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java.awt.geom
public class: AffineTransform [javadoc | source] 
java.lang.Object
   java.awt.geom.AffineTransform

All Implemented Interfaces:
    Cloneable, java$io$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 {@code (x,y)} into destination coordinates {@code (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.

Field Summary
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. 
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. 
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. 
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. 
public static final  int TYPE_MASK_SCALE    This constant is a bit mask for any of the scale flag bits. 
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. 
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. 
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. 
public static final  int TYPE_MASK_ROTATION    This constant is a bit mask for any of the rotation flag bits. 
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. 
static final  int APPLY_IDENTITY    This constant is used for the internal state variable to indicate that no calculations need to be performed and that the source coordinates only need to be copied to their destinations to complete the transformation equation of this transform. 
static final  int APPLY_TRANSLATE    This constant is used for the internal state variable to indicate that the translation components of the matrix (m02 and m12) need to be added to complete the transformation equation of this transform. 
static final  int APPLY_SCALE    This constant is used for the internal state variable to indicate that the scaling components of the matrix (m00 and m11) need to be factored in to complete the transformation equation of this transform. If the APPLY_SHEAR bit is also set then it indicates that the scaling components are not both 0.0. If the APPLY_SHEAR bit is not also set then it indicates that the scaling components are not both 1.0. If neither the APPLY_SHEAR nor the APPLY_SCALE bits are set then the scaling components are both 1.0, which means that the x and y components contribute to the transformed coordinate, but they are not multiplied by any scaling factor. 
static final  int APPLY_SHEAR    This constant is used for the internal state variable to indicate that the shearing components of the matrix (m01 and m10) need to be factored in to complete the transformation equation of this transform. The presence of this bit in the state variable changes the interpretation of the APPLY_SCALE bit as indicated in its documentation. 
 double m00    The X coordinate scaling element of the 3x3 affine transformation matrix.
    serial:
 
 double m10    The Y coordinate shearing element of the 3x3 affine transformation matrix.
    serial:
 
 double m01    The X coordinate shearing element of the 3x3 affine transformation matrix.
    serial:
 
 double m11    The Y coordinate scaling element of the 3x3 affine transformation matrix.
    serial:
 
 double m02    The X coordinate of the translation element of the 3x3 affine transformation matrix.
    serial:
 
 double m12    The Y coordinate of the translation element of the 3x3 affine transformation matrix.
    serial:
 
transient  int state    This field keeps track of which components of the matrix need to be applied when performing a transformation. 
Constructor:
 public 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 - 
 public AffineTransform(float[] flatmatrix) 
 public AffineTransform(double[] flatmatrix) 
 public AffineTransform(float m00,
    float m10,
    float m01,
    float m11,
    float m02,
    float m12) 
 public AffineTransform(double m00,
    double m10,
    double m01,
    double m11,
    double m02,
    double m12)
Method from java.awt.geom.AffineTransform Summary:
clone,   concatenate,   createInverse,   createTransformedShape,   deltaTransform,   deltaTransform,   equals,   getDeterminant,   getMatrix,   getQuadrantRotateInstance,   getQuadrantRotateInstance,   getRotateInstance,   getRotateInstance,   getRotateInstance,   getRotateInstance,   getScaleInstance,   getScaleX,   getScaleY,   getShearInstance,   getShearX,   getShearY,   getTranslateInstance,   getTranslateX,   getTranslateY,   getType,   hashCode,   inverseTransform,   inverseTransform,   invert,   isIdentity,   preConcatenate,   quadrantRotate,   quadrantRotate,   rotate,   rotate,   rotate,   rotate,   scale,   setToIdentity,   setToQuadrantRotation,   setToQuadrantRotation,   setToRotation,   setToRotation,   setToRotation,   setToRotation,   setToScale,   setToShear,   setToTranslation,   setTransform,   setTransform,   shear,   toString,   transform,   transform,   transform,   transform,   transform,   transform,   translate,   updateState
Methods from java.lang.Object:
clone,   equals,   finalize,   getClass,   hashCode,   notify,   notifyAll,   toString,   wait,   wait,   wait
Method from java.awt.geom.AffineTransform Detail:
 public Object clone()
    Returns a copy of this AffineTransform object.
 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]

 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.

 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.
 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.
 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].
 public boolean equals(Object obj)
    Returns true if this AffineTransform represents the same affine coordinate transform as the specified argument.
 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   |

 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 }
 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.
 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.
 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.
 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));

 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.
 public static AffineTransform getRotateInstance(double vecx,
    double vecy,
    double anchorx,
    double anchory)
    Returns a transform that rotates coordinates around an anchor point accordinate 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);

 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   ]

 public double getScaleX()
    Returns the X coordinate scaling element (m00) of the 3x3 affine transformation matrix.
 public double getScaleY()
    Returns the Y coordinate scaling element (m11) of the 3x3 affine transformation matrix.
 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   ]

 public double getShearX()
    Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.
 public double getShearY()
    Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.
 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   ]

 public double getTranslateX()
    Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.
 public double getTranslateY()
    Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.
 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 appriopriate 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.
 public int hashCode()
    Returns the hashcode for this transform.
 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.
 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].
 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.

 public boolean isIdentity()
    Returns true if this AffineTransform is an identity transform.
 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]

 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.
 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.
 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.
 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));

 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.
 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);

 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   ]

 public  void setToIdentity()
    Resets this transform to the Identity transform.
 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.
 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.
 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.
 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));

 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.
 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);

 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   ]

 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   ]

 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   ]

 public  void setTransform(AffineTransform Tx)
    Sets this transform to a copy of the transform in the specified AffineTransform object.
 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.
 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   ]

 public String toString()
    Returns a String that represents the value of this Object .
 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.
 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.

 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].
 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].
 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].
 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].
 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   ]

  void updateState()
    Manually recalculates the state of the transform when the matrix changes too much to predict the effects on the state. The following table specifies what the various settings of the state field say about the values of the corresponding matrix element fields. Note that the rules governing the SCALE fields are slightly different depending on whether the SHEAR flag is also set. 
                        SCALE            SHEAR          TRANSLATE
                   m00/m11          m01/m10          m02/m12

IDENTITY             1.0              0.0              0.0
TRANSLATE (TR)       1.0              0.0          not both 0.0
SCALE (SC)       not both 1.0         0.0              0.0
TR | SC          not both 1.0         0.0          not both 0.0
SHEAR (SH)           0.0          not both 0.0         0.0
TR | SH              0.0          not both 0.0     not both 0.0
SC | SH          not both 0.0     not both 0.0         0.0
TR | SC | SH     not both 0.0     not both 0.0     not both 0.0