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	/*
	* Copyright (c) 1996, 2013, Oracle and/or its affiliates. All rights reserved.
	* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
	*
	* This code is free software; you can redistribute it and/or modify it
	* under the terms of the GNU General Public License version 2 only, as
	* published by the Free Software Foundation. Oracle designates this
	* particular file as subject to the "Classpath" exception as provided
	* by Oracle in the LICENSE file that accompanied this code.
	*
	* This code is distributed in the hope that it will be useful, but WITHOUT
	* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
	* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
	* version 2 for more details (a copy is included in the LICENSE file that
	* accompanied this code).
	*
	* You should have received a copy of the GNU General Public License version
	* 2 along with this work; if not, write to the Free Software Foundation,
	* Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
	*
	* Please contact Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
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	package java.awt.geom;

	import java.awt.Shape;
	import java.beans.ConstructorProperties;

	/**
	* The <code>AffineTransform</code> 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.
	* <p>
	* 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:
	* <pre>
	* [ x'] [ m00 m01 m02 ] [ x ] [ m00x + m01y + m02 ]
	* [ y'] = [ m10 m11 m12 ] [ y ] = [ m10x + m11y + m12 ]
	* [ 1 ] [ 0 0 1 ] [ 1 ] [ 1 ]
	* </pre>
	* <h3><a name="quadrantapproximation">Handling 90-Degree Rotations</a></h3>
	* <p>
	* In some variations of the <code>rotate</code> methods in the
	* <code>AffineTransform</code> 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.
	* <p>
	* Since 90 degrees is represented as <code>PI/2</code> 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 <code>PI/2</code> but never close enough
	* for the sine or cosine to be exactly 0.0, 1.0 or -1.0.
	* The implementations of <code>Math.sin()</code> and
	* <code>Math.cos()</code> correspondingly never return 0.0
	* for any case other than <code>Math.sin(0.0)</code>.
	* 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.
	* <p>
	* The net result of these issues is that if the
	* <code>Math.sin()</code> and <code>Math.cos()</code> 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 <code>rotate(Math.PI/2.0)</code>,
	* 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.
	* <p>
	* 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 <em>theta</em> as a quadrant
	* rotation if either <code>Math.sin(<em>theta</em>)</code> or
	* <code>Math.cos(<em>theta</em>)</code> 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 <code>Math.PI/2.0</code>.
	*
	* @author Jim Graham
	* @since 1.2
	*/
	public class AffineTransform implements Cloneable, java.io.Serializable {

	/*
	* This constant is only useful for the cached type field.
	* It indicates that the type has been decached and must be recalculated.
	*/
	private static final int TYPE_UNKNOWN = -1;

	/**
	* 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.
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_IDENTITY = 0;

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_TRANSLATION = 1;

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_UNIFORM_SCALE = 2;

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_GENERAL_SCALE = 4;

	/**
	* This constant is a bit mask for any of the scale flag bits.
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @since 1.2
	*/
	public static final int TYPE_MASK_SCALE = (TYPE_UNIFORM_SCALE \|
	TYPE_GENERAL_SCALE);

	/**
	* 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.
	* @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
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_FLIP = 64;
	/* NOTE: TYPE_FLIP was added after GENERAL_TRANSFORM was in public
	* circulation and the flag bits could no longer be conveniently
	* renumbered without introducing binary incompatibility in outside
	* code.
	*/

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_QUADRANT_ROTATION = 8;

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_GENERAL_ROTATION = 16;

	/**
	* This constant is a bit mask for any of the rotation flag bits.
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @since 1.2
	*/
	public static final int TYPE_MASK_ROTATION = (TYPE_QUADRANT_ROTATION \|
	TYPE_GENERAL_ROTATION);

	/**
	* 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.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #getType
	* @since 1.2
	*/
	public static final int TYPE_GENERAL_TRANSFORM = 32;

	/**
	* 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.
	* @see #APPLY_TRANSLATE
	* @see #APPLY_SCALE
	* @see #APPLY_SHEAR
	* @see #state
	*/
	static final int APPLY_IDENTITY = 0;

	/**
	* 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.
	* @see #APPLY_IDENTITY
	* @see #APPLY_SCALE
	* @see #APPLY_SHEAR
	* @see #state
	*/
	static final int APPLY_TRANSLATE = 1;

	/**
	* 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.
	* @see #APPLY_IDENTITY
	* @see #APPLY_TRANSLATE
	* @see #APPLY_SHEAR
	* @see #state
	*/
	static final int APPLY_SCALE = 2;

	/**
	* 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.
	* @see #APPLY_IDENTITY
	* @see #APPLY_TRANSLATE
	* @see #APPLY_SCALE
	* @see #state
	*/
	static final int APPLY_SHEAR = 4;

	/*
	* For methods which combine together the state of two separate
	* transforms and dispatch based upon the combination, these constants
	* specify how far to shift one of the states so that the two states
	* are mutually non-interfering and provide constants for testing the
	* bits of the shifted (HI) state. The methods in this class use
	* the convention that the state of "this" transform is unshifted and
	* the state of the "other" or "argument" transform is shifted (HI).
	*/
	private static final int HI_SHIFT = 3;
	private static final int HI_IDENTITY = APPLY_IDENTITY << HI_SHIFT;
	private static final int HI_TRANSLATE = APPLY_TRANSLATE << HI_SHIFT;
	private static final int HI_SCALE = APPLY_SCALE << HI_SHIFT;
	private static final int HI_SHEAR = APPLY_SHEAR << HI_SHIFT;

	/**
	* The X coordinate scaling element of the 3x3
	* affine transformation matrix.
	*
	* @serial
	*/
	double m00;

	/**
	* The Y coordinate shearing element of the 3x3
	* affine transformation matrix.
	*
	* @serial
	*/
	double m10;

	/**
	* The X coordinate shearing element of the 3x3
	* affine transformation matrix.
	*
	* @serial
	*/
	double m01;

	/**
	* The Y coordinate scaling element of the 3x3
	* affine transformation matrix.
	*
	* @serial
	*/
	double m11;

	/**
	* The X coordinate of the translation element of the
	* 3x3 affine transformation matrix.
	*
	* @serial
	*/
	double m02;

	/**
	* The Y coordinate of the translation element of the
	* 3x3 affine transformation matrix.
	*
	* @serial
	*/
	double m12;

	/**
	* This field keeps track of which components of the matrix need to
	* be applied when performing a transformation.
	* @see #APPLY_IDENTITY
	* @see #APPLY_TRANSLATE
	* @see #APPLY_SCALE
	* @see #APPLY_SHEAR
	*/
	transient int state;

	/**
	* This field caches the current transformation type of the matrix.
	* @see #TYPE_IDENTITY
	* @see #TYPE_TRANSLATION
	* @see #TYPE_UNIFORM_SCALE
	* @see #TYPE_GENERAL_SCALE
	* @see #TYPE_FLIP
	* @see #TYPE_QUADRANT_ROTATION
	* @see #TYPE_GENERAL_ROTATION
	* @see #TYPE_GENERAL_TRANSFORM
	* @see #TYPE_UNKNOWN
	* @see #getType
	*/
	private transient int type;

	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;
	}

	/**
	* Constructs a new <code>AffineTransform</code> representing the
	* Identity transformation.
	* @since 1.2
	*/
	public AffineTransform() {
	m00 = m11 = 1.0;
	// m01 = m10 = m02 = m12 = 0.0; /* Not needed. */
	// state = APPLY_IDENTITY; /* Not needed. */
	// type = TYPE_IDENTITY; /* Not needed. */
	}

	/**
	* Constructs a new <code>AffineTransform</code> that is a copy of
	* the specified <code>AffineTransform</code> object.
	* @param Tx the <code>AffineTransform</code> object to copy
	* @since 1.2
	*/
	public AffineTransform(AffineTransform Tx) {
	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;
	}

	/**
	* Constructs a new <code>AffineTransform</code> from 6 floating point
	* values representing the 6 specifiable entries of the 3x3
	* transformation matrix.
	*
	* @param m00 the X coordinate scaling element of the 3x3 matrix
	* @param m10 the Y coordinate shearing element of the 3x3 matrix
	* @param m01 the X coordinate shearing element of the 3x3 matrix
	* @param m11 the Y coordinate scaling element of the 3x3 matrix
	* @param m02 the X coordinate translation element of the 3x3 matrix
	* @param m12 the Y coordinate translation element of the 3x3 matrix
	* @since 1.2
	*/
	@ConstructorProperties({ "scaleX", "shearY", "shearX", "scaleY", "translateX", "translateY" })
	public AffineTransform(float m00, float m10,
	float m01, float m11,
	float m02, float m12) {
	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
	}

	/**
	* Constructs a new <code>AffineTransform</code> from an array of
	* floating point values representing either the 4 non-translation
	* entries or the 6 specifiable entries of the 3x3 transformation
	* matrix. The values are retrieved from the array as
	* { m00 m10 m01 m11 [m02 m12]}.
	* @param flatmatrix the float array containing the values to be set
	* in the new <code>AffineTransform</code> object. The length of the
	* array is assumed to be at least 4. If the length of the array is
	* less than 6, only the first 4 values are taken. If the length of
	* the array is greater than 6, the first 6 values are taken.
	* @since 1.2
	*/
	public AffineTransform(float[] flatmatrix) {
	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	m02 = flatmatrix[4];
	m12 = flatmatrix[5];
	}
	updateState();
	}

	/**
	* Constructs a new <code>AffineTransform</code> from 6 double
	* precision values representing the 6 specifiable entries of the 3x3
	* transformation matrix.
	*
	* @param m00 the X coordinate scaling element of the 3x3 matrix
	* @param m10 the Y coordinate shearing element of the 3x3 matrix
	* @param m01 the X coordinate shearing element of the 3x3 matrix
	* @param m11 the Y coordinate scaling element of the 3x3 matrix
	* @param m02 the X coordinate translation element of the 3x3 matrix
	* @param m12 the Y coordinate translation element of the 3x3 matrix
	* @since 1.2
	*/
	public AffineTransform(double m00, double m10,
	double m01, double m11,
	double m02, double m12) {
	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
	}

	/**
	* Constructs a new <code>AffineTransform</code> 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 <code>AffineTransform</code> object. The length of the
	* array is assumed to be at least 4. If the length of the array is
	* less than 6, only the first 4 values are taken. If the length of
	* the array is greater than 6, the first 6 values are taken.
	* @since 1.2
	*/
	public AffineTransform(double[] flatmatrix) {
	m00 = flatmatrix[0];
	m10 = flatmatrix[1];
	m01 = flatmatrix[2];
	m11 = flatmatrix[3];
	if (flatmatrix.length > 5) {
	m02 = flatmatrix[4];
	m12 = flatmatrix[5];
	}
	updateState();
	}

	/**
	* Returns a transform representing a translation transformation.
	* The matrix representing the returned transform is:
	* <pre>
	* [ 1 0 tx ]
	* [ 0 1 ty ]
	* [ 0 0 1 ]
	* </pre>
	* @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 <code>AffineTransform</code> object that represents a
	* translation transformation, created with the specified vector.
	* @since 1.2
	*/
	public static AffineTransform getTranslateInstance(double tx, double ty) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToTranslation(tx, ty);
	return Tx;
	}

	/**
	* Returns a transform representing a rotation transformation.
	* The matrix representing the returned transform is:
	* <pre>
	* [ cos(theta) -sin(theta) 0 ]
	* [ sin(theta) cos(theta) 0 ]
	* [ 0 0 1 ]
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	* @param theta the angle of rotation measured in radians
	* @return an <code>AffineTransform</code> object that is a rotation
	* transformation, created with the specified angle of rotation.
	* @since 1.2
	*/
	public static AffineTransform getRotateInstance(double theta) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta);
	return Tx;
	}

	/**
	* 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).
	* <p>
	* This operation is equivalent to the following sequence of calls:
	* <pre>
	* 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
	* </pre>
	* The matrix representing the returned transform is:
	* <pre>
	* [ cos(theta) -sin(theta) x-xcos+ysin ]
	* [ sin(theta) cos(theta) y-xsin-ycos ]
	* [ 0 0 1 ]
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	*
	* @param theta the angle of rotation measured in radians
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @return an <code>AffineTransform</code> object that rotates
	* coordinates around the specified point by the specified angle of
	* rotation.
	* @since 1.2
	*/
	public static AffineTransform getRotateInstance(double theta,
	double anchorx,
	double anchory)
	{
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta, anchorx, anchory);
	return Tx;
	}

	/**
	* 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 <code>vecx</code> and <code>vecy</code> are 0.0,
	* an identity transform is returned.
	* This operation is equivalent to calling:
	* <pre>
	* AffineTransform.getRotateInstance(Math.atan2(vecy, vecx));
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @return an <code>AffineTransform</code> object that rotates
	* coordinates according to the specified rotation vector.
	* @since 1.6
	*/
	public static AffineTransform getRotateInstance(double vecx, double vecy) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(vecx, vecy);
	return Tx;
	}

	/**
	* Returns a transform that rotates coordinates around an anchor
	* point according to a rotation vector.
	* All coordinates rotate about the specified anchor coordinates
	* by the same amount.
	* The amount of rotation is such that coordinates along the former
	* positive X axis will subsequently align with the vector pointing
	* from the origin to the specified vector coordinates.
	* If both <code>vecx</code> and <code>vecy</code> are 0.0,
	* an identity transform is returned.
	* This operation is equivalent to calling:
	* <pre>
	* AffineTransform.getRotateInstance(Math.atan2(vecy, vecx),
	* anchorx, anchory);
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @return an <code>AffineTransform</code> object that rotates
	* coordinates around the specified point according to the
	* specified rotation vector.
	* @since 1.6
	*/
	public static AffineTransform getRotateInstance(double vecx,
	double vecy,
	double anchorx,
	double anchory)
	{
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(vecx, vecy, anchorx, anchory);
	return Tx;
	}

	/**
	* Returns a transform that rotates coordinates by the specified
	* number of quadrants.
	* This operation is equivalent to calling:
	* <pre>
	* AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @return an <code>AffineTransform</code> object that rotates
	* coordinates by the specified number of quadrants.
	* @since 1.6
	*/
	public static AffineTransform getQuadrantRotateInstance(int numquadrants) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToQuadrantRotation(numquadrants);
	return Tx;
	}

	/**
	* Returns a transform that rotates coordinates by the specified
	* number of quadrants around the specified anchor point.
	* This operation is equivalent to calling:
	* <pre>
	* AffineTransform.getRotateInstance(numquadrants * Math.PI / 2.0,
	* anchorx, anchory);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	*
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @return an <code>AffineTransform</code> object that rotates
	* coordinates by the specified number of quadrants around the
	* specified anchor point.
	* @since 1.6
	*/
	public static AffineTransform getQuadrantRotateInstance(int numquadrants,
	double anchorx,
	double anchory)
	{
	AffineTransform Tx = new AffineTransform();
	Tx.setToQuadrantRotation(numquadrants, anchorx, anchory);
	return Tx;
	}

	/**
	* Returns a transform representing a scaling transformation.
	* The matrix representing the returned transform is:
	* <pre>
	* [ sx 0 0 ]
	* [ 0 sy 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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 <code>AffineTransform</code> object that scales
	* coordinates by the specified factors.
	* @since 1.2
	*/
	public static AffineTransform getScaleInstance(double sx, double sy) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToScale(sx, sy);
	return Tx;
	}

	/**
	* Returns a transform representing a shearing transformation.
	* The matrix representing the returned transform is:
	* <pre>
	* [ 1 shx 0 ]
	* [ shy 1 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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 <code>AffineTransform</code> object that shears
	* coordinates by the specified multipliers.
	* @since 1.2
	*/
	public static AffineTransform getShearInstance(double shx, double shy) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToShear(shx, shy);
	return Tx;
	}

	/**
	* Retrieves the flag bits describing the conversion properties of
	* this transform.
	* The return value is either one of the constants TYPE_IDENTITY
	* or TYPE_GENERAL_TRANSFORM, or a combination of the
	* appropriate flag bits.
	* A valid combination of flag bits is an exclusive OR operation
	* that can combine
	* the TYPE_TRANSLATION flag bit
	* in addition to either of the
	* TYPE_UNIFORM_SCALE or TYPE_GENERAL_SCALE flag bits
	* as well as either of the
	* TYPE_QUADRANT_ROTATION or TYPE_GENERAL_ROTATION flag bits.
	* @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
	* @since 1.2
	*/
	public int getType() {
	if (type == TYPE_UNKNOWN) {
	calculateType();
	}
	return type;
	}

	/**
	* This is the utility function to calculate the flag bits when
	* they have not been cached.
	* @see #getType
	*/
	@SuppressWarnings("fallthrough")
	private void calculateType() {
	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;
	}

	/**
	* 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.
	* <p>
	* 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.
	* <p>
	* If this transform represents a uniform scale, as indicated by
	* the <code>getType</code> 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.
	* <p>
	* Mathematically, the determinant is calculated using the formula:
	* <pre>
	* \| m00 m01 m02 \|
	* \| m10 m11 m12 \| = m00 * m11 - m01 * m10
	* \| 0 0 1 \|
	* </pre>
	*
	* @return the determinant of the matrix used to transform the
	* coordinates.
	* @see #getType
	* @see #createInverse
	* @see #inverseTransform
	* @see #TYPE_UNIFORM_SCALE
	* @since 1.2
	*/
	@SuppressWarnings("fallthrough")
	public double getDeterminant() {
	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;
	}
	}

	/**
	* 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.
	* <pre>
	* 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
	* </pre>
	*/
	void updateState() {
	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;
	}
	}
	}
	}

	/*
	* Convenience method used internally to throw exceptions when
	* a case was forgotten in a switch statement.
	*/
	private void stateError() {
	throw new InternalError("missing case in transform state switch");
	}

	/**
	* 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
	* @since 1.2
	*/
	public void getMatrix(double[] flatmatrix) {
	flatmatrix[0] = m00;
	flatmatrix[1] = m10;
	flatmatrix[2] = m01;
	flatmatrix[3] = m11;
	if (flatmatrix.length > 5) {
	flatmatrix[4] = m02;
	flatmatrix[5] = m12;
	}
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getScaleX() {
	return m00;
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getScaleY() {
	return m11;
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getShearX() {
	return m01;
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getShearY() {
	return m10;
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getTranslateX() {
	return m02;
	}

	/**
	* 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
	* @since 1.2
	*/
	public double getTranslateY() {
	return m12;
	}

	/**
	* Concatenates this transform with a translation transformation.
	* This is equivalent to calling concatenate(T), where T is an
	* <code>AffineTransform</code> represented by the following matrix:
	* <pre>
	* [ 1 0 tx ]
	* [ 0 1 ty ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	public void translate(double tx, double ty) {
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return;
	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;
	}
	}

	// Utility methods to optimize rotate methods.
	// These tables translate the flags during predictable quadrant
	// rotations where the shear and scale values are swapped and negated.
	private static final int rot90conversion[] = {
	/* IDENTITY => */ APPLY_SHEAR,
	/* TRANSLATE (TR) => */ APPLY_SHEAR \| APPLY_TRANSLATE,
	/* SCALE (SC) => */ APPLY_SHEAR,
	/* SC \| TR => */ APPLY_SHEAR \| APPLY_TRANSLATE,
	/* SHEAR (SH) => */ APPLY_SCALE,
	/* SH \| TR => */ APPLY_SCALE \| APPLY_TRANSLATE,
	/* SH \| SC => */ APPLY_SHEAR \| APPLY_SCALE,
	/* SH \| SC \| TR => */ APPLY_SHEAR \| APPLY_SCALE \| APPLY_TRANSLATE,
	};
	private final void rotate90() {
	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;
	}
	private final void rotate180() {
	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;
	}
	private final void rotate270() {
	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;
	}

	/**
	* Concatenates this transform with a rotation transformation.
	* This is equivalent to calling concatenate(R), where R is an
	* <code>AffineTransform</code> represented by the following matrix:
	* <pre>
	* [ cos(theta) -sin(theta) 0 ]
	* [ sin(theta) cos(theta) 0 ]
	* [ 0 0 1 ]
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	* @param theta the angle of rotation measured in radians
	* @since 1.2
	*/
	public void rotate(double theta) {
	double sin = Math.sin(theta);
	if (sin == 1.0) {
	rotate90();
	} else if (sin == -1.0) {
	rotate270();
	} else {
	double cos = Math.cos(theta);
	if (cos == -1.0) {
	rotate180();
	} else if (cos != 1.0) {
	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();
	}
	}
	}

	/**
	* 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).
	* <p>
	* This operation is equivalent to the following sequence of calls:
	* <pre>
	* translate(anchorx, anchory); // S3: final translation
	* rotate(theta); // S2: rotate around anchor
	* translate(-anchorx, -anchory); // S1: translate anchor to origin
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	*
	* @param theta the angle of rotation measured in radians
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.2
	*/
	public void rotate(double theta, double anchorx, double anchory) {
	// REMIND: Simple for now - optimize later
	translate(anchorx, anchory);
	rotate(theta);
	translate(-anchorx, -anchory);
	}

	/**
	* 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 <code>vecx</code> and <code>vecy</code> are 0.0,
	* no additional rotation is added to this transform.
	* This operation is equivalent to calling:
	* <pre>
	* rotate(Math.atan2(vecy, vecx));
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @since 1.6
	*/
	public void rotate(double vecx, double vecy) {
	if (vecy == 0.0) {
	if (vecx < 0.0) {
	rotate180();
	}
	// If vecx > 0.0 - no rotation
	// If vecx == 0.0 - undefined rotation - treat as no rotation
	} else if (vecx == 0.0) {
	if (vecy > 0.0) {
	rotate90();
	} else { // vecy must be < 0.0
	rotate270();
	}
	} else {
	double len = Math.sqrt(vecx * vecx + vecy * vecy);
	double sin = vecy / len;
	double cos = vecx / len;
	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();
	}
	}

	/**
	* 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 <code>vecx</code> and <code>vecy</code> are 0.0,
	* the transform is not modified in any way.
	* This method is equivalent to calling:
	* <pre>
	* rotate(Math.atan2(vecy, vecx), anchorx, anchory);
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.6
	*/
	public void rotate(double vecx, double vecy,
	double anchorx, double anchory)
	{
	// REMIND: Simple for now - optimize later
	translate(anchorx, anchory);
	rotate(vecx, vecy);
	translate(-anchorx, -anchory);
	}

	/**
	* Concatenates this transform with a transform that rotates
	* coordinates by the specified number of quadrants.
	* This is equivalent to calling:
	* <pre>
	* rotate(numquadrants * Math.PI / 2.0);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @since 1.6
	*/
	public void quadrantRotate(int numquadrants) {
	switch (numquadrants & 3) {
	case 0:
	break;
	case 1:
	rotate90();
	break;
	case 2:
	rotate180();
	break;
	case 3:
	rotate270();
	break;
	}
	}

	/**
	* 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:
	* <pre>
	* rotate(numquadrants * Math.PI / 2.0, anchorx, anchory);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	*
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.6
	*/
	public void quadrantRotate(int numquadrants,
	double anchorx, double anchory)
	{
	switch (numquadrants & 3) {
	case 0:
	return;
	case 1:
	m02 += anchorx * (m00 - m01) + anchory * (m01 + m00);
	m12 += anchorx * (m10 - m11) + anchory * (m11 + m10);
	rotate90();
	break;
	case 2:
	m02 += anchorx * (m00 + m00) + anchory * (m01 + m01);
	m12 += anchorx * (m10 + m10) + anchory * (m11 + m11);
	rotate180();
	break;
	case 3:
	m02 += anchorx * (m00 + m01) + anchory * (m01 - m00);
	m12 += anchorx * (m10 + m11) + anchory * (m11 - m10);
	rotate270();
	break;
	}
	if (m02 == 0.0 && m12 == 0.0) {
	state &= ~APPLY_TRANSLATE;
	} else {
	state \|= APPLY_TRANSLATE;
	}
	}

	/**
	* Concatenates this transform with a scaling transformation.
	* This is equivalent to calling concatenate(S), where S is an
	* <code>AffineTransform</code> represented by the following matrix:
	* <pre>
	* [ sx 0 0 ]
	* [ 0 sy 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	@SuppressWarnings("fallthrough")
	public void scale(double sx, double sy) {
	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) {
	state &= APPLY_TRANSLATE;
	if (m00 == 1.0 && m11 == 1.0) {
	this.type = (state == APPLY_IDENTITY
	? TYPE_IDENTITY
	: TYPE_TRANSLATION);
	} else {
	state \|= APPLY_SCALE;
	this.type = TYPE_UNKNOWN;
	}
	this.state = state;
	}
	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;
	}
	}

	/**
	* Concatenates this transform with a shearing transformation.
	* This is equivalent to calling concatenate(SH), where SH is an
	* <code>AffineTransform</code> represented by the following matrix:
	* <pre>
	* [ 1 shx 0 ]
	* [ shy 1 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	public void shear(double shx, double shy) {
	int state = this.state;
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return;
	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;
	}
	}

	/**
	* Resets this transform to the Identity transform.
	* @since 1.2
	*/
	public void setToIdentity() {
	m00 = m11 = 1.0;
	m10 = m01 = m02 = m12 = 0.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
	}

	/**
	* Sets this transform to a translation transformation.
	* The matrix representing this transform becomes:
	* <pre>
	* [ 1 0 tx ]
	* [ 0 1 ty ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	public void setToTranslation(double tx, double ty) {
	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;
	}
	}

	/**
	* Sets this transform to a rotation transformation.
	* The matrix representing this transform becomes:
	* <pre>
	* [ cos(theta) -sin(theta) 0 ]
	* [ sin(theta) cos(theta) 0 ]
	* [ 0 0 1 ]
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	* @param theta the angle of rotation measured in radians
	* @since 1.2
	*/
	public void setToRotation(double theta) {
	double sin = Math.sin(theta);
	double cos;
	if (sin == 1.0 \|\| sin == -1.0) {
	cos = 0.0;
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	cos = Math.cos(theta);
	if (cos == -1.0) {
	sin = 0.0;
	state = APPLY_SCALE;
	type = TYPE_QUADRANT_ROTATION;
	} else if (cos == 1.0) {
	sin = 0.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
	} else {
	state = APPLY_SHEAR \| APPLY_SCALE;
	type = TYPE_GENERAL_ROTATION;
	}
	}
	m00 = cos;
	m10 = sin;
	m01 = -sin;
	m11 = cos;
	m02 = 0.0;
	m12 = 0.0;
	}

	/**
	* 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).
	* <p>
	* This operation is equivalent to the following sequence of calls:
	* <pre>
	* setToTranslation(anchorx, anchory); // S3: final translation
	* rotate(theta); // S2: rotate around anchor
	* translate(-anchorx, -anchory); // S1: translate anchor to origin
	* </pre>
	* The matrix representing this transform becomes:
	* <pre>
	* [ cos(theta) -sin(theta) x-xcos+ysin ]
	* [ sin(theta) cos(theta) y-xsin-ycos ]
	* [ 0 0 1 ]
	* </pre>
	* Rotating by a positive angle theta rotates points on the positive
	* X axis toward the positive Y axis.
	* Note also the discussion of
	* <a href="#quadrantapproximation">Handling 90-Degree Rotations</a>
	* above.
	*
	* @param theta the angle of rotation measured in radians
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.2
	*/
	public void setToRotation(double theta, double anchorx, double anchory) {
	setToRotation(theta);
	double sin = m10;
	double oneMinusCos = 1.0 - m00;
	m02 = anchorx * oneMinusCos + anchory * sin;
	m12 = anchory * oneMinusCos - anchorx * sin;
	if (m02 != 0.0 \|\| m12 != 0.0) {
	state \|= APPLY_TRANSLATE;
	type \|= TYPE_TRANSLATION;
	}
	}

	/**
	* 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 <code>vecx</code> and <code>vecy</code> are 0.0,
	* the transform is set to an identity transform.
	* This operation is equivalent to calling:
	* <pre>
	* setToRotation(Math.atan2(vecy, vecx));
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @since 1.6
	*/
	public void setToRotation(double vecx, double vecy) {
	double sin, cos;
	if (vecy == 0) {
	sin = 0.0;
	if (vecx < 0.0) {
	cos = -1.0;
	state = APPLY_SCALE;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	cos = 1.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
	}
	} else if (vecx == 0) {
	cos = 0.0;
	sin = (vecy > 0.0) ? 1.0 : -1.0;
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	double len = Math.sqrt(vecx * vecx + vecy * vecy);
	cos = vecx / len;
	sin = vecy / len;
	state = APPLY_SHEAR \| APPLY_SCALE;
	type = TYPE_GENERAL_ROTATION;
	}
	m00 = cos;
	m10 = sin;
	m01 = -sin;
	m11 = cos;
	m02 = 0.0;
	m12 = 0.0;
	}

	/**
	* 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 <code>vecx</code> and <code>vecy</code> are 0.0,
	* the transform is set to an identity transform.
	* This operation is equivalent to calling:
	* <pre>
	* setToTranslation(Math.atan2(vecy, vecx), anchorx, anchory);
	* </pre>
	*
	* @param vecx the X coordinate of the rotation vector
	* @param vecy the Y coordinate of the rotation vector
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.6
	*/
	public void setToRotation(double vecx, double vecy,
	double anchorx, double anchory)
	{
	setToRotation(vecx, vecy);
	double sin = m10;
	double oneMinusCos = 1.0 - m00;
	m02 = anchorx * oneMinusCos + anchory * sin;
	m12 = anchory * oneMinusCos - anchorx * sin;
	if (m02 != 0.0 \|\| m12 != 0.0) {
	state \|= APPLY_TRANSLATE;
	type \|= TYPE_TRANSLATION;
	}
	}

	/**
	* Sets this transform to a rotation transformation that rotates
	* coordinates by the specified number of quadrants.
	* This operation is equivalent to calling:
	* <pre>
	* setToRotation(numquadrants * Math.PI / 2.0);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @since 1.6
	*/
	public void setToQuadrantRotation(int numquadrants) {
	switch (numquadrants & 3) {
	case 0:
	m00 = 1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = 1.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
	break;
	case 1:
	m00 = 0.0;
	m10 = 1.0;
	m01 = -1.0;
	m11 = 0.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	break;
	case 2:
	m00 = -1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = -1.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_SCALE;
	type = TYPE_QUADRANT_ROTATION;
	break;
	case 3:
	m00 = 0.0;
	m10 = -1.0;
	m01 = 1.0;
	m11 = 0.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	break;
	}
	}

	/**
	* 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:
	* <pre>
	* setToRotation(numquadrants * Math.PI / 2.0, anchorx, anchory);
	* </pre>
	* Rotating by a positive number of quadrants rotates points on
	* the positive X axis toward the positive Y axis.
	*
	* @param numquadrants the number of 90 degree arcs to rotate by
	* @param anchorx the X coordinate of the rotation anchor point
	* @param anchory the Y coordinate of the rotation anchor point
	* @since 1.6
	*/
	public void setToQuadrantRotation(int numquadrants,
	double anchorx, double anchory)
	{
	switch (numquadrants & 3) {
	case 0:
	m00 = 1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = 1.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_IDENTITY;
	type = TYPE_IDENTITY;
	break;
	case 1:
	m00 = 0.0;
	m10 = 1.0;
	m01 = -1.0;
	m11 = 0.0;
	m02 = anchorx + anchory;
	m12 = anchory - anchorx;
	if (m02 == 0.0 && m12 == 0.0) {
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	state = APPLY_SHEAR \| APPLY_TRANSLATE;
	type = TYPE_QUADRANT_ROTATION \| TYPE_TRANSLATION;
	}
	break;
	case 2:
	m00 = -1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = -1.0;
	m02 = anchorx + anchorx;
	m12 = anchory + anchory;
	if (m02 == 0.0 && m12 == 0.0) {
	state = APPLY_SCALE;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	state = APPLY_SCALE \| APPLY_TRANSLATE;
	type = TYPE_QUADRANT_ROTATION \| TYPE_TRANSLATION;
	}
	break;
	case 3:
	m00 = 0.0;
	m10 = -1.0;
	m01 = 1.0;
	m11 = 0.0;
	m02 = anchorx - anchory;
	m12 = anchory + anchorx;
	if (m02 == 0.0 && m12 == 0.0) {
	state = APPLY_SHEAR;
	type = TYPE_QUADRANT_ROTATION;
	} else {
	state = APPLY_SHEAR \| APPLY_TRANSLATE;
	type = TYPE_QUADRANT_ROTATION \| TYPE_TRANSLATION;
	}
	break;
	}
	}

	/**
	* Sets this transform to a scaling transformation.
	* The matrix representing this transform becomes:
	* <pre>
	* [ sx 0 0 ]
	* [ 0 sy 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	public void setToScale(double sx, double sy) {
	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;
	}
	}

	/**
	* Sets this transform to a shearing transformation.
	* The matrix representing this transform becomes:
	* <pre>
	* [ 1 shx 0 ]
	* [ shy 1 0 ]
	* [ 0 0 1 ]
	* </pre>
	* @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
	* @since 1.2
	*/
	public void setToShear(double shx, double shy) {
	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;
	}
	}

	/**
	* Sets this transform to a copy of the transform in the specified
	* <code>AffineTransform</code> object.
	* @param Tx the <code>AffineTransform</code> object from which to
	* copy the transform
	* @since 1.2
	*/
	public void setTransform(AffineTransform Tx) {
	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;
	}

	/**
	* Sets this transform to the matrix specified by the 6
	* double precision values.
	*
	* @param m00 the X coordinate scaling element of the 3x3 matrix
	* @param m10 the Y coordinate shearing element of the 3x3 matrix
	* @param m01 the X coordinate shearing element of the 3x3 matrix
	* @param m11 the Y coordinate scaling element of the 3x3 matrix
	* @param m02 the X coordinate translation element of the 3x3 matrix
	* @param m12 the Y coordinate translation element of the 3x3 matrix
	* @since 1.2
	*/
	public void setTransform(double m00, double m10,
	double m01, double m11,
	double m02, double m12) {
	this.m00 = m00;
	this.m10 = m10;
	this.m01 = m01;
	this.m11 = m11;
	this.m02 = m02;
	this.m12 = m12;
	updateState();
	}

	/**
	* Concatenates an <code>AffineTransform</code> <code>Tx</code> to
	* this <code>AffineTransform</code> Cx in the most commonly useful
	* way to provide a new user space
	* that is mapped to the former user space by <code>Tx</code>.
	* Cx is updated to perform the combined transformation.
	* Transforming a point p by the updated transform Cx' is
	* equivalent to first transforming p by <code>Tx</code> 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 <code>Tx</code> is represented
	* by the matrix [Tx] then this method does the following:
	* <pre>
	* [this] = [this] x [Tx]
	* </pre>
	* @param Tx the <code>AffineTransform</code> object to be
	* concatenated with this <code>AffineTransform</code> object.
	* @see #preConcatenate
	* @since 1.2
	*/
	@SuppressWarnings("fallthrough")
	public void concatenate(AffineTransform Tx) {
	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();
	}

	/**
	* Concatenates an <code>AffineTransform</code> <code>Tx</code> to
	* this <code>AffineTransform</code> Cx
	* in a less commonly used way such that <code>Tx</code> 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
	* <code>Tx</code> like this:
	* Cx'(p) = Tx(Cx(p))
	* In matrix notation, if this transform Cx
	* is represented by the matrix [this] and <code>Tx</code> is
	* represented by the matrix [Tx] then this method does the
	* following:
	* <pre>
	* [this] = [Tx] x [this]
	* </pre>
	* @param Tx the <code>AffineTransform</code> object to be
	* concatenated with this <code>AffineTransform</code> object.
	* @see #concatenate
	* @since 1.2
	*/
	@SuppressWarnings("fallthrough")
	public void preConcatenate(AffineTransform Tx) {
	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();
	}

	/**
	* Returns an <code>AffineTransform</code> 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)).
	* <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 <code>getDeterminant</code> method can be used to determine if this
	* transform has no inverse, in which case an exception will be
	* thrown if the <code>createInverse</code> method is called.
	* @return a new <code>AffineTransform</code> object representing the
	* inverse transformation.
	* @see #getDeterminant
	* @exception NoninvertibleTransformException
	* if the matrix cannot be inverted.
	* @since 1.2
	*/
	public AffineTransform createInverse()
	throws NoninvertibleTransformException
	{
	double det;
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return null;
	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 */
	}

	/**
	* 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)).
	* <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 <code>getDeterminant</code> method can be used to determine if this
	* transform has no inverse, in which case an exception will be
	* thrown if the <code>invert</code> method is called.
	* @see #getDeterminant
	* @exception NoninvertibleTransformException
	* if the matrix cannot be inverted.
	* @since 1.6
	*/
	public void invert()
	throws NoninvertibleTransformException
	{
	double M00, M01, M02;
	double M10, M11, M12;
	double det;
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return;
	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);
	}
	m00 = M11 / det;
	m10 = -M10 / det;
	m01 = -M01 / det;
	m11 = M00 / det;
	m02 = (M01 * M12 - M11 * M02) / det;
	m12 = (M10 * M02 - M00 * M12) / det;
	break;
	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);
	}
	m00 = M11 / det;
	m10 = -M10 / det;
	m01 = -M01 / det;
	m11 = M00 / det;
	// m02 = 0.0;
	// m12 = 0.0;
	break;
	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");
	}
	// m00 = 0.0;
	m10 = 1.0 / M01;
	m01 = 1.0 / M10;
	// m11 = 0.0;
	m02 = -M12 / M10;
	m12 = -M02 / M01;
	break;
	case (APPLY_SHEAR):
	M01 = m01;
	M10 = m10;
	if (M01 == 0.0 \|\| M10 == 0.0) {
	throw new NoninvertibleTransformException("Determinant is 0");
	}
	// m00 = 0.0;
	m10 = 1.0 / M01;
	m01 = 1.0 / M10;
	// m11 = 0.0;
	// m02 = 0.0;
	// m12 = 0.0;
	break;
	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");
	}
	m00 = 1.0 / M00;
	// m10 = 0.0;
	// m01 = 0.0;
	m11 = 1.0 / M11;
	m02 = -M02 / M00;
	m12 = -M12 / M11;
	break;
	case (APPLY_SCALE):
	M00 = m00;
	M11 = m11;
	if (M00 == 0.0 \|\| M11 == 0.0) {
	throw new NoninvertibleTransformException("Determinant is 0");
	}
	m00 = 1.0 / M00;
	// m10 = 0.0;
	// m01 = 0.0;
	m11 = 1.0 / M11;
	// m02 = 0.0;
	// m12 = 0.0;
	break;
	case (APPLY_TRANSLATE):
	// m00 = 1.0;
	// m10 = 0.0;
	// m01 = 0.0;
	// m11 = 1.0;
	m02 = -m02;
	m12 = -m12;
	break;
	case (APPLY_IDENTITY):
	// m00 = 1.0;
	// m10 = 0.0;
	// m01 = 0.0;
	// m11 = 1.0;
	// m02 = 0.0;
	// m12 = 0.0;
	break;
	}
	}

	/**
	* Transforms the specified <code>ptSrc</code> and stores the result
	* in <code>ptDst</code>.
	* If <code>ptDst</code> is <code>null</code>, a new {@link Point2D}
	* object is allocated and then the result of the transformation is
	* stored in this object.
	* In either case, <code>ptDst</code>, which contains the
	* transformed point, is returned for convenience.
	* If <code>ptSrc</code> and <code>ptDst</code> are the same
	* object, the input point is correctly overwritten with
	* the transformed point.
	* @param ptSrc the specified <code>Point2D</code> to be transformed
	* @param ptDst the specified <code>Point2D</code> that stores the
	* result of transforming <code>ptSrc</code>
	* @return the <code>ptDst</code> after transforming
	* <code>ptSrc</code> and storing the result in <code>ptDst</code>.
	* @since 1.2
	*/
	public Point2D transform(Point2D ptSrc, Point2D 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 */
	return null;
	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 */
	}

	/**
	* Transforms an array of point objects by this transform.
	* If any element of the <code>ptDst</code> array is
	* <code>null</code>, a new <code>Point2D</code> object is allocated
	* and stored into that element before storing the results of the
	* transformation.
	* <p>
	* Note that this method does not take any precautions to
	* avoid problems caused by storing results into <code>Point2D</code>
	* objects that will be used as the source for calculations
	* further down the source array.
	* This method does guarantee that if a specified <code>Point2D</code>
	* 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 <code>Point2D</code> object for one
	* operation is the same object as the source <code>Point2D</code>
	* 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
	* @since 1.2
	*/
	public void transform(Point2D[] ptSrc, int srcOff,
	Point2D[] ptDst, int dstOff,
	int numPts) {
	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 */
	return;
	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 */
	}

	/**
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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
	* @since 1.2
	*/
	public void transform(float[] srcPts, int srcOff,
	float[] dstPts, int dstOff,
	int numPts) {
	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 */
	return;
	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 */
	}

	/**
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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
	* @since 1.2
	*/
	public void transform(double[] srcPts, int srcOff,
	double[] dstPts, int dstOff,
	int numPts) {
	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 */
	return;
	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 */
	}

	/**
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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
	* @since 1.2
	*/
	public void transform(float[] srcPts, int srcOff,
	double[] dstPts, int dstOff,
	int numPts) {
	double M00, M01, M02, M10, M11, M12; // For caching
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return;
	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 */
	}

	/**
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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
	* @since 1.2
	*/
	public void transform(double[] srcPts, int srcOff,
	float[] dstPts, int dstOff,
	int numPts) {
	double M00, M01, M02, M10, M11, M12; // For caching
	switch (state) {
	default:
	stateError();
	/* NOTREACHED */
	return;
	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 */
	}

	/**
	* Inverse transforms the specified <code>ptSrc</code> and stores the
	* result in <code>ptDst</code>.
	* If <code>ptDst</code> is <code>null</code>, a new
	* <code>Point2D</code> object is allocated and then the result of the
	* transform is stored in this object.
	* In either case, <code>ptDst</code>, which contains the transformed
	* point, is returned for convenience.
	* If <code>ptSrc</code> and <code>ptDst</code> 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 <code>ptDst</code>, which contains the result of the
	* inverse transform.
	* @exception NoninvertibleTransformException if the matrix cannot be
	* inverted.
	* @since 1.2
	*/
	@SuppressWarnings("fallthrough")
	public Point2D inverseTransform(Point2D ptSrc, Point2D ptDst)
	throws NoninvertibleTransformException
	{
	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 */
	}

	/**
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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.
	* @since 1.2
	*/
	public void inverseTransform(double[] srcPts, int srcOff,
	double[] dstPts, int dstOff,
	int numPts)
	throws NoninvertibleTransformException
	{
	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 */
	return;
	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 */
	}

	/**
	* Transforms the relative distance vector specified by
	* <code>ptSrc</code> and stores the result in <code>ptDst</code>.
	* A relative distance vector is transformed without applying the
	* translation components of the affine transformation matrix
	* using the following equations:
	* <pre>
	* [ x' ] [ m00 m01 (m02) ] [ x ] [ m00x + m01y ]
	* [ y' ] = [ m10 m11 (m12) ] [ y ] = [ m10x + m11y ]
	* [ (1) ] [ (0) (0) ( 1 ) ] [ (1) ] [ (1) ]
	* </pre>
	* If <code>ptDst</code> is <code>null</code>, a new
	* <code>Point2D</code> object is allocated and then the result of the
	* transform is stored in this object.
	* In either case, <code>ptDst</code>, which contains the
	* transformed point, is returned for convenience.
	* If <code>ptSrc</code> and <code>ptDst</code> 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 <code>ptDst</code>, which contains the result of the
	* transformation.
	* @since 1.2
	*/
	public Point2D deltaTransform(Point2D ptSrc, Point2D 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 */
	return null;
	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 */
	}

	/**
	* 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:
	* <pre>
	* [ x' ] [ m00 m01 (m02) ] [ x ] [ m00x + m01y ]
	* [ y' ] = [ m10 m11 (m12) ] [ y ] = [ m10x + m11y ]
	* [ (1) ] [ (0) (0) ( 1 ) ] [ (1) ] [ (1) ]
	* </pre>
	* 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 <code>[x0, y0, x1, y1, ..., xn, yn]</code>.
	* @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
	* @since 1.2
	*/
	public void deltaTransform(double[] srcPts, int srcOff,
	double[] dstPts, int dstOff,
	int numPts) {
	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 */
	return;
	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 */
	}

	/**
	* Returns a new {@link Shape} object defined by the geometry of the
	* specified <code>Shape</code> after it has been transformed by
	* this transform.
	* @param pSrc the specified <code>Shape</code> object to be
	* transformed by this transform.
	* @return a new <code>Shape</code> object that defines the geometry
	* of the transformed <code>Shape</code>, or null if {@code pSrc} is null.
	* @since 1.2
	*/
	public Shape createTransformedShape(Shape pSrc) {
	if (pSrc == null) {
	return null;
	}
	return new Path2D.Double(pSrc, this);
	}

	// Round values to sane precision for printing
	// Note that Math.sin(Math.PI) has an error of about 10^-16
	private static double _matround(double matval) {
	return Math.rint(matval * 1E15) / 1E15;
	}

	/**
	* Returns a <code>String</code> that represents the value of this
	* {@link Object}.
	* @return a <code>String</code> representing the value of this
	* <code>Object</code>.
	* @since 1.2
	*/
	public String toString() {
	return ("AffineTransform[["
	+ _matround(m00) + ", "
	+ _matround(m01) + ", "
	+ _matround(m02) + "], ["
	+ _matround(m10) + ", "
	+ _matround(m11) + ", "
	+ _matround(m12) + "]]");
	}

	/**
	* Returns <code>true</code> if this <code>AffineTransform</code> is
	* an identity transform.
	* @return <code>true</code> if this <code>AffineTransform</code> is
	* an identity transform; <code>false</code> otherwise.
	* @since 1.2
	*/
	public boolean isIdentity() {
	return (state == APPLY_IDENTITY \|\| (getType() == TYPE_IDENTITY));
	}

	/**
	* Returns a copy of this <code>AffineTransform</code> object.
	* @return an <code>Object</code> that is a copy of this
	* <code>AffineTransform</code> object.
	* @since 1.2
	*/
	public Object clone() {
	try {
	return super.clone();
	} catch (CloneNotSupportedException e) {
	// this shouldn't happen, since we are Cloneable
	throw new InternalError(e);
	}
	}

	/**
	* Returns the hashcode for this transform.
	* @return a hash code for this transform.
	* @since 1.2
	*/
	public int hashCode() {
	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)));
	}

	/**
	* Returns <code>true</code> if this <code>AffineTransform</code>
	* represents the same affine coordinate transform as the specified
	* argument.
	* @param obj the <code>Object</code> to test for equality with this
	* <code>AffineTransform</code>
	* @return <code>true</code> if <code>obj</code> equals this
	* <code>AffineTransform</code> object; <code>false</code> otherwise.
	* @since 1.2
	*/
	public boolean equals(Object obj) {
	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));
	}

	/* Serialization support. A readObject method is neccessary because
	* the state field is part of the implementation of this particular
	* AffineTransform and not part of the public specification. The
	* state variable's value needs to be recalculated on the fly by the
	* readObject method as it is in the 6-argument matrix constructor.
	*/

	/*
	* JDK 1.2 serialVersionUID
	*/
	private static final long serialVersionUID = 1330973210523860834L;

	private void writeObject(java.io.ObjectOutputStream s)
	throws java.lang.ClassNotFoundException, java.io.IOException
	{
	s.defaultWriteObject();
	}

	private void readObject(java.io.ObjectInputStream s)
	throws java.lang.ClassNotFoundException, java.io.IOException
	{
	s.defaultReadObject();
	updateState();
	}
	}

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