Module java.desktop
Package java.awt.geom

# Class AffineTransform

java.lang.Object
java.awt.geom.AffineTransform

All Implemented Interfaces:
  `Serializable`, `Cloneable`

public class AffineTransform extends Object implements Cloneable, Serializable
The `AffineTransform` class represents a 2D affine transform that performs a linear mapping from 2D coordinates to other 2D coordinates that preserves the "straightness" and "parallelness" of lines. Affine transformations can be constructed using sequences of translations, scales, flips, rotations, and shears.

Such a coordinate transformation can be represented by a 3 row by 3 column matrix with an implied last row of [ 0 0 1 ]. This matrix transforms source coordinates `(x,y)` into destination coordinates `(x',y')` by considering them to be a column vector and multiplying the coordinate vector by the matrix according to the following process:

          [ x']   [  m00  m01  m02  ] [ x ]   [ m00x + m01y + m02 ]
          [ y'] = [  m10  m11  m12  ] [ y ] = [ m10x + m11y + m12 ]
          [ 1 ]   [   0    0    1   ] [ 1 ]   [         1         ]

## Handling 90-Degree Rotations

In some variations of the `rotate` methods in the `AffineTransform` class, a double-precision argument specifies the angle of rotation in radians. These methods have special handling for rotations of approximately 90 degrees (including multiples such as 180, 270, and 360 degrees), so that the common case of quadrant rotation is handled more efficiently. This special handling can cause angles very close to multiples of 90 degrees to be treated as if they were exact multiples of 90 degrees. For small multiples of 90 degrees the range of angles treated as a quadrant rotation is approximately 0.00000121 degrees wide. This section explains why such special care is needed and how it is implemented.

Since 90 degrees is represented as `PI/2` in radians, and since PI is a transcendental (and therefore irrational) number, it is not possible to exactly represent a multiple of 90 degrees as an exact double precision value measured in radians. As a result it is theoretically impossible to describe quadrant rotations (90, 180, 270 or 360 degrees) using these values. Double precision floating point values can get very close to non-zero multiples of `PI/2` but never close enough for the sine or cosine to be exactly 0.0, 1.0 or -1.0. The implementations of `Math.sin()` and `Math.cos()` correspondingly never return 0.0 for any case other than `Math.sin(0.0)`. These same implementations do, however, return exactly 1.0 and -1.0 for some range of numbers around each multiple of 90 degrees since the correct answer is so close to 1.0 or -1.0 that the double precision significand cannot represent the difference as accurately as it can for numbers that are near 0.0.

The net result of these issues is that if the `Math.sin()` and `Math.cos()` methods are used to directly generate the values for the matrix modifications during these radian-based rotation operations then the resulting transform is never strictly classifiable as a quadrant rotation even for a simple case like `rotate(Math.PI/2.0)`, due to minor variations in the matrix caused by the non-0.0 values obtained for the sine and cosine. If these transforms are not classified as quadrant rotations then subsequent code which attempts to optimize further operations based upon the type of the transform will be relegated to its most general implementation.

Because quadrant rotations are fairly common, this class should handle these cases reasonably quickly, both in applying the rotations to the transform and in applying the resulting transform to the coordinates. To facilitate this optimal handling, the methods which take an angle of rotation measured in radians attempt to detect angles that are intended to be quadrant rotations and treat them as such. These methods therefore treat an angle theta as a quadrant rotation if either `Math.sin(theta)` or `Math.cos(theta)` returns exactly 1.0 or -1.0. As a rule of thumb, this property holds true for a range of approximately 0.0000000211 radians (or 0.00000121 degrees) around small multiples of `Math.PI/2.0`.

Since:
  1.2
See Also:
  - Serialized Form

- ## Field Summary

  Fields
  Modifier and Type
  Field
  Description
  `static final int`
  `TYPE_FLIP`
  This flag bit indicates that the transform defined by this object performs a mirror image flip about some axis which changes the normally right handed coordinate system into a left handed system in addition to the conversions indicated by other flag bits.
  `static final int`
  `TYPE_GENERAL_ROTATION`
  This flag bit indicates that the transform defined by this object performs a rotation by an arbitrary angle in addition to the conversions indicated by other flag bits.
  `static final int`
  `TYPE_GENERAL_SCALE`
  This flag bit indicates that the transform defined by this object performs a general scale in addition to the conversions indicated by other flag bits.
  `static final int`
  `TYPE_GENERAL_TRANSFORM`
  This constant indicates that the transform defined by this object performs an arbitrary conversion of the input coordinates.
  `static final int`
  `TYPE_IDENTITY`
  This constant indicates that the transform defined by this object is an identity transform.
  `static final int`
  `TYPE_MASK_ROTATION`
  This constant is a bit mask for any of the rotation flag bits.
  `static final int`
  `TYPE_MASK_SCALE`
  This constant is a bit mask for any of the scale flag bits.
  `static final int`
  `TYPE_QUADRANT_ROTATION`
  This flag bit indicates that the transform defined by this object performs a quadrant rotation by some multiple of 90 degrees in addition to the conversions indicated by other flag bits.
  `static final int`
  `TYPE_TRANSLATION`
  This flag bit indicates that the transform defined by this object performs a translation in addition to the conversions indicated by other flag bits.
  `static final int`
  `TYPE_UNIFORM_SCALE`
  This flag bit indicates that the transform defined by this object performs a uniform scale in addition to the conversions indicated by other flag bits.

- ## Constructor Summary

  Constructors
  Constructor
  Description
  `AffineTransform()`
  Constructs a new `AffineTransform` representing the Identity transformation.
  `AffineTransform(double[] flatmatrix)`
  Constructs a new `AffineTransform` from an array of double precision values representing either the 4 non-translation entries or the 6 specifiable entries of the 3x3 transformation matrix.
  `AffineTransform(double m00, double m10, double m01, double m11, double m02, double m12)`
  Constructs a new `AffineTransform` from 6 double precision values representing the 6 specifiable entries of the 3x3 transformation matrix.
  `AffineTransform(float[] flatmatrix)`
  Constructs a new `AffineTransform` from an array of floating point values representing either the 4 non-translation entries or the 6 specifiable entries of the 3x3 transformation matrix.
  `AffineTransform(float m00, float m10, float m01, float m11, float m02, float m12)`
  Constructs a new `AffineTransform` from 6 floating point values representing the 6 specifiable entries of the 3x3 transformation matrix.
  `AffineTransform(AffineTransform Tx)`
  Constructs a new `AffineTransform` that is a copy of the specified `AffineTransform` object.

- ## Method Summary

  Modifier and Type
  Method
  Description
  `Object`
  `clone()`
  Returns a copy of this `AffineTransform` object.
  `void`
  `concatenate(AffineTransform Tx)`
  Concatenates an `AffineTransform Tx` to this `AffineTransform` Cx in the most commonly useful way to provide a new user space that is mapped to the former user space by `Tx`.
  `AffineTransform`
  `createInverse()`
  Returns an `AffineTransform` object representing the inverse transformation.
  `Shape`
  `createTransformedShape(Shape pSrc)`
  Returns a new `Shape` object defined by the geometry of the specified `Shape` after it has been transformed by this transform.
  `void`
  `deltaTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)`
  Transforms an array of relative distance vectors by this transform.
  `Point2D`
  `deltaTransform(Point2D ptSrc, Point2D ptDst)`
  Transforms the relative distance vector specified by `ptSrc` and stores the result in `ptDst`.
  `boolean`
  `equals(Object obj)`
  Returns `true` if this `AffineTransform` represents the same affine coordinate transform as the specified argument.
  `double`
  `getDeterminant()`
  Returns the determinant of the matrix representation of the transform.
  `void`
  `getMatrix(double[] flatmatrix)`
  Retrieves the 6 specifiable values in the 3x3 affine transformation matrix and places them into an array of double precisions values.
  `static AffineTransform`
  `getQuadrantRotateInstance(int numquadrants)`
  Returns a transform that rotates coordinates by the specified number of quadrants.
  `static AffineTransform`
  `getQuadrantRotateInstance(int numquadrants, double anchorx, double anchory)`
  Returns a transform that rotates coordinates by the specified number of quadrants around the specified anchor point.
  `static AffineTransform`
  `getRotateInstance(double theta)`
  Returns a transform representing a rotation transformation.
  `static AffineTransform`
  `getRotateInstance(double vecx, double vecy)`
  Returns a transform that rotates coordinates according to a rotation vector.
  `static AffineTransform`
  `getRotateInstance(double theta, double anchorx, double anchory)`
  Returns a transform that rotates coordinates around an anchor point.
  `static AffineTransform`
  `getRotateInstance(double vecx, double vecy, double anchorx, double anchory)`
  Returns a transform that rotates coordinates around an anchor point according to a rotation vector.
  `static AffineTransform`
  `getScaleInstance(double sx, double sy)`
  Returns a transform representing a scaling transformation.
  `double`
  `getScaleX()`
  Returns the `m00` element of the 3x3 affine transformation matrix.
  `double`
  `getScaleY()`
  Returns the `m11` element of the 3x3 affine transformation matrix.
  `static AffineTransform`
  `getShearInstance(double shx, double shy)`
  Returns a transform representing a shearing transformation.
  `double`
  `getShearX()`
  Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.
  `double`
  `getShearY()`
  Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.
  `static AffineTransform`
  `getTranslateInstance(double tx, double ty)`
  Returns a transform representing a translation transformation.
  `double`
  `getTranslateX()`
  Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
  `double`
  `getTranslateY()`
  Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.
  `int`
  `getType()`
  Retrieves the flag bits describing the conversion properties of this transform.
  `int`
  `hashCode()`
  Returns the hashcode for this transform.
  `void`
  `inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)`
  Inverse transforms an array of double precision coordinates by this transform.
  `Point2D`
  `inverseTransform(Point2D ptSrc, Point2D ptDst)`
  Inverse transforms the specified `ptSrc` and stores the result in `ptDst`.
  `void`
  `invert()`
  Sets this transform to the inverse of itself.
  `boolean`
  `isIdentity()`
  Returns `true` if this `AffineTransform` is an identity transform.
  `void`
  `preConcatenate(AffineTransform Tx)`
  Concatenates an `AffineTransform Tx` to this `AffineTransform` Cx in a less commonly used way such that `Tx` modifies the coordinate transformation relative to the absolute pixel space rather than relative to the existing user space.
  `void`
  `quadrantRotate(int numquadrants)`
  Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants.
  `void`
  `quadrantRotate(int numquadrants, double anchorx, double anchory)`
  Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants around the specified anchor point.
  `void`
  `rotate(double theta)`
  Concatenates this transform with a rotation transformation.
  `void`
  `rotate(double vecx, double vecy)`
  Concatenates this transform with a transform that rotates coordinates according to a rotation vector.
  `void`
  `rotate(double theta, double anchorx, double anchory)`
  Concatenates this transform with a transform that rotates coordinates around an anchor point.
  `void`
  `rotate(double vecx, double vecy, double anchorx, double anchory)`
  Concatenates this transform with a transform that rotates coordinates around an anchor point according to a rotation vector.
  `void`
  `scale(double sx, double sy)`
  Concatenates this transform with a scaling transformation.
  `void`
  `setToIdentity()`
  Resets this transform to the Identity transform.
  `void`
  `setToQuadrantRotation(int numquadrants)`
  Sets this transform to a rotation transformation that rotates coordinates by the specified number of quadrants.
  `void`
  `setToQuadrantRotation(int numquadrants, double anchorx, double anchory)`
  Sets this transform to a translated rotation transformation that rotates coordinates by the specified number of quadrants around the specified anchor point.
  `void`
  `setToRotation(double theta)`
  Sets this transform to a rotation transformation.
  `void`
  `setToRotation(double vecx, double vecy)`
  Sets this transform to a rotation transformation that rotates coordinates according to a rotation vector.
  `void`
  `setToRotation(double theta, double anchorx, double anchory)`
  Sets this transform to a translated rotation transformation.
  `void`
  `setToRotation(double vecx, double vecy, double anchorx, double anchory)`
  Sets this transform to a rotation transformation that rotates coordinates around an anchor point according to a rotation vector.
  `void`
  `setToScale(double sx, double sy)`
  Sets this transform to a scaling transformation.
  `void`
  `setToShear(double shx, double shy)`
  Sets this transform to a shearing transformation.
  `void`
  `setToTranslation(double tx, double ty)`
  Sets this transform to a translation transformation.
  `void`
  `setTransform(double m00, double m10, double m01, double m11, double m02, double m12)`
  Sets this transform to the matrix specified by the 6 double precision values.
  `void`
  `setTransform(AffineTransform Tx)`
  Sets this transform to a copy of the transform in the specified `AffineTransform` object.
  `void`
  `shear(double shx, double shy)`
  Concatenates this transform with a shearing transformation.
  `String`
  `toString()`
  Returns a `String` that represents the value of this `Object`.
  `void`
  `transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)`
  Transforms an array of double precision coordinates by this transform.
  `void`
  `transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)`
  Transforms an array of double precision coordinates by this transform and stores the results into an array of floats.
  `void`
  `transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)`
  Transforms an array of floating point coordinates by this transform and stores the results into an array of doubles.
  `void`
  `transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)`
  Transforms an array of floating point coordinates by this transform.
  `void`
  `transform(Point2D[] ptSrc, int srcOff, Point2D[] ptDst, int dstOff, int numPts)`
  Transforms an array of point objects by this transform.
  `Point2D`
  `transform(Point2D ptSrc, Point2D ptDst)`
  Transforms the specified `ptSrc` and stores the result in `ptDst`.
  `void`
  `translate(double tx, double ty)`
  Concatenates this transform with a translation transformation.

  ### Methods declared in class java.lang.Object

  `finalize, getClass, notify, notifyAll, wait, wait, wait`

- ## Field Details

  - ### TYPE_IDENTITY

    public static final int TYPE_IDENTITY
    This constant indicates that the transform defined by this object is an identity transform. An identity transform is one in which the output coordinates are always the same as the input coordinates. If this transform is anything other than the identity transform, the type will either be the constant GENERAL_TRANSFORM or a combination of the appropriate flag bits for the various coordinate conversions that this transform performs.
    Since:
      1.2
    See Also:
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_TRANSLATION

    public static final int TYPE_TRANSLATION
    This flag bit indicates that the transform defined by this object performs a translation in addition to the conversions indicated by other flag bits. A translation moves the coordinates by a constant amount in x and y without changing the length or angle of vectors.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_UNIFORM_SCALE

    public static final int TYPE_UNIFORM_SCALE
    This flag bit indicates that the transform defined by this object performs a uniform scale in addition to the conversions indicated by other flag bits. A uniform scale multiplies the length of vectors by the same amount in both the x and y directions without changing the angle between vectors. This flag bit is mutually exclusive with the TYPE_GENERAL_SCALE flag.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_GENERAL_SCALE

    public static final int TYPE_GENERAL_SCALE
    This flag bit indicates that the transform defined by this object performs a general scale in addition to the conversions indicated by other flag bits. A general scale multiplies the length of vectors by different amounts in the x and y directions without changing the angle between perpendicular vectors. This flag bit is mutually exclusive with the TYPE_UNIFORM_SCALE flag.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_MASK_SCALE

    public static final int TYPE_MASK_SCALE
    This constant is a bit mask for any of the scale flag bits.
    Since:
      1.2
    See Also:
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - Constant Field Values

  - ### TYPE_FLIP

    public static final int TYPE_FLIP
    This flag bit indicates that the transform defined by this object performs a mirror image flip about some axis which changes the normally right handed coordinate system into a left handed system in addition to the conversions indicated by other flag bits. A right handed coordinate system is one where the positive X axis rotates counterclockwise to overlay the positive Y axis similar to the direction that the fingers on your right hand curl when you stare end on at your thumb. A left handed coordinate system is one where the positive X axis rotates clockwise to overlay the positive Y axis similar to the direction that the fingers on your left hand curl. There is no mathematical way to determine the angle of the original flipping or mirroring transformation since all angles of flip are identical given an appropriate adjusting rotation.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_QUADRANT_ROTATION

    public static final int TYPE_QUADRANT_ROTATION
    This flag bit indicates that the transform defined by this object performs a quadrant rotation by some multiple of 90 degrees in addition to the conversions indicated by other flag bits. A rotation changes the angles of vectors by the same amount regardless of the original direction of the vector and without changing the length of the vector. This flag bit is mutually exclusive with the TYPE_GENERAL_ROTATION flag.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_GENERAL_ROTATION

    public static final int TYPE_GENERAL_ROTATION
    This flag bit indicates that the transform defined by this object performs a rotation by an arbitrary angle in addition to the conversions indicated by other flag bits. A rotation changes the angles of vectors by the same amount regardless of the original direction of the vector and without changing the length of the vector. This flag bit is mutually exclusive with the TYPE_QUADRANT_ROTATION flag.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`
      - `getType()`
      - Constant Field Values

  - ### TYPE_MASK_ROTATION

    public static final int TYPE_MASK_ROTATION
    This constant is a bit mask for any of the rotation flag bits.
    Since:
      1.2
    See Also:
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - Constant Field Values

  - ### TYPE_GENERAL_TRANSFORM

    public static final int TYPE_GENERAL_TRANSFORM
    This constant indicates that the transform defined by this object performs an arbitrary conversion of the input coordinates. If this transform can be classified by any of the above constants, the type will either be the constant TYPE_IDENTITY or a combination of the appropriate flag bits for the various coordinate conversions that this transform performs.
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_FLIP`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `getType()`
      - Constant Field Values

- ## Constructor Details

  - ### AffineTransform

    public AffineTransform()
    Constructs a new `AffineTransform` representing the Identity transformation.
    Since:
      1.2

  - ### AffineTransform

    public AffineTransform(AffineTransform Tx)
    Constructs a new `AffineTransform` that is a copy of the specified `AffineTransform` object.
    Parameters:
      `Tx` - the `AffineTransform` object to copy
    Since:
      1.2

  - ### AffineTransform

    @ConstructorProperties({"scaleX","shearY","shearX","scaleY","translateX","translateY"}) public AffineTransform(float m00, float m10, float m01, float m11, float m02, float m12)
    Constructs a new `AffineTransform` from 6 floating point values representing the 6 specifiable entries of the 3x3 transformation matrix.
    Parameters:
      `m00` - the X coordinate scaling element of the 3x3 matrix
      `m10` - the Y coordinate shearing element of the 3x3 matrix
      `m01` - the X coordinate shearing element of the 3x3 matrix
      `m11` - the Y coordinate scaling element of the 3x3 matrix
      `m02` - the X coordinate translation element of the 3x3 matrix
      `m12` - the Y coordinate translation element of the 3x3 matrix
    Since:
      1.2

  - ### AffineTransform

    public AffineTransform(float[] flatmatrix)
    Constructs a new `AffineTransform` from an array of floating point values representing either the 4 non-translation entries or the 6 specifiable entries of the 3x3 transformation matrix. The values are retrieved from the array as { m00 m10 m01 m11 [m02 m12]}.
    Parameters:
      `flatmatrix` - the float array containing the values to be set in the new `AffineTransform` object. The length of the array is assumed to be at least 4. If the length of the array is less than 6, only the first 4 values are taken. If the length of the array is greater than 6, the first 6 values are taken.
    Since:
      1.2

  - ### AffineTransform

    public AffineTransform(double m00, double m10, double m01, double m11, double m02, double m12)
    Constructs a new `AffineTransform` from 6 double precision values representing the 6 specifiable entries of the 3x3 transformation matrix.
    Parameters:
      `m00` - the X coordinate scaling element of the 3x3 matrix
      `m10` - the Y coordinate shearing element of the 3x3 matrix
      `m01` - the X coordinate shearing element of the 3x3 matrix
      `m11` - the Y coordinate scaling element of the 3x3 matrix
      `m02` - the X coordinate translation element of the 3x3 matrix
      `m12` - the Y coordinate translation element of the 3x3 matrix
    Since:
      1.2

  - ### AffineTransform

    public AffineTransform(double[] flatmatrix)
    Constructs a new `AffineTransform` from an array of double precision values representing either the 4 non-translation entries or the 6 specifiable entries of the 3x3 transformation matrix. The values are retrieved from the array as { m00 m10 m01 m11 [m02 m12]}.
    Parameters:
      `flatmatrix` - the double array containing the values to be set in the new `AffineTransform` object. The length of the array is assumed to be at least 4. If the length of the array is less than 6, only the first 4 values are taken. If the length of the array is greater than 6, the first 6 values are taken.
    Since:
      1.2

- ## Method Details

  - ### getTranslateInstance

    public static AffineTransform getTranslateInstance(double tx, double ty)
    Returns a transform representing a translation transformation. The matrix representing the returned transform is:

                  [   1    0    tx  ]
                  [   0    1    ty  ]
                  [   0    0    1   ]

    Parameters:
      `tx` - the distance by which coordinates are translated in the X axis direction
      `ty` - the distance by which coordinates are translated in the Y axis direction
    Returns:
      an `AffineTransform` object that represents a translation transformation, created with the specified vector.
    Since:
      1.2

  - ### getRotateInstance

    public static AffineTransform getRotateInstance(double theta)
    Returns a transform representing a rotation transformation. The matrix representing the returned transform is:

                  [   cos(theta)    -sin(theta)    0   ]
                  [   sin(theta)     cos(theta)    0   ]
                  [       0              0         1   ]

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
    Returns:
      an `AffineTransform` object that is a rotation transformation, created with the specified angle of rotation.
    Since:
      1.2

  - ### getRotateInstance

    public static AffineTransform getRotateInstance(double theta, double anchorx, double anchory)
    Returns a transform that rotates coordinates around an anchor point. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

    This operation is equivalent to the following sequence of calls:

             AffineTransform Tx = new AffineTransform();
             Tx.translate(anchorx, anchory);    // S3: final translation
             Tx.rotate(theta);                  // S2: rotate around anchor
             Tx.translate(-anchorx, -anchory);  // S1: translate anchor to origin

    The matrix representing the returned transform is:

                  [   cos(theta)    -sin(theta)    x-x*cos+y*sin  ]
                  [   sin(theta)     cos(theta)    y-x*sin-y*cos  ]
                  [       0              0               1        ]

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Returns:
      an `AffineTransform` object that rotates coordinates around the specified point by the specified angle of rotation.
    Since:
      1.2

  - ### getRotateInstance

    public static AffineTransform getRotateInstance(double vecx, double vecy)
    Returns a transform that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, an identity transform is returned. This operation is equivalent to calling:

             AffineTransform.getRotateInstance(Math.atan2(vecy, vecx));

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
    Returns:
      an `AffineTransform` object that rotates coordinates according to the specified rotation vector.
    Since:
      1.6

  - ### getRotateInstance

    public static AffineTransform getRotateInstance(double vecx, double vecy, double anchorx, double anchory)
    Returns a transform that rotates coordinates around an anchor point according to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, an identity transform is returned. This operation is equivalent to calling:

             AffineTransform.getRotateInstance(Math.atan2(vecy, vecx),
                                               anchorx, anchory);

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Returns:
      an `AffineTransform` object that rotates coordinates around the specified point according to the specified rotation vector.
    Since:
      1.6

  - ### getQuadrantRotateInstance

    public static AffineTransform getQuadrantRotateInstance(int numquadrants)
    Returns a transform that rotates coordinates by the specified number of quadrants. This operation is equivalent to calling:

             AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
    Returns:
      an `AffineTransform` object that rotates coordinates by the specified number of quadrants.
    Since:
      1.6

  - ### getQuadrantRotateInstance

    public static AffineTransform getQuadrantRotateInstance(int numquadrants, double anchorx, double anchory)
    Returns a transform that rotates coordinates by the specified number of quadrants around the specified anchor point. This operation is equivalent to calling:

             AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0,
                                               anchorx, anchory);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Returns:
      an `AffineTransform` object that rotates coordinates by the specified number of quadrants around the specified anchor point.
    Since:
      1.6

  - ### getScaleInstance

    public static AffineTransform getScaleInstance(double sx, double sy)
    Returns a transform representing a scaling transformation. The matrix representing the returned transform is:

                  [   sx   0    0   ]
                  [   0    sy   0   ]
                  [   0    0    1   ]

    Parameters:
      `sx` - the factor by which coordinates are scaled along the X axis direction
      `sy` - the factor by which coordinates are scaled along the Y axis direction
    Returns:
      an `AffineTransform` object that scales coordinates by the specified factors.
    Since:
      1.2

  - ### getShearInstance

    public static AffineTransform getShearInstance(double shx, double shy)
    Returns a transform representing a shearing transformation. The matrix representing the returned transform is:

                  [   1   shx   0   ]
                  [  shy   1    0   ]
                  [   0    0    1   ]

    Parameters:
      `shx` - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
      `shy` - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate
    Returns:
      an `AffineTransform` object that shears coordinates by the specified multipliers.
    Since:
      1.2

  - ### getType

    public int getType()
    Retrieves the flag bits describing the conversion properties of this transform. The return value is either one of the constants TYPE_IDENTITY or TYPE_GENERAL_TRANSFORM, or a combination of the appropriate flag bits. A valid combination of flag bits is an exclusive OR operation that can combine the TYPE_TRANSLATION flag bit in addition to either of the TYPE_UNIFORM_SCALE or TYPE_GENERAL_SCALE flag bits as well as either of the TYPE_QUADRANT_ROTATION or TYPE_GENERAL_ROTATION flag bits.
    Returns:
      the OR combination of any of the indicated flags that apply to this transform
    Since:
      1.2
    See Also:
      - `TYPE_IDENTITY`
      - `TYPE_TRANSLATION`
      - `TYPE_UNIFORM_SCALE`
      - `TYPE_GENERAL_SCALE`
      - `TYPE_QUADRANT_ROTATION`
      - `TYPE_GENERAL_ROTATION`
      - `TYPE_GENERAL_TRANSFORM`

  - ### getDeterminant

    public double getDeterminant()
    Returns the determinant of the matrix representation of the transform. The determinant is useful both to determine if the transform can be inverted and to get a single value representing the combined X and Y scaling of the transform.

    If the determinant is non-zero, then this transform is invertible and the various methods that depend on the inverse transform do not need to throw a `NoninvertibleTransformException`. If the determinant is zero then this transform can not be inverted since the transform maps all input coordinates onto a line or a point. If the determinant is near enough to zero then inverse transform operations might not carry enough precision to produce meaningful results.

    If this transform represents a uniform scale, as indicated by the `getType` method then the determinant also represents the square of the uniform scale factor by which all of the points are expanded from or contracted towards the origin. If this transform represents a non-uniform scale or more general transform then the determinant is not likely to represent a value useful for any purpose other than determining if inverse transforms are possible.

    Mathematically, the determinant is calculated using the formula:

                  |  m00  m01  m02  |
                  |  m10  m11  m12  |  =  m00 * m11 - m01 * m10
                  |   0    0    1   |

    Returns:
      the determinant of the matrix used to transform the coordinates.
    Since:
      1.2
    See Also:
      - `getType()`
      - `createInverse()`
      - `inverseTransform(java.awt.geom.Point2D, java.awt.geom.Point2D)`
      - `TYPE_UNIFORM_SCALE`

  - ### getMatrix

    public void getMatrix(double[] flatmatrix)
    Retrieves the 6 specifiable values in the 3x3 affine transformation matrix and places them into an array of double precisions values. The values are stored in the array as { m00 m10 m01 m11 m02 m12 }. An array of 4 doubles can also be specified, in which case only the first four elements representing the non-transform parts of the array are retrieved and the values are stored into the array as { m00 m10 m01 m11 }
    Parameters:
      `flatmatrix` - the double array used to store the returned values.
    Since:
      1.2
    See Also:
      - `getScaleX()`
      - `getScaleY()`
      - `getShearX()`
      - `getShearY()`
      - `getTranslateX()`
      - `getTranslateY()`

  - ### getScaleX

    public double getScaleX()
    Returns the `m00` element of the 3x3 affine transformation matrix. This matrix factor determines how input X coordinates will affect output X coordinates and is one element of the scale of the transform. To measure the full amount by which X coordinates are stretched or contracted by this transform, use the following code:

             Point2D p = new Point2D.Double(1, 0);
             p = tx.deltaTransform(p, p);
             double scaleX = p.distance(0, 0);

    Returns:
      a double value that is `m00` element of the 3x3 affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### getScaleY

    public double getScaleY()
    Returns the `m11` element of the 3x3 affine transformation matrix. This matrix factor determines how input Y coordinates will affect output Y coordinates and is one element of the scale of the transform. To measure the full amount by which Y coordinates are stretched or contracted by this transform, use the following code:

             Point2D p = new Point2D.Double(0, 1);
             p = tx.deltaTransform(p, p);
             double scaleY = p.distance(0, 0);

    Returns:
      a double value that is `m11` element of the 3x3 affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### getShearX

    public double getShearX()
    Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.
    Returns:
      a double value that is the X coordinate of the shearing element of the affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### getShearY

    public double getShearY()
    Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.
    Returns:
      a double value that is the Y coordinate of the shearing element of the affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### getTranslateX

    public double getTranslateX()
    Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
    Returns:
      a double value that is the X coordinate of the translation element of the affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### getTranslateY

    public double getTranslateY()
    Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.
    Returns:
      a double value that is the Y coordinate of the translation element of the affine transformation matrix.
    Since:
      1.2
    See Also:
      - `getMatrix(double[])`

  - ### translate

    public void translate(double tx, double ty)
    Concatenates this transform with a translation transformation. This is equivalent to calling concatenate(T), where T is an `AffineTransform` represented by the following matrix:

                  [   1    0    tx  ]
                  [   0    1    ty  ]
                  [   0    0    1   ]

    Parameters:
      `tx` - the distance by which coordinates are translated in the X axis direction
      `ty` - the distance by which coordinates are translated in the Y axis direction
    Since:
      1.2

  - ### rotate

    public void rotate(double theta)
    Concatenates this transform with a rotation transformation. This is equivalent to calling concatenate(R), where R is an `AffineTransform` represented by the following matrix:

                  [   cos(theta)    -sin(theta)    0   ]
                  [   sin(theta)     cos(theta)    0   ]
                  [       0              0         1   ]

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
    Since:
      1.2

  - ### rotate

    public void rotate(double theta, double anchorx, double anchory)
    Concatenates this transform with a transform that rotates coordinates around an anchor point. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

    This operation is equivalent to the following sequence of calls:

             translate(anchorx, anchory);      // S3: final translation
             rotate(theta);                    // S2: rotate around anchor
             translate(-anchorx, -anchory);    // S1: translate anchor to origin

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.2

  - ### rotate

    public void rotate(double vecx, double vecy)
    Concatenates this transform with a transform that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, no additional rotation is added to this transform. This operation is equivalent to calling:

                  rotate(Math.atan2(vecy, vecx));

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
    Since:
      1.6

  - ### rotate

    public void rotate(double vecx, double vecy, double anchorx, double anchory)
    Concatenates this transform with a transform that rotates coordinates around an anchor point according to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, the transform is not modified in any way. This method is equivalent to calling:

             rotate(Math.atan2(vecy, vecx), anchorx, anchory);

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.6

  - ### quadrantRotate

    public void quadrantRotate(int numquadrants)
    Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants. This is equivalent to calling:

             rotate(numquadrants * Math.PI / 2.0);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
    Since:
      1.6

  - ### quadrantRotate

    public void quadrantRotate(int numquadrants, double anchorx, double anchory)
    Concatenates this transform with a transform that rotates coordinates by the specified number of quadrants around the specified anchor point. This method is equivalent to calling:

             rotate(numquadrants * Math.PI / 2.0, anchorx, anchory);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.6

  - ### scale

    public void scale(double sx, double sy)
    Concatenates this transform with a scaling transformation. This is equivalent to calling concatenate(S), where S is an `AffineTransform` represented by the following matrix:

                  [   sx   0    0   ]
                  [   0    sy   0   ]
                  [   0    0    1   ]

    Parameters:
      `sx` - the factor by which coordinates are scaled along the X axis direction
      `sy` - the factor by which coordinates are scaled along the Y axis direction
    Since:
      1.2

  - ### shear

    public void shear(double shx, double shy)
    Concatenates this transform with a shearing transformation. This is equivalent to calling concatenate(SH), where SH is an `AffineTransform` represented by the following matrix:

                  [   1   shx   0   ]
                  [  shy   1    0   ]
                  [   0    0    1   ]

    Parameters:
      `shx` - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
      `shy` - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate
    Since:
      1.2

  - ### setToIdentity

    public void setToIdentity()
    Resets this transform to the Identity transform.
    Since:
      1.2

  - ### setToTranslation

    public void setToTranslation(double tx, double ty)
    Sets this transform to a translation transformation. The matrix representing this transform becomes:

                  [   1    0    tx  ]
                  [   0    1    ty  ]
                  [   0    0    1   ]

    Parameters:
      `tx` - the distance by which coordinates are translated in the X axis direction
      `ty` - the distance by which coordinates are translated in the Y axis direction
    Since:
      1.2

  - ### setToRotation

    public void setToRotation(double theta)
    Sets this transform to a rotation transformation. The matrix representing this transform becomes:

                  [   cos(theta)    -sin(theta)    0   ]
                  [   sin(theta)     cos(theta)    0   ]
                  [       0              0         1   ]

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
    Since:
      1.2

  - ### setToRotation

    public void setToRotation(double theta, double anchorx, double anchory)
    Sets this transform to a translated rotation transformation. This operation is equivalent to translating the coordinates so that the anchor point is at the origin (S1), then rotating them about the new origin (S2), and finally translating so that the intermediate origin is restored to the coordinates of the original anchor point (S3).

    This operation is equivalent to the following sequence of calls:

             setToTranslation(anchorx, anchory); // S3: final translation
             rotate(theta);                      // S2: rotate around anchor
             translate(-anchorx, -anchory);      // S1: translate anchor to origin

    The matrix representing this transform becomes:

                  [   cos(theta)    -sin(theta)    x-x*cos+y*sin  ]
                  [   sin(theta)     cos(theta)    y-x*sin-y*cos  ]
                  [       0              0               1        ]

    Rotating by a positive angle theta rotates points on the positive X axis toward the positive Y axis. Note also the discussion of Handling 90-Degree Rotations above.
    Parameters:
      `theta` - the angle of rotation measured in radians
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.2

  - ### setToRotation

    public void setToRotation(double vecx, double vecy)
    Sets this transform to a rotation transformation that rotates coordinates according to a rotation vector. All coordinates rotate about the origin by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, the transform is set to an identity transform. This operation is equivalent to calling:

             setToRotation(Math.atan2(vecy, vecx));

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
    Since:
      1.6

  - ### setToRotation

    public void setToRotation(double vecx, double vecy, double anchorx, double anchory)
    Sets this transform to a rotation transformation that rotates coordinates around an anchor point according to a rotation vector. All coordinates rotate about the specified anchor coordinates by the same amount. The amount of rotation is such that coordinates along the former positive X axis will subsequently align with the vector pointing from the origin to the specified vector coordinates. If both `vecx` and `vecy` are 0.0, the transform is set to an identity transform. This operation is equivalent to calling:

             setToTranslation(Math.atan2(vecy, vecx), anchorx, anchory);

    Parameters:
      `vecx` - the X coordinate of the rotation vector
      `vecy` - the Y coordinate of the rotation vector
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.6

  - ### setToQuadrantRotation

    public void setToQuadrantRotation(int numquadrants)
    Sets this transform to a rotation transformation that rotates coordinates by the specified number of quadrants. This operation is equivalent to calling:

             setToRotation(numquadrants * Math.PI / 2.0);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
    Since:
      1.6

  - ### setToQuadrantRotation

    public void setToQuadrantRotation(int numquadrants, double anchorx, double anchory)
    Sets this transform to a translated rotation transformation that rotates coordinates by the specified number of quadrants around the specified anchor point. This operation is equivalent to calling:

             setToRotation(numquadrants * Math.PI / 2.0, anchorx, anchory);

    Rotating by a positive number of quadrants rotates points on the positive X axis toward the positive Y axis.
    Parameters:
      `numquadrants` - the number of 90 degree arcs to rotate by
      `anchorx` - the X coordinate of the rotation anchor point
      `anchory` - the Y coordinate of the rotation anchor point
    Since:
      1.6

  - ### setToScale

    public void setToScale(double sx, double sy)
    Sets this transform to a scaling transformation. The matrix representing this transform becomes:

                  [   sx   0    0   ]
                  [   0    sy   0   ]
                  [   0    0    1   ]

    Parameters:
      `sx` - the factor by which coordinates are scaled along the X axis direction
      `sy` - the factor by which coordinates are scaled along the Y axis direction
    Since:
      1.2

  - ### setToShear

    public void setToShear(double shx, double shy)
    Sets this transform to a shearing transformation. The matrix representing this transform becomes:

                  [   1   shx   0   ]
                  [  shy   1    0   ]
                  [   0    0    1   ]

    Parameters:
      `shx` - the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
      `shy` - the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate
    Since:
      1.2

  - ### setTransform

    public void setTransform(AffineTransform Tx)
    Sets this transform to a copy of the transform in the specified `AffineTransform` object.
    Parameters:
      `Tx` - the `AffineTransform` object from which to copy the transform
    Since:
      1.2

  - ### setTransform

    public void setTransform(double m00, double m10, double m01, double m11, double m02, double m12)
    Sets this transform to the matrix specified by the 6 double precision values.
    Parameters:
      `m00` - the X coordinate scaling element of the 3x3 matrix
      `m10` - the Y coordinate shearing element of the 3x3 matrix
      `m01` - the X coordinate shearing element of the 3x3 matrix
      `m11` - the Y coordinate scaling element of the 3x3 matrix
      `m02` - the X coordinate translation element of the 3x3 matrix
      `m12` - the Y coordinate translation element of the 3x3 matrix
    Since:
      1.2

  - ### concatenate

    public void concatenate(AffineTransform Tx)
    Concatenates an `AffineTransform Tx` to this `AffineTransform` Cx in the most commonly useful way to provide a new user space that is mapped to the former user space by `Tx`. Cx is updated to perform the combined transformation. Transforming a point p by the updated transform Cx' is equivalent to first transforming p by `Tx` and then transforming the result by the original transform Cx like this: Cx'(p) = Cx(Tx(p)) In matrix notation, if this transform Cx is represented by the matrix [this] and `Tx` is represented by the matrix [Tx] then this method does the following:

                  [this] = [this] x [Tx]

    Parameters:
      `Tx` - the `AffineTransform` object to be concatenated with this `AffineTransform` object.
    Since:
      1.2
    See Also:
      - `preConcatenate(java.awt.geom.AffineTransform)`

  - ### preConcatenate

    public void preConcatenate(AffineTransform Tx)
    Concatenates an `AffineTransform Tx` to this `AffineTransform` Cx in a less commonly used way such that `Tx` modifies the coordinate transformation relative to the absolute pixel space rather than relative to the existing user space. Cx is updated to perform the combined transformation. Transforming a point p by the updated transform Cx' is equivalent to first transforming p by the original transform Cx and then transforming the result by `Tx` like this: Cx'(p) = Tx(Cx(p)) In matrix notation, if this transform Cx is represented by the matrix [this] and `Tx` is represented by the matrix [Tx] then this method does the following:

                  [this] = [Tx] x [this]

    Parameters:
      `Tx` - the `AffineTransform` object to be concatenated with this `AffineTransform` object.
    Since:
      1.2
    See Also:
      - `concatenate(java.awt.geom.AffineTransform)`

  - ### createInverse

    public AffineTransform createInverse() throws NoninvertibleTransformException
    Returns an `AffineTransform` object representing the inverse transformation. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

    If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The `getDeterminant` method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the `createInverse` method is called.

    Returns:
      a new `AffineTransform` object representing the inverse transformation.
    Throws:
      `NoninvertibleTransformException` - if the matrix cannot be inverted.
    Since:
      1.2
    See Also:
      - `getDeterminant()`

  - ### invert

    public void invert() throws NoninvertibleTransformException
    Sets this transform to the inverse of itself. The inverse transform Tx' of this transform Tx maps coordinates transformed by Tx back to their original coordinates. In other words, Tx'(Tx(p)) = p = Tx(Tx'(p)).

    If this transform maps all coordinates onto a point or a line then it will not have an inverse, since coordinates that do not lie on the destination point or line will not have an inverse mapping. The `getDeterminant` method can be used to determine if this transform has no inverse, in which case an exception will be thrown if the `invert` method is called.

    Throws:
      `NoninvertibleTransformException` - if the matrix cannot be inverted.
    Since:
      1.6
    See Also:
      - `getDeterminant()`

  - ### transform

    public Point2D transform(Point2D ptSrc, Point2D ptDst)
    Transforms the specified `ptSrc` and stores the result in `ptDst`. If `ptDst` is `null`, a new `Point2D` object is allocated and then the result of the transformation is stored in this object. In either case, `ptDst`, which contains the transformed point, is returned for convenience. If `ptSrc` and `ptDst` are the same object, the input point is correctly overwritten with the transformed point.
    Parameters:
      `ptSrc` - the specified `Point2D` to be transformed
      `ptDst` - the specified `Point2D` that stores the result of transforming `ptSrc`
    Returns:
      the `ptDst` after transforming `ptSrc` and storing the result in `ptDst`.
    Since:
      1.2

  - ### transform

    public void transform(Point2D[] ptSrc, int srcOff, Point2D[] ptDst, int dstOff, int numPts)
    Transforms an array of point objects by this transform. If any element of the `ptDst` array is `null`, a new `Point2D` object is allocated and stored into that element before storing the results of the transformation.

    Note that this method does not take any precautions to avoid problems caused by storing results into `Point2D` objects that will be used as the source for calculations further down the source array. This method does guarantee that if a specified `Point2D` object is both the source and destination for the same single point transform operation then the results will not be stored until the calculations are complete to avoid storing the results on top of the operands. If, however, the destination `Point2D` object for one operation is the same object as the source `Point2D` object for another operation further down the source array then the original coordinates in that point are overwritten before they can be converted.

    Parameters:
      `ptSrc` - the array containing the source point objects
      `srcOff` - the offset to the first point object to be transformed in the source array
      `ptDst` - the array into which the transform point objects are returned
      `dstOff` - the offset to the location of the first transformed point object that is stored in the destination array
      `numPts` - the number of point objects to be transformed
    Since:
      1.2

  - ### transform

    public void transform(float[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)
    Transforms an array of floating point coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the specified offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
      `srcOff` - the offset to the first point to be transformed in the source array
      `dstPts` - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
      `dstOff` - the offset to the location of the first transformed point that is stored in the destination array
      `numPts` - the number of points to be transformed
    Since:
      1.2

  - ### transform

    public void transform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
    Transforms an array of double precision coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the indicated offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
      `srcOff` - the offset to the first point to be transformed in the source array
      `dstPts` - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
      `dstOff` - the offset to the location of the first transformed point that is stored in the destination array
      `numPts` - the number of point objects to be transformed
    Since:
      1.2

  - ### transform

    public void transform(float[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
    Transforms an array of floating point coordinates by this transform and stores the results into an array of doubles. The coordinates are stored in the arrays starting at the specified offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
      `srcOff` - the offset to the first point to be transformed in the source array
      `dstPts` - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
      `dstOff` - the offset to the location of the first transformed point that is stored in the destination array
      `numPts` - the number of points to be transformed
    Since:
      1.2

  - ### transform

    public void transform(double[] srcPts, int srcOff, float[] dstPts, int dstOff, int numPts)
    Transforms an array of double precision coordinates by this transform and stores the results into an array of floats. The coordinates are stored in the arrays starting at the specified offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
      `srcOff` - the offset to the first point to be transformed in the source array
      `dstPts` - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
      `dstOff` - the offset to the location of the first transformed point that is stored in the destination array
      `numPts` - the number of point objects to be transformed
    Since:
      1.2

  - ### inverseTransform

    public Point2D inverseTransform(Point2D ptSrc, Point2D ptDst) throws NoninvertibleTransformException
    Inverse transforms the specified `ptSrc` and stores the result in `ptDst`. If `ptDst` is `null`, a new `Point2D` object is allocated and then the result of the transform is stored in this object. In either case, `ptDst`, which contains the transformed point, is returned for convenience. If `ptSrc` and `ptDst` are the same object, the input point is correctly overwritten with the transformed point.
    Parameters:
      `ptSrc` - the point to be inverse transformed
      `ptDst` - the resulting transformed point
    Returns:
      `ptDst`, which contains the result of the inverse transform.
    Throws:
      `NoninvertibleTransformException` - if the matrix cannot be inverted.
    Since:
      1.2

  - ### inverseTransform

    public void inverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts) throws NoninvertibleTransformException
    Inverse transforms an array of double precision coordinates by this transform. The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the specified offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
      `srcOff` - the offset to the first point to be transformed in the source array
      `dstPts` - the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
      `dstOff` - the offset to the location of the first transformed point that is stored in the destination array
      `numPts` - the number of point objects to be transformed
    Throws:
      `NoninvertibleTransformException` - if the matrix cannot be inverted.
    Since:
      1.2

  - ### deltaTransform

    public Point2D deltaTransform(Point2D ptSrc, Point2D ptDst)
    Transforms the relative distance vector specified by `ptSrc` and stores the result in `ptDst`. A relative distance vector is transformed without applying the translation components of the affine transformation matrix using the following equations:

          [  x' ]   [  m00  m01 (m02) ] [  x  ]   [ m00x + m01y ]
          [  y' ] = [  m10  m11 (m12) ] [  y  ] = [ m10x + m11y ]
          [ (1) ]   [  (0)  (0) ( 1 ) ] [ (1) ]   [     (1)     ]

    If `ptDst` is `null`, a new `Point2D` object is allocated and then the result of the transform is stored in this object. In either case, `ptDst`, which contains the transformed point, is returned for convenience. If `ptSrc` and `ptDst` are the same object, the input point is correctly overwritten with the transformed point.
    Parameters:
      `ptSrc` - the distance vector to be delta transformed
      `ptDst` - the resulting transformed distance vector
    Returns:
      `ptDst`, which contains the result of the transformation.
    Since:
      1.2

  - ### deltaTransform

    public void deltaTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
    Transforms an array of relative distance vectors by this transform. A relative distance vector is transformed without applying the translation components of the affine transformation matrix using the following equations:

          [  x' ]   [  m00  m01 (m02) ] [  x  ]   [ m00x + m01y ]
          [  y' ] = [  m10  m11 (m12) ] [  y  ] = [ m10x + m11y ]
          [ (1) ]   [  (0)  (0) ( 1 ) ] [ (1) ]   [     (1)     ]

    The two coordinate array sections can be exactly the same or can be overlapping sections of the same array without affecting the validity of the results. This method ensures that no source coordinates are overwritten by a previous operation before they can be transformed. The coordinates are stored in the arrays starting at the indicated offset in the order `[x0, y0, x1, y1, ..., xn, yn]`.
    Parameters:
      `srcPts` - the array containing the source distance vectors. Each vector is stored as a pair of relative x, y coordinates.
      `srcOff` - the offset to the first vector to be transformed in the source array
      `dstPts` - the array into which the transformed distance vectors are returned. Each vector is stored as a pair of relative x, y coordinates.
      `dstOff` - the offset to the location of the first transformed vector that is stored in the destination array
      `numPts` - the number of vector coordinate pairs to be transformed
    Since:
      1.2

  - ### createTransformedShape

    public Shape createTransformedShape(Shape pSrc)
    Returns a new `Shape` object defined by the geometry of the specified `Shape` after it has been transformed by this transform.
    Parameters:
      `pSrc` - the specified `Shape` object to be transformed by this transform.
    Returns:
      a new `Shape` object that defines the geometry of the transformed `Shape`, or null if `pSrc` is null.
    Since:
      1.2

  - ### toString

    public String toString()
    Returns a `String` that represents the value of this `Object`.
    Overrides:
      `toString` in class `Object`
    Returns:
      a `String` representing the value of this `Object`.
    Since:
      1.2

  - ### isIdentity

    public boolean isIdentity()
    Returns `true` if this `AffineTransform` is an identity transform.
    Returns:
      `true` if this `AffineTransform` is an identity transform; `false` otherwise.
    Since:
      1.2

  - ### clone

    public Object clone()
    Returns a copy of this `AffineTransform` object.
    Overrides:
      `clone` in class `Object`
    Returns:
      an `Object` that is a copy of this `AffineTransform` object.
    Since:
      1.2
    See Also:
      - `Cloneable`

  - ### hashCode

    public int hashCode()
    Returns the hashcode for this transform.
    Overrides:
      `hashCode` in class `Object`
    Returns:
      a hash code for this transform.
    Since:
      1.2
    See Also:
      - `Object.equals(java.lang.Object)`
      - `System.identityHashCode(java.lang.Object)`

  - ### equals

    public boolean equals(Object obj)
    Returns `true` if this `AffineTransform` represents the same affine coordinate transform as the specified argument.
    Overrides:
      `equals` in class `Object`
    Parameters:
      `obj` - the `Object` to test for equality with this `AffineTransform`
    Returns:
      `true` if `obj` equals this `AffineTransform` object; `false` otherwise.
    Since:
      1.2
    See Also:
      - `Object.hashCode()`
      - `HashMap`