createHomothecy
```
@Deprecated
public static AffineTransform2D createHomothecy(Point2D center,
                                                            double k)
```
    Deprecated. replaced by scaling (0.11.1)
  - createLineReflection
```
public static AffineTransform2D createLineReflection(LinearShape2D line)
```
    Creates a reflection by the given line. The resulting transform is indirect.
  - createPointReflection
```
public static AffineTransform2D createPointReflection(Point2D center)
```
    Returns a center reflection around a point. The resulting transform is equivalent to a rotation by 180 around this point.
    
    Parameters:
    
    center - the center of the reflection
    
    Returns:
    
    an instance of AffineTransform2D representing a point reflection
  - createQuadrantRotation
```
public static AffineTransform2D createQuadrantRotation(int numQuadrant)
```
    Creates a rotation composed of the given number of rotations by 90 degrees around the origin.
  - createQuadrantRotation
```
public static AffineTransform2D createQuadrantRotation(Point2D center,
                                                       int numQuadrant)
```
    Creates a rotation composed of the given number of rotations by 90 degrees around the given point.
  - createQuadrantRotation
```
public static AffineTransform2D createQuadrantRotation(double x0,
                                                       double y0,
                                                       int numQuadrant)
```
    Creates a rotation composed of the given number of rotations by 90 degrees around the point given by (x0,y0).
  - createRotation
```
public static AffineTransform2D createRotation(double angle)
```
    Creates a rotation around the origin, with angle in radians.
  - createRotation
```
public static AffineTransform2D createRotation(Point2D center,
                                               double angle)
```
    Creates a rotation around the specified point, with angle in radians.
  - createRotation
```
public static AffineTransform2D createRotation(double cx,
                                               double cy,
                                               double angle)
```
    Creates a rotation around the specified point, with angle in radians. If the angular distance of the angle with a multiple of PI/2 is lower than the threshold Shape2D.ACCURACY, the method assumes equality.
  - createScaling
```
public static AffineTransform2D createScaling(double sx,
                                              double sy)
```
    Creates a scaling by the given coefficients, centered on the origin.
  - createScaling
```
public static AffineTransform2D createScaling(Point2D center,
                                              double sx,
                                              double sy)
```
    Creates a scaling by the given coefficients, centered on the point given by (x0,y0).
  - createShear
```
public static AffineTransform2D createShear(double shx,
                                            double shy)
```
    Creates a Shear transform, using the classical Java notation.
    
    Parameters:
    
    shx - shear in x-axis
    
    shy - shear in y-axis
    
    Returns:
    
    a shear transform
  - createTransform
```
public static AffineTransform2D createTransform(java.awt.geom.AffineTransform transform)
```
    Creates a new transform from a java AWT transform.
  - createTranslation
```
public static AffineTransform2D createTranslation(Vector2D vect)
```
    Return a translation by the given vector.
  - createTranslation
```
public static AffineTransform2D createTranslation(double dx,
                                                  double dy)
```
    Return a translation by the given vector.
  - isIdentity
```
public static boolean isIdentity(AffineTransform2D trans)
```
    Checks if the given transform is the identity transform.
  - isDirect
```
public static boolean isDirect(AffineTransform2D trans)
```
    Checks if the transform is direct, i.e. it preserves the orientation of transformed shapes.
    
    Returns:
    
    true if transform is direct.
  - isIsometry
```
public static boolean isIsometry(AffineTransform2D trans)
```
    Checks if the transform is an isometry, i.e. a compound of translation, rotation and reflection. Isometry keeps area of shapes unchanged, but can change orientation (direct or indirect).
    
    Returns:
    
    true in case of isometry.
  - isMotion
```
public static boolean isMotion(AffineTransform2D trans)
```
    Checks if the transform is a motion, i.e. a compound of translations and rotations. Motions are special case of isometries that keep orientation (directed or undirected) of shapes unchanged.
    
    Returns:
    
    true in case of motion.
  - isSimilarity
```
public static boolean isSimilarity(AffineTransform2D trans)
```
    Checks if the transform is an similarity, i.e. transformation which keeps unchanged the global shape, up to a scaling factor.
    
    Returns:
    
    true in case of similarity.
  - coefficients
```
public double[] coefficients()
```
    Returns coefficients of the transform in a linear array of 6 double.
  - affineMatrix
```
public double[][] affineMatrix()
```
    Returns the 3x3 square matrix representing the transform.
    
    Returns:
    
    the 3x3 affine transform representing the matrix
  - asAwtTransform
```
public java.awt.geom.AffineTransform asAwtTransform()
```
    Returns this transform as an instance of java AWT AffineTransform.
  - concatenate
```
public AffineTransform2D concatenate(AffineTransform2D that)
```
    Returns the affine transform created by applying first the affine transform given by that, then this affine transform. This is the equivalent method of the 'concatenate' method in java.awt.geom.AffineTransform.
    
    Parameters:
    
    that - the transform to apply first
    
    Returns:
    
    the composition this * that
    
    Since:
    
    0.6.3
  - chain
```
public AffineTransform2D chain(AffineTransform2D that)
```
    Returns the affine transform created by applying first this affine transform, then the affine transform given by that. This the equivalent method of the 'preConcatenate' method in java.awt.geom.AffineTransform. shape = shape.transform(T1.chain(T2).chain(T3)); is equivalent to the sequence: shape = shape.transform(T1); shape = shape.transform(T2); shape = shape.transform(T3);
    Parameters:
    
    that - the transform to apply in a second step
    
    Returns:
    
    the composition that * this
    
    Since:
    
    0.6.3
  - preConcatenate
```
public AffineTransform2D preConcatenate(AffineTransform2D that)
```
    Return the affine transform created by applying first this affine transform, then the affine transform given by that. This the equivalent method of the 'preConcatenate' method in java.awt.geom.AffineTransform.
    
    Parameters:
    
    that - the transform to apply in a second step
    
    Returns:
    
    the composition that * this
    
    Since:
    
    0.6.3
  - isSimilarity
```
public boolean isSimilarity()
```
    Tests if this affine transform is a similarity.
  - isMotion
```
public boolean isMotion()
```
    Tests if this affine transform is a motion, i.e. is composed only of rotations and translations.
  - isIsometry
```
public boolean isIsometry()
```
    Tests if this affine transform is an isometry, i.e. is equivalent to a compound of translations, rotations and reflections. Isometry keeps area of shapes unchanged, but can change orientation (direct or indirect).
    
    Returns:
    
    true in case of isometry.
  - isDirect
```
public boolean isDirect()
```
    Tests if this affine transform is direct, i.e. the sign of the determinant of the associated matrix is positive. Direct transforms preserve the orientation of transformed shapes.
  - isIdentity
```
public boolean isIdentity()
```
    Tests is this affine transform is equal to the identity transform.
    
    Returns:
    
    true if this transform is the identity transform
  - invert
```
public AffineTransform2D invert()
```
    Returns the inverse transform. If the transform is not invertible, throws a new NonInvertibleTransform2DException.
    
    Specified by:
    
    invert in interface Bijection2D
    
    Since:
    
    0.6.3
  - transform
```
public Point2D transform(Point2D p)
```
    Computes the coordinates of the transformed point.
    
    Specified by:
    
    transform in interface Transform2D
  - transform
```
public Point2D[] transform(Point2D[] src,
                           Point2D[] dst)
```
    Description copied from interface: Transform2D
    
    Transforms an array of points, and returns the transformed points.
    
    Specified by:
    
    transform in interface Transform2D
  - almostEquals
```
public boolean almostEquals(GeometricObject2D obj,
                            double eps)
```
    Description copied from interface: GeometricObject2D
    
    Checks if the two objects are similar up to a given threshold value. This method can be used to compare the results of geometric computations, that introduce errors due to numerical computations.
    
    Specified by:
    
    almostEquals in interface GeometricObject2D
    
    Parameters:
    
    obj - the object to compare
    
    eps - a threshold value, for example the minimal coordinate difference
    
    Returns:
    
    true if both object have the same value up to the threshold
  - toString
```
public java.lang.String toString()
```
    Displays the coefficients of the transform, row by row.
    
    Overrides:
    
    toString in class java.lang.Object
  - equals
```
public boolean equals(java.lang.Object obj)
```
    Overrides:
    
    equals in class java.lang.Object
  - clone
```
@Deprecated
public AffineTransform2D clone()
```
    Deprecated. immutable objects do not need to be cloned (0.11.2)
    
    Overrides:
    
    clone in class java.lang.Object

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Class AffineTransform2D

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

AffineTransform2D

AffineTransform2D

AffineTransform2D

AffineTransform2D

AffineTransform2D

Method Detail

createIdentity

create

create

create

createGlideReflection

createHomothecy

createLineReflection

createPointReflection

createQuadrantRotation

createQuadrantRotation

createQuadrantRotation

createRotation

createRotation

createRotation

createScaling

createScaling

createShear

createTransform

createTranslation

createTranslation

isIdentity

isDirect

isIsometry

isMotion

isSimilarity

coefficients

affineMatrix

asAwtTransform

concatenate

chain

preConcatenate

isSimilarity

isMotion

isIsometry

isDirect

isIdentity

invert

transform

transform

almostEquals

toString

equals

clone