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AffineTransform.javaAPI DocJava SE 5 API100777Fri Aug 26 14:56:52 BST 2005java.awt.geom

AffineTransform

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 ]
version
1.71, 12/19/03
author
Jim Graham

Fields Summary
private static final int
TYPE_UNKNOWN
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.
private static final int
HI_SHIFT
private static final int
HI_IDENTITY
private static final int
HI_TRANSLATE
private static final int
HI_SCALE
private static final int
HI_SHEAR
double
m00
The X coordinate scaling element of the 3x3 affine transformation matrix.
double
m10
The Y coordinate shearing element of the 3x3 affine transformation matrix.
double
m01
The X coordinate shearing element of the 3x3 affine transformation matrix.
double
m11
The Y coordinate scaling element of the 3x3 affine transformation matrix.
double
m02
The X coordinate of the translation element of the 3x3 affine transformation matrix.
double
m12
The Y coordinate of the translation element of the 3x3 affine transformation matrix.
transient int
state
This field keeps track of which components of the matrix need to be applied when performing a transformation.
private transient int
type
This field caches the current transformation type of the matrix.
private static int[]
rot90conversion
Constructors Summary
private AffineTransform(double m00, double m10, double m01, double m11, double m02, double m12, int state)


        
			       
			       
			      
	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	this.state = state;
	this.type = TYPE_UNKNOWN;
public AffineTransform()
Constructs a new AffineTransform representing the Identity transformation.

	m00 = m11 = 1.0;
	// m01 = m10 = m02 = m12 = 0.0;		/* Not needed. */
	// state = APPLY_IDENTITY;		/* Not needed. */
	// type = TYPE_IDENTITY;		/* Not needed. */
public AffineTransform(AffineTransform Tx)
Constructs a new AffineTransform that is a copy of the specified AffineTransform object.

param
Tx the AffineTransform object to copy

	this.m00 = Tx.m00;
	this.m10 = Tx.m10;
	this.m01 = Tx.m01;
	this.m11 = Tx.m11;
	this.m02 = Tx.m02;
	this.m12 = Tx.m12;
	this.state = Tx.state;
	this.type = Tx.type;
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.

param
m00, m01, m02, m10, m11, m12 the 6 floating point values that compose the 3x3 transformation matrix

	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
public AffineTransform(float[] flatmatrix)
Constructs a new AffineTransform from an array of floating point values representing either the 4 non-translation enries or the 6 specifiable entries of the 3x3 transformation matrix. The values are retrieved from the array as { m00 m10 m01 m11 [m02 m12]}.

param
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.

	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	    m02 = flatmatrix[4];
	    m12 = flatmatrix[5];
	}
	updateState();
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.

param
m00, m01, m02, m10, m11, m12 the 6 floating point values that compose the 3x3 transformation matrix

	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
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]}.

param
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.

	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	    m02 = flatmatrix[4];
	    m12 = flatmatrix[5];
	}
	updateState();
Methods Summary
private static double_matround(double matval)

	return Math.rint(matval * 1E15) / 1E15;
private voidcalculateType()
This is the utility function to calculate the flag bits when they have not been cached.

see
#getType

	int ret = TYPE_IDENTITY;
	boolean sgn0, sgn1;
	double M0, M1, M2, M3;
	updateState();
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	case (APPLY_SHEAR | APPLY_SCALE):
	    if ((M0 = m00) * (M2 = m01) + (M3 = m10) * (M1 = m11) != 0) {
		// Transformed unit vectors are not perpendicular...
		this.type = TYPE_GENERAL_TRANSFORM;
		return;
	    }
	    sgn0 = (M0 >= 0.0);
	    sgn1 = (M1 >= 0.0);
	    if (sgn0 == sgn1) {
		// sgn(M0) == sgn(M1) therefore sgn(M2) == -sgn(M3)
		// This is the "unflipped" (right-handed) state
		if (M0 != M1 || M2 != -M3) {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_GENERAL_SCALE);
		} else if (M0 * M1 - M2 * M3 != 1.0) {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_UNIFORM_SCALE);
		} else {
		    ret |= TYPE_GENERAL_ROTATION;
		}
	    } else {
		// sgn(M0) == -sgn(M1) therefore sgn(M2) == sgn(M3)
		// This is the "flipped" (left-handed) state
		if (M0 != -M1 || M2 != M3) {
		    ret |= (TYPE_GENERAL_ROTATION |
			    TYPE_FLIP |
			    TYPE_GENERAL_SCALE);
		} else if (M0 * M1 - M2 * M3 != 1.0) {
		    ret |= (TYPE_GENERAL_ROTATION |
			    TYPE_FLIP |
			    TYPE_UNIFORM_SCALE);
		} else {
		    ret |= (TYPE_GENERAL_ROTATION | TYPE_FLIP);
		}
	    }
	    break;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	case (APPLY_SHEAR):
	    sgn0 = ((M0 = m01) >= 0.0);
	    sgn1 = ((M1 = m10) >= 0.0);
	    if (sgn0 != sgn1) {
		// Different signs - simple 90 degree rotation
		if (M0 != -M1) {
		    ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		} else if (M0 != 1.0 && M0 != -1.0) {
		    ret |= (TYPE_QUADRANT_ROTATION | TYPE_UNIFORM_SCALE);
		} else {
		    ret |= TYPE_QUADRANT_ROTATION;
		}
	    } else {
		// Same signs - 90 degree rotation plus an axis flip too
		if (M0 == M1) {
		    ret |= (TYPE_QUADRANT_ROTATION |
			    TYPE_FLIP |
			    TYPE_UNIFORM_SCALE);
		} else {
		    ret |= (TYPE_QUADRANT_ROTATION |
			    TYPE_FLIP |
			    TYPE_GENERAL_SCALE);
		}
	    }
	    break;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    /* NOBREAK */
	case (APPLY_SCALE):
	    sgn0 = ((M0 = m00) >= 0.0);
	    sgn1 = ((M1 = m11) >= 0.0);
	    if (sgn0 == sgn1) {
		if (sgn0) {
		    // Both scaling factors non-negative - simple scale
		    // Note: APPLY_SCALE implies M0, M1 are not both 1
		    if (M0 == M1) {
			ret |= TYPE_UNIFORM_SCALE;
		    } else {
			ret |= TYPE_GENERAL_SCALE;
		    }
		} else {
		    // Both scaling factors negative - 180 degree rotation
		    if (M0 != M1) {
			ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		    } else if (M0 != -1.0) {
			ret |= (TYPE_QUADRANT_ROTATION | TYPE_UNIFORM_SCALE);
		    } else {
			ret |= TYPE_QUADRANT_ROTATION;
		    }
		}
	    } else {
		// Scaling factor signs different - flip about some axis
		if (M0 == -M1) {
		    if (M0 == 1.0 || M0 == -1.0) {
			ret |= TYPE_FLIP;
		    } else {
			ret |= (TYPE_FLIP | TYPE_UNIFORM_SCALE);
		    }
		} else {
		    ret |= (TYPE_FLIP | TYPE_GENERAL_SCALE);
		}
	    }
	    break;
	case (APPLY_TRANSLATE):
	    ret = TYPE_TRANSLATION;
	    break;
	case (APPLY_IDENTITY):
	    break;
	}
	this.type = ret;
public java.lang.Objectclone()
Returns a copy of this AffineTransform object.

return
an Object that is a copy of this AffineTransform object.

	try {
	    return super.clone();
	} catch (CloneNotSupportedException e) { 
	    // this shouldn't happen, since we are Cloneable
	    throw new InternalError();
	}
public voidconcatenate(java.awt.geom.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]

param
Tx the AffineTransform object to be concatenated with this AffineTransform object.
see
#preConcatenate

        double M0, M1;
	double T00, T01, T10, T11;
	double T02, T12;
	int mystate = state;
	int txstate = Tx.state;
	switch ((txstate << HI_SHIFT) | mystate) {

	    /* ---------- Tx == IDENTITY cases ---------- */
	case (HI_IDENTITY | APPLY_IDENTITY):
	case (HI_IDENTITY | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SCALE):
	case (HI_IDENTITY | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SHEAR):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    return;

	    /* ---------- this == IDENTITY cases ---------- */
	case (HI_SHEAR | HI_SCALE | HI_TRANSLATE | APPLY_IDENTITY):
	    m01 = Tx.m01;
	    m10 = Tx.m10;
	    /* NOBREAK */
	case (HI_SCALE | HI_TRANSLATE | APPLY_IDENTITY):
	    m00 = Tx.m00;
	    m11 = Tx.m11;
	    /* NOBREAK */
	case (HI_TRANSLATE | APPLY_IDENTITY):
	    m02 = Tx.m02;
	    m12 = Tx.m12;
	    state = txstate;
	    type = Tx.type;
	    return;
	case (HI_SHEAR | HI_SCALE | APPLY_IDENTITY):
	    m01 = Tx.m01;
	    m10 = Tx.m10;
	    /* NOBREAK */
	case (HI_SCALE | APPLY_IDENTITY):
	    m00 = Tx.m00;
	    m11 = Tx.m11;
	    state = txstate;
	    type = Tx.type;
	    return;
	case (HI_SHEAR | HI_TRANSLATE | APPLY_IDENTITY):
	    m02 = Tx.m02;
	    m12 = Tx.m12;
	    /* NOBREAK */
	case (HI_SHEAR | APPLY_IDENTITY):
	    m01 = Tx.m01;
	    m10 = Tx.m10;
            m00 = m11 = 0.0;
	    state = txstate;
	    type = Tx.type;
	    return;

	    /* ---------- Tx == TRANSLATE cases ---------- */
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE):
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SHEAR):
	case (HI_TRANSLATE | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SCALE):
	case (HI_TRANSLATE | APPLY_TRANSLATE):
	    translate(Tx.m02, Tx.m12);
	    return;

	    /* ---------- Tx == SCALE cases ---------- */
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE):
	case (HI_SCALE | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR):
	case (HI_SCALE | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SCALE):
	case (HI_SCALE | APPLY_TRANSLATE):
	    scale(Tx.m00, Tx.m11);
	    return;

	    /* ---------- Tx == SHEAR cases ---------- */
	case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE):
	    T01 = Tx.m01; T10 = Tx.m10;
	    M0 = m00;
	    m00 = m01 * T10;
	    m01 = M0 * T01;
	    M0 = m10;
	    m10 = m11 * T10;
	    m11 = M0 * T01;
	    type = TYPE_UNKNOWN;
	    return;
	case (HI_SHEAR | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SHEAR):
	    m00 = m01 * Tx.m10;
	    m01 = 0.0;
	    m11 = m10 * Tx.m01;
	    m10 = 0.0;
	    state = mystate ^ (APPLY_SHEAR | APPLY_SCALE);
	    type = TYPE_UNKNOWN;
	    return;
	case (HI_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SCALE):
	    m01 = m00 * Tx.m01;
	    m00 = 0.0;
	    m10 = m11 * Tx.m10;
	    m11 = 0.0;
	    state = mystate ^ (APPLY_SHEAR | APPLY_SCALE);
	    type = TYPE_UNKNOWN;
	    return;
	case (HI_SHEAR | APPLY_TRANSLATE):
	    m00 = 0.0;
	    m01 = Tx.m01;
	    m10 = Tx.m10;
	    m11 = 0.0;
	    state = APPLY_TRANSLATE | APPLY_SHEAR;
	    type = TYPE_UNKNOWN;
	    return;
	}
	// If Tx has more than one attribute, it is not worth optimizing
	// all of those cases...
	T00 = Tx.m00; T01 = Tx.m01; T02 = Tx.m02;
	T10 = Tx.m10; T11 = Tx.m11; T12 = Tx.m12;
	switch (mystate) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE):
	    state = mystate | txstate;
	    /* NOBREAK */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M0 = m00;
	    M1 = m01;
	    m00  = T00 * M0 + T10 * M1;
	    m01  = T01 * M0 + T11 * M1;
	    m02 += T02 * M0 + T12 * M1;

	    M0 = m10;
	    M1 = m11;
	    m10  = T00 * M0 + T10 * M1;
	    m11  = T01 * M0 + T11 * M1;
	    m12 += T02 * M0 + T12 * M1;
	    type = TYPE_UNKNOWN;
	    return;

	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    M0 = m01;
	    m00  = T10 * M0;
	    m01  = T11 * M0;
	    m02 += T12 * M0;

	    M0 = m10;
	    m10  = T00 * M0;
	    m11  = T01 * M0;
	    m12 += T02 * M0;
	    break;

	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    M0 = m00;
	    m00  = T00 * M0;
	    m01  = T01 * M0;
	    m02 += T02 * M0;

	    M0 = m11;
	    m10  = T10 * M0;
	    m11  = T11 * M0;
	    m12 += T12 * M0;
	    break;

	case (APPLY_TRANSLATE):
	    m00  = T00;
	    m01  = T01;
	    m02 += T02;

	    m10  = T10;
	    m11  = T11;
	    m12 += T12;
	    state = txstate | APPLY_TRANSLATE;
	    type = TYPE_UNKNOWN;
	    return;
	}
	updateState();
public java.awt.geom.AffineTransformcreateInverse()
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.

return
a new AffineTransform object representing the inverse transformation.
see
#getDeterminant
exception
NoninvertibleTransformException if the matrix cannot be inverted.

	double det;
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    det = m00 * m11 - m01 * m10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    return new AffineTransform( m11 / det, -m10 / det,
				       -m01 / det,  m00 / det,
				       (m01 * m12 - m11 * m02) / det,
				       (m10 * m02 - m00 * m12) / det,
				       (APPLY_SHEAR |
					APPLY_SCALE |
					APPLY_TRANSLATE));
	case (APPLY_SHEAR | APPLY_SCALE):
	    det = m00 * m11 - m01 * m10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    return new AffineTransform( m11 / det, -m10 / det,
				       -m01 / det,  m00 / det,
				        0.0,        0.0,
				       (APPLY_SHEAR | APPLY_SCALE));
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    if (m01 == 0.0 || m10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform( 0.0,        1.0 / m01,
				        1.0 / m10,  0.0,
				       -m12 / m10, -m02 / m01,
				       (APPLY_SHEAR | APPLY_TRANSLATE));
	case (APPLY_SHEAR):
	    if (m01 == 0.0 || m10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform(0.0,       1.0 / m01,
				       1.0 / m10, 0.0,
				       0.0,       0.0,
				       (APPLY_SHEAR));
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    if (m00 == 0.0 || m11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform( 1.0 / m00,  0.0,
				        0.0,        1.0 / m11,
				       -m02 / m00, -m12 / m11,
				       (APPLY_SCALE | APPLY_TRANSLATE));
	case (APPLY_SCALE):
	    if (m00 == 0.0 || m11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform(1.0 / m00, 0.0,
				       0.0,       1.0 / m11,
				       0.0,       0.0,
				       (APPLY_SCALE));
	case (APPLY_TRANSLATE):
	    return new AffineTransform( 1.0,  0.0,
				        0.0,  1.0,
				       -m02, -m12,
				       (APPLY_TRANSLATE));
	case (APPLY_IDENTITY):
	    return new AffineTransform();
	}

	/* NOTREACHED */
public java.awt.ShapecreateTransformedShape(java.awt.Shape pSrc)
Returns a new {@link Shape} object defined by the geometry of the specified Shape after it has been transformed by this transform.

param
pSrc the specified Shape object to be transformed by this transform.
return
a new Shape object that defines the geometry of the transformed Shape.

        if (pSrc == null) {
            return null;
        }
        
        if (pSrc instanceof GeneralPath) {
            return ((GeneralPath)pSrc).createTransformedShape(this);
        } else {
            PathIterator pi = pSrc.getPathIterator(this);
            GeneralPath gp = new GeneralPath(pi.getWindingRule());
	    gp.append(pi, false);
            return gp;
        }

	/* NOTREACHED */
public java.awt.geom.Point2DdeltaTransform(java.awt.geom.Point2D ptSrc, java.awt.geom.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.

param
ptSrc the distance vector to be delta transformed
param
ptDst the resulting transformed distance vector
return
ptDst, which contains the result of the transformation.

	if (ptDst == null) {
	    if (ptSrc instanceof Point2D.Double) {
		ptDst = new Point2D.Double();
	    } else {
		ptDst = new Point2D.Float();
	    }
	}
	// Copy source coords into local variables in case src == dst
	double x = ptSrc.getX();
	double y = ptSrc.getY();
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    ptDst.setLocation(x * m00 + y * m01, x * m10 + y * m11);
	    return ptDst;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    ptDst.setLocation(y * m01, x * m10);
	    return ptDst;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    ptDst.setLocation(x * m00, y * m11);
	    return ptDst;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    ptDst.setLocation(x, y);
	    return ptDst;
	}

	/* NOTREACHED */
public voiddeltaTransform(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].

param
srcPts the array containing the source distance vectors. Each vector is stored as a pair of relative x, y coordinates.
param
dstPts the array into which the transformed distance vectors are returned. Each vector is stored as a pair of relative x, y coordinates.
param
srcOff the offset to the first vector to be transformed in the source array
param
dstOff the offset to the location of the first transformed vector that is stored in the destination array
param
numPts the number of vector coordinate pairs to be transformed

	double M00, M01, M10, M11;	// For caching
	if (dstPts == srcPts &&
	    dstOff > srcOff && dstOff < srcOff + numPts * 2)
	{
	    // If the arrays overlap partially with the destination higher
	    // than the source and we transform the coordinates normally
	    // we would overwrite some of the later source coordinates
	    // with results of previous transformations.
	    // To get around this we use arraycopy to copy the points
	    // to their final destination with correct overwrite
	    // handling and then transform them in place in the new
	    // safer location.
	    System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2);
	    // srcPts = dstPts;		// They are known to be equal.
	    srcOff = dstOff;
	}
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = x * M00 + y * M01;
		dstPts[dstOff++] = x * M10 + y * M11;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = srcPts[srcOff++] * M01;
		dstPts[dstOff++] = x * M10;
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++] * M00;
		dstPts[dstOff++] = srcPts[srcOff++] * M11;
	    }
	    return;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    if (srcPts != dstPts || srcOff != dstOff) {
		System.arraycopy(srcPts, srcOff, dstPts, dstOff,
				 numPts * 2);
	    }
	    return;
	}

	/* NOTREACHED */
public booleanequals(java.lang.Object obj)
Returns true if this AffineTransform represents the same affine coordinate transform as the specified argument.

param
obj the Object to test for equality with this AffineTransform
return
true if obj equals this AffineTransform object; false otherwise.

        if (!(obj instanceof AffineTransform)) {
            return false;
        }

        AffineTransform a = (AffineTransform)obj;

	return ((m00 == a.m00) && (m01 == a.m01) && (m02 == a.m02) &&
		(m10 == a.m10) && (m11 == a.m11) && (m12 == a.m12));
public doublegetDeterminant()
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 {@link 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 |

return
the determinant of the matrix used to transform the coordinates.
see
#getType
see
#createInverse
see
#inverseTransform
see
#TYPE_UNIFORM_SCALE

	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    return m00 * m11 - m01 * m10;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    return -(m01 * m10);
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    return m00 * m11;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    return 1.0;
	}
public voidgetMatrix(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 }

param
flatmatrix the double array used to store the returned values.
see
#getScaleX
see
#getScaleY
see
#getShearX
see
#getShearY
see
#getTranslateX
see
#getTranslateY

	flatmatrix[0] = m00;
	flatmatrix[1] = m10;
	flatmatrix[2] = m01;
	flatmatrix[3] = m11;
	if (flatmatrix.length > 5) {
	    flatmatrix[4] = m02;
	    flatmatrix[5] = m12;
	}
public static java.awt.geom.AffineTransformgetRotateInstance(double theta, double x, double y)
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.setToTranslation(x, y); // S3: final translation
Tx.rotate(theta); // S2: rotate around anchor
Tx.translate(-x, -y); // 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 with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians
param
x, y the coordinates of the anchor point of the rotation
return
an AffineTransform object that rotates coordinates around the specified point by the specified angle of rotation.

	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta, x, y);
	return Tx;
public static java.awt.geom.AffineTransformgetRotateInstance(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 with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians
return
an AffineTransform object that is a rotation transformation, created with the specified angle of rotation.

	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta);
	return Tx;
public static java.awt.geom.AffineTransformgetScaleInstance(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 ]

param
sx the factor by which coordinates are scaled along the X axis direction
param
sy the factor by which coordinates are scaled along the Y axis direction
return
an AffineTransform object that scales coordinates by the specified factors.

	AffineTransform Tx = new AffineTransform();
	Tx.setToScale(sx, sy);
	return Tx;
public doublegetScaleX()
Returns the X coordinate scaling element (m00) of the 3x3 affine transformation matrix.

return
a double value that is the X coordinate of the scaling element of the affine transformation matrix.
see
#getMatrix

	return m00;
public doublegetScaleY()
Returns the Y coordinate scaling element (m11) of the 3x3 affine transformation matrix.

return
a double value that is the Y coordinate of the scaling element of the affine transformation matrix.
see
#getMatrix

	return m11;
public static java.awt.geom.AffineTransformgetShearInstance(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 ]

param
shx the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
param
shy the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate
return
an AffineTransform object that shears coordinates by the specified multipliers.

	AffineTransform Tx = new AffineTransform();
	Tx.setToShear(shx, shy);
	return Tx;
public doublegetShearX()
Returns the X coordinate shearing element (m01) of the 3x3 affine transformation matrix.

return
a double value that is the X coordinate of the shearing element of the affine transformation matrix.
see
#getMatrix

	return m01;
public doublegetShearY()
Returns the Y coordinate shearing element (m10) of the 3x3 affine transformation matrix.

return
a double value that is the Y coordinate of the shearing element of the affine transformation matrix.
see
#getMatrix

	return m10;
public static java.awt.geom.AffineTransformgetTranslateInstance(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 ]

param
tx the distance by which coordinates are translated in the X axis direction
param
ty the distance by which coordinates are translated in the Y axis direction
return
an AffineTransform object that represents a translation transformation, created with the specified vector.

	AffineTransform Tx = new AffineTransform();
	Tx.setToTranslation(tx, ty);
	return Tx;
public doublegetTranslateX()
Returns the X coordinate of the translation element (m02) of the 3x3 affine transformation matrix.

return
a double value that is the X coordinate of the translation element of the affine transformation matrix.
see
#getMatrix

	return m02;
public doublegetTranslateY()
Returns the Y coordinate of the translation element (m12) of the 3x3 affine transformation matrix.

return
a double value that is the Y coordinate of the translation element of the affine transformation matrix.
see
#getMatrix

	return m12;
public intgetType()
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.

return
the OR combination of any of the indicated flags that apply to this transform
see
#TYPE_IDENTITY
see
#TYPE_TRANSLATION
see
#TYPE_UNIFORM_SCALE
see
#TYPE_GENERAL_SCALE
see
#TYPE_QUADRANT_ROTATION
see
#TYPE_GENERAL_ROTATION
see
#TYPE_GENERAL_TRANSFORM

	if (type == TYPE_UNKNOWN) {
	    calculateType();
	}
	return type;
public inthashCode()
Returns the hashcode for this transform.

return
a hash code for this transform.

	long bits = Double.doubleToLongBits(m00);
	bits = bits * 31 + Double.doubleToLongBits(m01);
	bits = bits * 31 + Double.doubleToLongBits(m02);
	bits = bits * 31 + Double.doubleToLongBits(m10);
	bits = bits * 31 + Double.doubleToLongBits(m11);
	bits = bits * 31 + Double.doubleToLongBits(m12);
	return (((int) bits) ^ ((int) (bits >> 32)));
public java.awt.geom.Point2DinverseTransform(java.awt.geom.Point2D ptSrc, java.awt.geom.Point2D ptDst)
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.

param
ptSrc the point to be inverse transformed
param
ptDst the resulting transformed point
return
ptDst, which contains the result of the inverse transform.
exception
NoninvertibleTransformException if the matrix cannot be inverted.

	if (ptDst == null) {
	    if (ptSrc instanceof Point2D.Double) {
		ptDst = new Point2D.Double();
	    } else {
		ptDst = new Point2D.Float();
	    }
	}
	// Copy source coords into local variables in case src == dst
	double x = ptSrc.getX();
	double y = ptSrc.getY();
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    x -= m02;
	    y -= m12;
	    /* NOBREAK */
	case (APPLY_SHEAR | APPLY_SCALE):
	    double det = m00 * m11 - m01 * m10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    ptDst.setLocation((x * m11 - y * m01) / det,
			      (y * m00 - x * m10) / det);
	    return ptDst;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    x -= m02;
	    y -= m12;
	    /* NOBREAK */
	case (APPLY_SHEAR):
	    if (m01 == 0.0 || m10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    ptDst.setLocation(y / m10, x / m01);
	    return ptDst;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    x -= m02;
	    y -= m12;
	    /* NOBREAK */
	case (APPLY_SCALE):
	    if (m00 == 0.0 || m11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    ptDst.setLocation(x / m00, y / m11);
	    return ptDst;
	case (APPLY_TRANSLATE):
	    ptDst.setLocation(x - m02, y - m12);
	    return ptDst;
	case (APPLY_IDENTITY):
	    ptDst.setLocation(x, y);
	    return ptDst;
	}

	/* NOTREACHED */
public voidinverseTransform(double[] srcPts, int srcOff, double[] dstPts, int dstOff, int numPts)
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].

param
srcPts the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
param
dstPts the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
param
srcOff the offset to the first point to be transformed in the source array
param
dstOff the offset to the location of the first transformed point that is stored in the destination array
param
numPts the number of point objects to be transformed
exception
NoninvertibleTransformException if the matrix cannot be inverted.

	double M00, M01, M02, M10, M11, M12;	// For caching
	double det;
	if (dstPts == srcPts &&
	    dstOff > srcOff && dstOff < srcOff + numPts * 2)
	{
	    // If the arrays overlap partially with the destination higher
	    // than the source and we transform the coordinates normally
	    // we would overwrite some of the later source coordinates
	    // with results of previous transformations.
	    // To get around this we use arraycopy to copy the points
	    // to their final destination with correct overwrite
	    // handling and then transform them in place in the new
	    // safer location.
	    System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2);
	    // srcPts = dstPts;		// They are known to be equal.
	    srcOff = dstOff;
	}
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M01 = m01; M02 = m02;
	    M10 = m10; M11 = m11; M12 = m12;
	    det = M00 * M11 - M01 * M10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++] - M02;
		double y = srcPts[srcOff++] - M12;
		dstPts[dstOff++] = (x * M11 - y * M01) / det;
		dstPts[dstOff++] = (y * M00 - x * M10) / det;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    det = M00 * M11 - M01 * M10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = (x * M11 - y * M01) / det;
		dstPts[dstOff++] = (y * M00 - x * M10) / det;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M01 = m01; M02 = m02;
	    M10 = m10; M12 = m12;
	    if (M01 == 0.0 || M10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++] - M02;
		dstPts[dstOff++] = (srcPts[srcOff++] - M12) / M10;
		dstPts[dstOff++] = x / M01;
	    }
	    return;
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    if (M01 == 0.0 || M10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = srcPts[srcOff++] / M10;
		dstPts[dstOff++] = x / M01;
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M02 = m02;
	    M11 = m11; M12 = m12;
	    if (M00 == 0.0 || M11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (srcPts[srcOff++] - M02) / M00;
		dstPts[dstOff++] = (srcPts[srcOff++] - M12) / M11;
	    }
	    return;
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    if (M00 == 0.0 || M11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++] / M00;
		dstPts[dstOff++] = srcPts[srcOff++] / M11;
	    }
	    return;
	case (APPLY_TRANSLATE):
	    M02 = m02; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++] - M02;
		dstPts[dstOff++] = srcPts[srcOff++] - M12;
	    }
	    return;
	case (APPLY_IDENTITY):
	    if (srcPts != dstPts || srcOff != dstOff) {
		System.arraycopy(srcPts, srcOff, dstPts, dstOff,
				 numPts * 2);
	    }
	    return;
	}

	/* NOTREACHED */
public booleanisIdentity()
Returns true if this AffineTransform is an identity transform.

return
true if this AffineTransform is an identity transform; false otherwise.

        return (state == APPLY_IDENTITY || (getType() == TYPE_IDENTITY));
public voidpreConcatenate(java.awt.geom.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]

param
Tx the AffineTransform object to be concatenated with this AffineTransform object.
see
#concatenate

	double M0, M1;
	double T00, T01, T10, T11;
	double T02, T12;
	int mystate = state;
	int txstate = Tx.state;
	switch ((txstate << HI_SHIFT) | mystate) {
	case (HI_IDENTITY | APPLY_IDENTITY):
	case (HI_IDENTITY | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SCALE):
	case (HI_IDENTITY | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SHEAR):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE):
	case (HI_IDENTITY | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    // Tx is IDENTITY...
	    return;

	case (HI_TRANSLATE | APPLY_IDENTITY):
	case (HI_TRANSLATE | APPLY_SCALE):
	case (HI_TRANSLATE | APPLY_SHEAR):
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE):
	    // Tx is TRANSLATE, this has no TRANSLATE
	    m02 = Tx.m02;
	    m12 = Tx.m12;
	    state = mystate | APPLY_TRANSLATE;
	    type |= TYPE_TRANSLATION;
	    return;

	case (HI_TRANSLATE | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    // Tx is TRANSLATE, this has one too
	    m02 = m02 + Tx.m02;
	    m12 = m12 + Tx.m12;
	    return;

	case (HI_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_IDENTITY):
	    // Only these two existing states need a new state
	    state = mystate | APPLY_SCALE;
	    /* NOBREAK */
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE):
	case (HI_SCALE | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR):
	case (HI_SCALE | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SCALE):
	    // Tx is SCALE, this is anything
	    T00 = Tx.m00;
	    T11 = Tx.m11;
	    if ((mystate & APPLY_SHEAR) != 0) {
		m01 = m01 * T00;
		m10 = m10 * T11;
		if ((mystate & APPLY_SCALE) != 0) {
		    m00 = m00 * T00;
		    m11 = m11 * T11;
		}
	    } else {
		m00 = m00 * T00;
		m11 = m11 * T11;
	    }
	    if ((mystate & APPLY_TRANSLATE) != 0) {
		m02 = m02 * T00;
		m12 = m12 * T11;
	    }
	    type = TYPE_UNKNOWN;
	    return;
	case (HI_SHEAR | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SHEAR):
	    mystate = mystate | APPLY_SCALE;
	    /* NOBREAK */
	case (HI_SHEAR | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_IDENTITY):
	case (HI_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SCALE):
	    state = mystate ^ APPLY_SHEAR;
	    /* NOBREAK */
	case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SHEAR | APPLY_SHEAR | APPLY_SCALE):
	    // Tx is SHEAR, this is anything
	    T01 = Tx.m01;
	    T10 = Tx.m10;

	    M0 = m00;
	    m00 = m10 * T01;
	    m10 = M0 * T10;

	    M0 = m01;
	    m01 = m11 * T01;
	    m11 = M0 * T10;

	    M0 = m02;
	    m02 = m12 * T01;
	    m12 = M0 * T10;
	    type = TYPE_UNKNOWN;
	    return;
	}
	// If Tx has more than one attribute, it is not worth optimizing
	// all of those cases...
	T00 = Tx.m00; T01 = Tx.m01; T02 = Tx.m02;
	T10 = Tx.m10; T11 = Tx.m11; T12 = Tx.m12;
	switch (mystate) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M0 = m02;
	    M1 = m12;
	    T02 += M0 * T00 + M1 * T01;
	    T12 += M0 * T10 + M1 * T11;

	    /* NOBREAK */
	case (APPLY_SHEAR | APPLY_SCALE):
	    m02 = T02;
	    m12 = T12;

	    M0 = m00;
	    M1 = m10;
	    m00 = M0 * T00 + M1 * T01;
	    m10 = M0 * T10 + M1 * T11;

	    M0 = m01;
	    M1 = m11;
	    m01 = M0 * T00 + M1 * T01;
	    m11 = M0 * T10 + M1 * T11;
	    break;

	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M0 = m02;
	    M1 = m12;
	    T02 += M0 * T00 + M1 * T01;
	    T12 += M0 * T10 + M1 * T11;

	    /* NOBREAK */
	case (APPLY_SHEAR):
	    m02 = T02;
	    m12 = T12;

	    M0 = m10;
	    m00 = M0 * T01;
	    m10 = M0 * T11;

	    M0 = m01;
	    m01 = M0 * T00;
	    m11 = M0 * T10;
	    break;

	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M0 = m02;
	    M1 = m12;
	    T02 += M0 * T00 + M1 * T01;
	    T12 += M0 * T10 + M1 * T11;

	    /* NOBREAK */
	case (APPLY_SCALE):
	    m02 = T02;
	    m12 = T12;

	    M0 = m00;
	    m00 = M0 * T00;
	    m10 = M0 * T10;

	    M0 = m11;
	    m01 = M0 * T01;
	    m11 = M0 * T11;
	    break;

	case (APPLY_TRANSLATE):
	    M0 = m02;
	    M1 = m12;
	    T02 += M0 * T00 + M1 * T01;
	    T12 += M0 * T10 + M1 * T11;

	    /* NOBREAK */
	case (APPLY_IDENTITY):
	    m02 = T02;
	    m12 = T12;

	    m00 = T00;
	    m10 = T10;

	    m01 = T01;
	    m11 = T11;

	    state = mystate | txstate;
	    type = TYPE_UNKNOWN;
	    return;
	}
	updateState();
private voidreadObject(java.io.ObjectInputStream s)

	s.defaultReadObject();
	updateState();
public voidrotate(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 with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians

	double sin = Math.sin(theta);
	double cos = Math.cos(theta);
	if (Math.abs(sin) < 1E-15) {
	    if (cos < 0.0) {
		m00 = -m00;
		m11 = -m11;
		int state = this.state;
		if ((state & (APPLY_SHEAR)) != 0) {
		    // If there was a shear, then this rotation has no
		    // effect on the state.
		    m01 = -m01;
		    m10 = -m10;
		} else {
		    // No shear means the SCALE state may toggle when
		    // m00 and m11 are negated.
		    if (m00 == 1.0 && m11 == 1.0) {
			this.state = state & ~APPLY_SCALE;
		    } else {
			this.state = state | APPLY_SCALE;
		    }
		}
		type = TYPE_UNKNOWN;
	    }
	    return;
	}
	if (Math.abs(cos) < 1E-15) {
	    if (sin < 0.0) {
		double M0 = m00;
		m00 = -m01;
		m01 = M0;
		M0 = m10;
		m10 = -m11;
		m11 = M0;
	    } else {
		double M0 = m00;
		m00 = m01;
		m01 = -M0;
		M0 = m10;
		m10 = m11;
		m11 = -M0;
	    }
	    int state = rot90conversion[this.state];
	    if ((state & (APPLY_SHEAR | APPLY_SCALE)) == APPLY_SCALE &&
		m00 == 1.0 && m11 == 1.0)
	    {
		state -= APPLY_SCALE;
	    }
	    this.state = state;
	    type = TYPE_UNKNOWN;
	    return;
	}
	double M0, M1;
	M0 = m00;
	M1 = m01;
	m00 =  cos * M0 + sin * M1;
	m01 = -sin * M0 + cos * M1;
	M0 = m10;
	M1 = m11;
	m10 =  cos * M0 + sin * M1;
	m11 = -sin * M0 + cos * M1;
	updateState();
public voidrotate(double theta, double x, double y)
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(x, y); // S3: final translation
rotate(theta); // S2: rotate around anchor
translate(-x, -y); // S1: translate anchor to origin
Rotating with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians
param
x, y the coordinates of the anchor point of the rotation


                                                                          		 	   				    		 	                                                
            
	// REMIND: Simple for now - optimize later
	translate(x, y);
	rotate(theta);
	translate(-x, -y);
public voidscale(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 ]

param
sx the factor by which coordinates are scaled along the X axis direction
param
sy the factor by which coordinates are scaled along the Y axis direction

	int state = this.state;
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    m00 *= sx;
	    m11 *= sy;
	    /* NOBREAK */
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    m01 *= sy;
	    m10 *= sx;
	    if (m01 == 0 && m10 == 0) {
		this.state = state - APPLY_SHEAR;
		// REMIND: Is it possible for m00 and m11 to be both 1.0?
	    }
	    this.type = TYPE_UNKNOWN;
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    m00 *= sx;
	    m11 *= sy;
	    if (m00 == 1.0 && m11 == 1.0) {
		this.state = (state &= APPLY_TRANSLATE);
		this.type = (state == APPLY_IDENTITY
			     ? TYPE_IDENTITY
			     : TYPE_TRANSLATION);
	    } else {
		this.type = TYPE_UNKNOWN;
	    }
	    return;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    m00 = sx;
	    m11 = sy;
	    if (sx != 1.0 || sy != 1.0) {
		this.state = state | APPLY_SCALE;
		this.type = TYPE_UNKNOWN;
	    }
	    return;
	}
public voidsetToIdentity()
Resets this transform to the Identity transform.

	m00 = m11 = 1.0;
	m10 = m01 = m02 = m12 = 0.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
public voidsetToRotation(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 with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians

	m02 = 0.0;
	m12 = 0.0;
	double sin = Math.sin(theta);
	double cos = Math.cos(theta);
	if (Math.abs(sin) < 1E-15) {
	    m01 = m10 = 0.0;
	    if (cos < 0) {
		m00 = m11 = -1.0;
		state = APPLY_SCALE;
		type = TYPE_QUADRANT_ROTATION;
	    } else {
		m00 = m11 = 1.0;
		state = APPLY_IDENTITY;
		type = TYPE_IDENTITY;
	    }
	    return;
	}
	if (Math.abs(cos) < 1E-15) {
	    m00 = m11 = 0.0;
	    if (sin < 0.0) {
		m01 = 1.0;
		m10 = -1.0;
	    } else {
		m01 = -1.0;
		m10 = 1.0;
	    }
	    state = APPLY_SHEAR;
	    type = TYPE_QUADRANT_ROTATION;
	    return;
	}
	m00 = cos;
	m01 = -sin;
	m10 = sin;
	m11 = cos;
	state = APPLY_SHEAR | APPLY_SCALE;
	type = TYPE_GENERAL_ROTATION;
	return;
public voidsetToRotation(double theta, double x, double y)
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(x, y); // S3: final translation
rotate(theta); // S2: rotate around anchor
translate(-x, -y); // 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 with a positive angle theta rotates points on the positive x axis toward the positive y axis.

param
theta the angle of rotation in radians
param
x, y the coordinates of the anchor point of the rotation

	setToRotation(theta);
	double sin = m10;
	double oneMinusCos = 1.0 - m00;
	m02 = x * oneMinusCos + y * sin;
	m12 = y * oneMinusCos - x * sin;
	if (m02 != 0.0 || m12 != 0.0) {
	    state |= APPLY_TRANSLATE;
	    type |= TYPE_TRANSLATION;
	}
	return;
public voidsetToScale(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 ]

param
sx the factor by which coordinates are scaled along the X axis direction
param
sy the factor by which coordinates are scaled along the Y axis direction

	m00 = sx;
	m10 = 0.0;
	m01 = 0.0;
	m11 = sy;
	m02 = 0.0;
	m12 = 0.0;
	if (sx != 1.0 || sy != 1.0) {
	    state = APPLY_SCALE;
	    type = TYPE_UNKNOWN;
	} else {
	    state = APPLY_IDENTITY;
	    type = TYPE_IDENTITY;
	}
public voidsetToShear(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 ]

param
shx the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
param
shy the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate

	m00 = 1.0;
	m01 = shx;
	m10 = shy;
	m11 = 1.0;
	m02 = 0.0;
	m12 = 0.0;
	if (shx != 0.0 || shy != 0.0) {
	    state = (APPLY_SHEAR | APPLY_SCALE);
	    type = TYPE_UNKNOWN;
	} else {
	    state = APPLY_IDENTITY;
	    type = TYPE_IDENTITY;
	}
public voidsetToTranslation(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 ]

param
tx the distance by which coordinates are translated in the X axis direction
param
ty the distance by which coordinates are translated in the Y axis direction

	m00 = 1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = 1.0;
	m02 = tx;
	m12 = ty;
	if (tx != 0.0 || ty != 0.0) {
	    state = APPLY_TRANSLATE;
	    type = TYPE_TRANSLATION;
	} else {
	    state = APPLY_IDENTITY;
	    type = TYPE_IDENTITY;
	}
public voidsetTransform(java.awt.geom.AffineTransform Tx)
Sets this transform to a copy of the transform in the specified AffineTransform object.

param
Tx the AffineTransform object from which to copy the transform

	this.m00 = Tx.m00;
	this.m10 = Tx.m10;
	this.m01 = Tx.m01;
	this.m11 = Tx.m11;
	this.m02 = Tx.m02;
	this.m12 = Tx.m12;
	this.state = Tx.state;
	this.type = Tx.type;
public voidsetTransform(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.

param
m00, m01, m02, m10, m11, m12 the 6 floating point values that compose the 3x3 transformation matrix

	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
public voidshear(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 ]

param
shx the multiplier by which coordinates are shifted in the direction of the positive X axis as a factor of their Y coordinate
param
shy the multiplier by which coordinates are shifted in the direction of the positive Y axis as a factor of their X coordinate

	int state = this.state;
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    double M0, M1;
	    M0 = m00;
	    M1 = m01;
	    m00 = M0 + M1 * shy;
	    m01 = M0 * shx + M1;

	    M0 = m10;
	    M1 = m11;
	    m10 = M0 + M1 * shy;
	    m11 = M0 * shx + M1;
	    updateState();
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    m00 = m01 * shy;
	    m11 = m10 * shx;
	    if (m00 != 0.0 || m11 != 0.0) {
		this.state = state | APPLY_SCALE;
	    }
	    this.type = TYPE_UNKNOWN;
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    m01 = m00 * shx;
	    m10 = m11 * shy;
	    if (m01 != 0.0 || m10 != 0.0) {
		this.state = state | APPLY_SHEAR;
	    }
	    this.type = TYPE_UNKNOWN;
	    return;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    m01 = shx;
	    m10 = shy;
	    if (m01 != 0.0 || m10 != 0.0) {
		this.state = state | APPLY_SCALE | APPLY_SHEAR;
		this.type = TYPE_UNKNOWN;
	    }
	    return;
	}
private voidstateError()

	throw new InternalError("missing case in transform state switch");
public java.lang.StringtoString()
Returns a String that represents the value of this {@link Object}.

return
a String representing the value of this Object.

	return ("AffineTransform[["
		+ _matround(m00) + ", "
		+ _matround(m01) + ", "
		+ _matround(m02) + "], ["
		+ _matround(m10) + ", "
		+ _matround(m11) + ", "
		+ _matround(m12) + "]]");
public java.awt.geom.Point2Dtransform(java.awt.geom.Point2D ptSrc, java.awt.geom.Point2D ptDst)
Transforms the specified ptSrc and stores the result in ptDst. If ptDst is null, a new {@link 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.

param
ptSrc the specified Point2D to be transformed
param
ptDst the specified Point2D that stores the result of transforming ptSrc
return
the ptDst after transforming ptSrc and stroring the result in ptDst.

	if (ptDst == null) {
	    if (ptSrc instanceof Point2D.Double) {
		ptDst = new Point2D.Double();
	    } else {
		ptDst = new Point2D.Float();
	    }
	}
	// Copy source coords into local variables in case src == dst
	double x = ptSrc.getX();
	double y = ptSrc.getY();
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    ptDst.setLocation(x * m00 + y * m01 + m02,
			      x * m10 + y * m11 + m12);
	    return ptDst;
	case (APPLY_SHEAR | APPLY_SCALE):
	    ptDst.setLocation(x * m00 + y * m01, x * m10 + y * m11);
	    return ptDst;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    ptDst.setLocation(y * m01 + m02, x * m10 + m12);
	    return ptDst;
	case (APPLY_SHEAR):
	    ptDst.setLocation(y * m01, x * m10);
	    return ptDst;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    ptDst.setLocation(x * m00 + m02, y * m11 + m12);
	    return ptDst;
	case (APPLY_SCALE):
	    ptDst.setLocation(x * m00, y * m11);
	    return ptDst;
	case (APPLY_TRANSLATE):
	    ptDst.setLocation(x + m02, y + m12);
	    return ptDst;
	case (APPLY_IDENTITY):
	    ptDst.setLocation(x, y);
	    return ptDst;
	}

	/* NOTREACHED */
public voidtransform(java.awt.geom.Point2D[] ptSrc, int srcOff, java.awt.geom.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.

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

	int state = this.state;
        while (--numPts >= 0) {
            // Copy source coords into local variables in case src == dst
	    Point2D src = ptSrc[srcOff++];
            double x = src.getX();
            double y = src.getY();
	    Point2D dst = ptDst[dstOff++];
	    if (dst == null) {
		if (src instanceof Point2D.Double) {
		    dst = new Point2D.Double();
		} else {
		    dst = new Point2D.Float();
		}
		ptDst[dstOff - 1] = dst;
	    }
	    switch (state) {
	    default:
		stateError();
		/* NOTREACHED */
	    case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
		dst.setLocation(x * m00 + y * m01 + m02,
				x * m10 + y * m11 + m12);
		break;
	    case (APPLY_SHEAR | APPLY_SCALE):
		dst.setLocation(x * m00 + y * m01, x * m10 + y * m11);
		break;
	    case (APPLY_SHEAR | APPLY_TRANSLATE):
		dst.setLocation(y * m01 + m02, x * m10 + m12);
		break;
	    case (APPLY_SHEAR):
		dst.setLocation(y * m01, x * m10);
		break;
	    case (APPLY_SCALE | APPLY_TRANSLATE):
		dst.setLocation(x * m00 + m02, y * m11 + m12);
		break;
	    case (APPLY_SCALE):
		dst.setLocation(x * m00, y * m11);
		break;
	    case (APPLY_TRANSLATE):
		dst.setLocation(x + m02, y + m12);
		break;
	    case (APPLY_IDENTITY):
		dst.setLocation(x, y);
		break;
	    }
	}

	/* NOTREACHED */
public voidtransform(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].

param
srcPts the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
param
dstPts the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
param
srcOff the offset to the first point to be transformed in the source array
param
dstOff the offset to the location of the first transformed point that is stored in the destination array
param
numPts the number of points to be transformed

	double M00, M01, M02, M10, M11, M12;	// For caching
	if (dstPts == srcPts &&
	    dstOff > srcOff && dstOff < srcOff + numPts * 2)
	{
	    // If the arrays overlap partially with the destination higher
	    // than the source and we transform the coordinates normally
	    // we would overwrite some of the later source coordinates
	    // with results of previous transformations.
	    // To get around this we use arraycopy to copy the points
	    // to their final destination with correct overwrite
	    // handling and then transform them in place in the new
	    // safer location.
	    System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2);
	    // srcPts = dstPts;		// They are known to be equal.
	    srcOff = dstOff;
	}
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M01 = m01; M02 = m02;
	    M10 = m10; M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M00 * x + M01 * y + M02);
		dstPts[dstOff++] = (float) (M10 * x + M11 * y + M12);
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M00 * x + M01 * y);
		dstPts[dstOff++] = (float) (M10 * x + M11 * y);
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M01 = m01; M02 = m02;
	    M10 = m10; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (M10 * x + M12);
	    }
	    return;
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++]);
		dstPts[dstOff++] = (float) (M10 * x);
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M02 = m02;
	    M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++] + M12);
	    }
	    return;
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++]);
		dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++]);
	    }
	    return;
	case (APPLY_TRANSLATE):
	    M02 = m02; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (srcPts[srcOff++] + M12);
	    }
	    return;
	case (APPLY_IDENTITY):
	    if (srcPts != dstPts || srcOff != dstOff) {
		System.arraycopy(srcPts, srcOff, dstPts, dstOff,
				 numPts * 2);
	    }
	    return;
	}

	/* NOTREACHED */
public voidtransform(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].

param
srcPts the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
param
dstPts the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
param
srcOff the offset to the first point to be transformed in the source array
param
dstOff the offset to the location of the first transformed point that is stored in the destination array
param
numPts the number of point objects to be transformed

	double M00, M01, M02, M10, M11, M12;	// For caching
	if (dstPts == srcPts &&
	    dstOff > srcOff && dstOff < srcOff + numPts * 2)
	{
	    // If the arrays overlap partially with the destination higher
	    // than the source and we transform the coordinates normally
	    // we would overwrite some of the later source coordinates
	    // with results of previous transformations.
	    // To get around this we use arraycopy to copy the points
	    // to their final destination with correct overwrite
	    // handling and then transform them in place in the new
	    // safer location.
	    System.arraycopy(srcPts, srcOff, dstPts, dstOff, numPts * 2);
	    // srcPts = dstPts;		// They are known to be equal.
	    srcOff = dstOff;
	}
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M01 = m01; M02 = m02;
	    M10 = m10; M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = M00 * x + M01 * y + M02;
		dstPts[dstOff++] = M10 * x + M11 * y + M12;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = M00 * x + M01 * y;
		dstPts[dstOff++] = M10 * x + M11 * y;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M01 = m01; M02 = m02;
	    M10 = m10; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = M01 * srcPts[srcOff++] + M02;
		dstPts[dstOff++] = M10 * x + M12;
	    }
	    return;
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = M01 * srcPts[srcOff++];
		dstPts[dstOff++] = M10 * x;
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M02 = m02;
	    M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = M00 * srcPts[srcOff++] + M02;
		dstPts[dstOff++] = M11 * srcPts[srcOff++] + M12;
	    }
	    return;
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = M00 * srcPts[srcOff++];
		dstPts[dstOff++] = M11 * srcPts[srcOff++];
	    }
	    return;
	case (APPLY_TRANSLATE):
	    M02 = m02; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++] + M02;
		dstPts[dstOff++] = srcPts[srcOff++] + M12;
	    }
	    return;
	case (APPLY_IDENTITY):
	    if (srcPts != dstPts || srcOff != dstOff) {
		System.arraycopy(srcPts, srcOff, dstPts, dstOff,
				 numPts * 2);
	    }
	    return;
	}

	/* NOTREACHED */
public voidtransform(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].

param
srcPts the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
param
dstPts the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
param
srcOff the offset to the first point to be transformed in the source array
param
dstOff the offset to the location of the first transformed point that is stored in the destination array
param
numPts the number of points to be transformed

	double M00, M01, M02, M10, M11, M12;	// For caching
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M01 = m01; M02 = m02;
	    M10 = m10; M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = M00 * x + M01 * y + M02;
		dstPts[dstOff++] = M10 * x + M11 * y + M12;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = M00 * x + M01 * y;
		dstPts[dstOff++] = M10 * x + M11 * y;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M01 = m01; M02 = m02;
	    M10 = m10; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = M01 * srcPts[srcOff++] + M02;
		dstPts[dstOff++] = M10 * x + M12;
	    }
	    return;
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = M01 * srcPts[srcOff++];
		dstPts[dstOff++] = M10 * x;
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M02 = m02;
	    M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = M00 * srcPts[srcOff++] + M02;
		dstPts[dstOff++] = M11 * srcPts[srcOff++] + M12;
	    }
	    return;
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = M00 * srcPts[srcOff++];
		dstPts[dstOff++] = M11 * srcPts[srcOff++];
	    }
	    return;
	case (APPLY_TRANSLATE):
	    M02 = m02; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++] + M02;
		dstPts[dstOff++] = srcPts[srcOff++] + M12;
	    }
	    return;
	case (APPLY_IDENTITY):
	    while (--numPts >= 0) {
		dstPts[dstOff++] = srcPts[srcOff++];
		dstPts[dstOff++] = srcPts[srcOff++];
	    }
	    return;
	}

	/* NOTREACHED */
public voidtransform(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].

param
srcPts the array containing the source point coordinates. Each point is stored as a pair of x, y coordinates.
param
dstPts the array into which the transformed point coordinates are returned. Each point is stored as a pair of x, y coordinates.
param
srcOff the offset to the first point to be transformed in the source array
param
dstOff the offset to the location of the first transformed point that is stored in the destination array
param
numPts the number of point objects to be transformed

	double M00, M01, M02, M10, M11, M12;	// For caching
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M01 = m01; M02 = m02;
	    M10 = m10; M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M00 * x + M01 * y + M02);
		dstPts[dstOff++] = (float) (M10 * x + M11 * y + M12);
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    M00 = m00; M01 = m01;
	    M10 = m10; M11 = m11;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		double y = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M00 * x + M01 * y);
		dstPts[dstOff++] = (float) (M10 * x + M11 * y);
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    M01 = m01; M02 = m02;
	    M10 = m10; M12 = m12;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (M10 * x + M12);
	    }
	    return;
	case (APPLY_SHEAR):
	    M01 = m01; M10 = m10;
	    while (--numPts >= 0) {
		double x = srcPts[srcOff++];
		dstPts[dstOff++] = (float) (M01 * srcPts[srcOff++]);
		dstPts[dstOff++] = (float) (M10 * x);
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    M00 = m00; M02 = m02;
	    M11 = m11; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++] + M12);
	    }
	    return;
	case (APPLY_SCALE):
	    M00 = m00; M11 = m11;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (M00 * srcPts[srcOff++]);
		dstPts[dstOff++] = (float) (M11 * srcPts[srcOff++]);
	    }
	    return;
	case (APPLY_TRANSLATE):
	    M02 = m02; M12 = m12;
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (srcPts[srcOff++] + M02);
		dstPts[dstOff++] = (float) (srcPts[srcOff++] + M12);
	    }
	    return;
	case (APPLY_IDENTITY):
	    while (--numPts >= 0) {
		dstPts[dstOff++] = (float) (srcPts[srcOff++]);
		dstPts[dstOff++] = (float) (srcPts[srcOff++]);
	    }
	    return;
	}

	/* NOTREACHED */
public voidtranslate(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 ]

param
tx the distance by which coordinates are translated in the X axis direction
param
ty the distance by which coordinates are translated in the Y axis direction

	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    m02 = tx * m00 + ty * m01 + m02;
	    m12 = tx * m10 + ty * m11 + m12;
	    if (m02 == 0.0 && m12 == 0.0) {
		state = APPLY_SHEAR | APPLY_SCALE;
		if (type != TYPE_UNKNOWN) {
		    type -= TYPE_TRANSLATION;
		}
	    }
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    m02 = tx * m00 + ty * m01;
	    m12 = tx * m10 + ty * m11;
	    if (m02 != 0.0 || m12 != 0.0) {
		state = APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE;
		type |= TYPE_TRANSLATION;
	    }
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    m02 = ty * m01 + m02;
	    m12 = tx * m10 + m12;
	    if (m02 == 0.0 && m12 == 0.0) {
		state = APPLY_SHEAR;
		if (type != TYPE_UNKNOWN) {
		    type -= TYPE_TRANSLATION;
		}
	    }
	    return;
	case (APPLY_SHEAR):
	    m02 = ty * m01;
	    m12 = tx * m10;
	    if (m02 != 0.0 || m12 != 0.0) {
		state = APPLY_SHEAR | APPLY_TRANSLATE;
		type |= TYPE_TRANSLATION;
	    }
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    m02 = tx * m00 + m02;
	    m12 = ty * m11 + m12;
	    if (m02 == 0.0 && m12 == 0.0) {
		state = APPLY_SCALE;
		if (type != TYPE_UNKNOWN) {
		    type -= TYPE_TRANSLATION;
		}
	    }
	    return;
	case (APPLY_SCALE):
	    m02 = tx * m00;
	    m12 = ty * m11;
	    if (m02 != 0.0 || m12 != 0.0) {
		state = APPLY_SCALE | APPLY_TRANSLATE;
		type |= TYPE_TRANSLATION;
	    }
	    return;
	case (APPLY_TRANSLATE):
	    m02 = tx + m02;
	    m12 = ty + m12;
	    if (m02 == 0.0 && m12 == 0.0) {
		state = APPLY_IDENTITY;
		type = TYPE_IDENTITY;
	    }
	    return;
	case (APPLY_IDENTITY):
	    m02 = tx;
	    m12 = ty;
	    if (tx != 0.0 || ty != 0.0) {
		state = APPLY_TRANSLATE;
		type = TYPE_TRANSLATION;
	    }
	    return;
	}
voidupdateState()
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


	if (m01 == 0.0 && m10 == 0.0) {
	    if (m00 == 1.0 && m11 == 1.0) {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = APPLY_IDENTITY;
		    type = TYPE_IDENTITY;
		} else {
		    state = APPLY_TRANSLATE;
		    type = TYPE_TRANSLATION;
		}
	    } else {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = APPLY_SCALE;
		    type = TYPE_UNKNOWN;
		} else {
		    state = (APPLY_SCALE | APPLY_TRANSLATE);
		    type = TYPE_UNKNOWN;
		}
	    }
	} else {
	    if (m00 == 0.0 && m11 == 0.0) {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = APPLY_SHEAR;
		    type = TYPE_UNKNOWN;
		} else {
		    state = (APPLY_SHEAR | APPLY_TRANSLATE);
		    type = TYPE_UNKNOWN;
		}
	    } else {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = (APPLY_SHEAR | APPLY_SCALE);
		    type = TYPE_UNKNOWN;
		} else {
		    state = (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE);
		    type = TYPE_UNKNOWN;
		}
	    }
	}
private voidwriteObject(java.io.ObjectOutputStream s)

	s.defaultWriteObject();