/*
 * @(#)AffineTransform.java	1.62 00/02/02
 *
 * Copyright 1996-2000 Sun Microsystems, Inc. All Rights Reserved.
 * 
 * This software is the proprietary information of Sun Microsystems, Inc.  
 * Use is subject to license terms.
 * 
 */

package java.awt.geom;

import java.awt.Shape;

/**
 * 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)</code> into
 * destination coordinates <code>(x', y')</code> 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>
 *
 * @version 1.62, 02/02/00
 * @author Jim Graham
 */
public class AffineTransform implements Cloneable, java.io.Serializable {
    /**
     * 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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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;

    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;
    }

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

    /**
     * Constructs a new <code>AffineTransform</code> from 6 floating point
     * values representing the 6 specifiable entries of the 3x3
     * transformation matrix.
     * @param m00, m01, m02, m10, m11, m12 the 
     * 6 floating point values that compose the 3x3 transformation matrix
     */
    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 
     * enries or the 6 specifiable entries of the 3x3 transformation
     * matrix.  The values are retrieved from the array as 
     * { m00 m10 m01 m11 [m02 m12]}.
     * @param flatmatrix the float array containing the values to be set
     * in the new <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.
     */
    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, m01, m02, m10, m11, m12 the 
     * 6 floating point values that compose the 3x3 transformation matrix
     */
    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.
     */
    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.
     */
    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 with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @return an <code>AffineTransform</code> object that is a rotation
     *	transformation, created with the specified angle of rotation.
     */
    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.setToTranslation(x, y);	// S3: final translation
     *	    Tx.rotate(theta);		// S2: rotate around anchor
     *	    Tx.translate(-x, -y);	// S1: translate anchor to origin
     * </pre>
     * The matrix representing the returned transform is:
     * <pre>
     *		[   cos(theta)    -sin(theta)    x-x*cos+y*sin  ]
     *		[   sin(theta)     cos(theta)    y-x*sin-y*cos  ]
     *		[       0              0               1        ]
     * </pre>
     * Rotating with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @param x, y the coordinates of the anchor point of the
     * rotation
     * @return an <code>AffineTransform</code> object that rotates 
     *	coordinates around the specified point by the specified angle of
     *	rotation.
     */
    public static AffineTransform getRotateInstance(double theta,
						    double x, double y) {
	AffineTransform Tx = new AffineTransform();
	Tx.setToRotation(theta, x, y);
	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.
     */
    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.
     */
    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
     * appriopriate flag bits.
     * A valid combination of flag bits is an exclusive OR operation
     * that can combine
     * the TYPE_TRANSLATION flag bit
     * in addition to either of the
     * TYPE_UNIFORM_SCALE or TYPE_GENERAL_SCALE flag bits
     * as well as either of the
     * TYPE_QUADRANT_ROTATION or TYPE_GENERAL_ROTATION flag bits.
     * @return the OR combination of any of the indicated flags that
     * apply to this transform
     * @see #TYPE_IDENTITY
     * @see #TYPE_TRANSLATION
     * @see #TYPE_UNIFORM_SCALE
     * @see #TYPE_GENERAL_SCALE
     * @see #TYPE_QUADRANT_ROTATION
     * @see #TYPE_GENERAL_ROTATION
     * @see #TYPE_GENERAL_TRANSFORM
     */
    public int getType() {
	int ret = TYPE_IDENTITY;
	boolean sgn0, sgn1;
	double M0, M1, M2, M3;
	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...
		return TYPE_GENERAL_TRANSFORM;
	    }
	    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_UNIFORM_SCALE);
		} else {
		    ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		}
	    } 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
		    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_UNIFORM_SCALE);
		    } else {
			ret |= (TYPE_QUADRANT_ROTATION | TYPE_GENERAL_SCALE);
		    }
		}
	    } 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;
	}
	return 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
     */
    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.
     */
    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;
		} else {
		    state = APPLY_TRANSLATE;
		}
	    } else {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = APPLY_SCALE;
		} else {
		    state = (APPLY_SCALE | APPLY_TRANSLATE);
		}
	    }
	} else {
	    if (m00 == 0.0 && m11 == 0.0) {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = APPLY_SHEAR;
		} else {
		    state = (APPLY_SHEAR | APPLY_TRANSLATE);
		}
	    } else {
		if (m02 == 0.0 && m12 == 0.0) {
		    state = (APPLY_SHEAR | APPLY_SCALE);
		} else {
		    state = (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE);
		}
	    }
	}
    }

    /*
     * 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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    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
     */
    public void translate(double tx, double ty) {
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    m02 = tx * m00 + ty * m01 + m02;
	    m12 = tx * m10 + ty * m11 + m12;
	    return;
	case (APPLY_SHEAR | APPLY_SCALE):
	    m02 = tx * m00 + ty * m01;
	    m12 = tx * m10 + ty * m11;
	    state = APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE;
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    m02 = ty * m01 + m02;
	    m12 = tx * m10 + m12;
	    return;
	case (APPLY_SHEAR):
	    m02 = ty * m01;
	    m12 = tx * m10;
	    state = APPLY_SHEAR | APPLY_TRANSLATE;
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    m02 = tx * m00 + m02;
	    m12 = ty * m11 + m12;
	    return;
	case (APPLY_SCALE):
	    m02 = tx * m00;
	    m12 = ty * m11;
	    state = APPLY_SCALE | APPLY_TRANSLATE;
	    return;
	case (APPLY_TRANSLATE):
	    m02 = tx + m02;
	    m12 = ty + m12;
	    return;
	case (APPLY_IDENTITY):
	    m02 = tx;
	    m12 = ty;
	    state = APPLY_TRANSLATE;
	    return;
	}
    }

    /**
     * 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 with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     */
    public void rotate(double theta) {
	double sin = Math.sin(theta);
	double cos = Math.cos(theta);
	if (Math.abs(sin) < 1E-15) {
	    if (cos < 0.0) {
		m00 = -m00;
		m11 = -m11;
		int state = this.state;
		if ((state & (APPLY_SHEAR)) != 0) {
		    // If there was a shear, then this rotation has no
		    // effect on the state.
		    m01 = -m01;
		    m10 = -m10;
		} else {
		    // No shear means the SCALE state may toggle when
		    // m00 and m11 are negated.
		    if (m00 == 1.0 && m11 == 1.0) {
			this.state = state & ~APPLY_SCALE;
		    } else {
			this.state = state | APPLY_SCALE;
		    }
		}
	    }
	    return;
	}
	if (Math.abs(cos) < 1E-15) {
	    if (sin < 0.0) {
		double M0 = m00;
		m00 = -m01;
		m01 = M0;
		M0 = m10;
		m10 = -m11;
		m11 = M0;
	    } else {
		double M0 = m00;
		m00 = m01;
		m01 = -M0;
		M0 = m10;
		m10 = m11;
		m11 = -M0;
	    }
	    state = rot90conversion[state];
	    return;
	}
	double M0, M1;
	M0 = m00;
	M1 = m01;
	m00 =  cos * M0 + sin * M1;
	m01 = -sin * M0 + cos * M1;
	M0 = m10;
	M1 = m11;
	m10 =  cos * M0 + sin * M1;
	m11 = -sin * M0 + cos * M1;
	updateState();
    }
    private static int rot90conversion[] = {
	APPLY_SHEAR, APPLY_SHEAR | APPLY_TRANSLATE,
	APPLY_SHEAR, APPLY_SHEAR | APPLY_TRANSLATE,
	APPLY_SCALE, APPLY_SCALE | APPLY_TRANSLATE,
	APPLY_SHEAR | APPLY_SCALE,
	APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE,
    };

    /**
     * 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(x, y);	// S3: final translation
     *		rotate(theta);		// S2: rotate around anchor
     *		translate(-x, -y);	// S1: translate anchor to origin
     * </pre>
     * Rotating with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @param x, y the coordinates of the anchor point of the
     * rotation
     */
    public void rotate(double theta, double x, double y) {
	// REMIND: Simple for now - optimize later
	translate(x, y);
	rotate(theta);
	translate(-x, -y);
    }

    /**
     * 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 
    */
    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;
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    m00 *= sx;
	    m11 *= sy;
	    return;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    m00 = sx;
	    m11 = sy;
	    this.state = state | APPLY_SCALE;
	    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
     */
    public void shear(double shx, double shy) {
	int state = this.state;
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SHEAR | APPLY_SCALE):
	    double M0, M1;
	    M0 = m00;
	    M1 = m01;
	    m00 = M0 + M1 * shy;
	    m01 = M0 * shx + M1;

	    M0 = m10;
	    M1 = m11;
	    m10 = M0 + M1 * shy;
	    m11 = M0 * shx + M1;
	    return;
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	case (APPLY_SHEAR):
	    m00 = m01 * shy;
	    m11 = m10 * shx;
	    this.state = state | APPLY_SCALE;
	    return;
	case (APPLY_SCALE | APPLY_TRANSLATE):
	case (APPLY_SCALE):
	    m01 = m00 * shx;
	    m10 = m11 * shy;
	    this.state = state | APPLY_SHEAR;
	    return;
	case (APPLY_TRANSLATE):
	case (APPLY_IDENTITY):
	    m01 = shx;
	    m10 = shy;
	    this.state = state | APPLY_SCALE | APPLY_SHEAR;
	    return;
	}
    }

    /**
     * Resets this transform to the Identity transform.
     */
    public void setToIdentity() {
	m00 = m11 = 1.0;
	m10 = m01 = m02 = m12 = 0.0;
	state = APPLY_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
     */
    public void setToTranslation(double tx, double ty) {
	m00 = 1.0;
	m10 = 0.0;
	m01 = 0.0;
	m11 = 1.0;
	m02 = tx;
	m12 = ty;
	state = APPLY_TRANSLATE;
    }

    /**
     * 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 with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     */
    public void setToRotation(double theta) {
	m02 = 0.0;
	m12 = 0.0;
	double sin = Math.sin(theta);
	double cos = Math.cos(theta);
	if (Math.abs(sin) < 1E-15) {
	    m01 = m10 = 0.0;
	    if (cos < 0) {
		m00 = m11 = -1.0;
		state = APPLY_SCALE;
	    } else {
		m00 = m11 = 1.0;
		state = APPLY_IDENTITY;
	    }
	    return;
	}
	if (Math.abs(cos) < 1E-15) {
	    m00 = m11 = 0.0;
	    if (sin < 0.0) {
		m01 = 1.0;
		m10 = -1.0;
	    } else {
		m01 = -1.0;
		m10 = 1.0;
	    }
	    state = APPLY_SHEAR;
	    return;
	}
	m00 = cos;
	m01 = -sin;
	m10 = sin;
	m11 = cos;
	state = APPLY_SHEAR | APPLY_SCALE;
	return;
    }

    /**
     * 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(x, y);	// S3: final translation
     *	    rotate(theta);		// S2: rotate around anchor
     *	    translate(-x, -y);		// S1: translate anchor to origin
     * </pre>
     * The matrix representing this transform becomes:
     * <pre>
     *		[   cos(theta)    -sin(theta)    x-x*cos+y*sin  ]
     *		[   sin(theta)     cos(theta)    y-x*sin-y*cos  ]
     *		[       0              0               1        ]
     * </pre>
     * Rotating with a positive angle theta rotates points on the positive
     * x axis toward the positive y axis.
     * @param theta the angle of rotation in radians
     * @param x, y the coordinates of the anchor point of the
     * rotation
     */
    public void setToRotation(double theta, double x, double y) {
	setToRotation(theta);
	double sin = m10;
	double oneMinusCos = 1.0 - m00;
	m02 = x * oneMinusCos + y * sin;
	m12 = y * oneMinusCos - x * sin;
	state |= APPLY_TRANSLATE;
	return;
    }

    /**
     * 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
     */
    public void setToScale(double sx, double sy) {
	m00 = sx;
	m10 = 0.0;
	m01 = 0.0;
	m11 = sy;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_SCALE;
    }

    /**
     * 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
     */
    public void setToShear(double shx, double shy) {
	m00 = 1.0;
	m01 = shx;
	m10 = shy;
	m11 = 1.0;
	m02 = 0.0;
	m12 = 0.0;
	state = APPLY_SHEAR | APPLY_SCALE;
    }

    /**
     * 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
     */
    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;
    }

    /**
     * Sets this transform to the matrix specified by the 6
     * double precision values.
     * @param m00, m01, m02, m10, m11, m12 the
     * 6 floating point values that compose the 3x3 transformation matrix
     */
    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
     */
    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;
	    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;
	    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;
	    return;

	    /* ---------- Tx == TRANSLATE cases ---------- */
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    T02 = Tx.m02;
	    T12 = Tx.m12;
	    m02 = T02 * m00 + T12 * m01 + m02;
	    m12 = T02 * m10 + T12 * m11 + m12;
	    return;
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_SCALE):
	    T02 = Tx.m02;
	    T12 = Tx.m12;
	    m02 = T02 * m00 + T12 * m01;
	    m12 = T02 * m10 + T12 * m11;
	    state = APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE;
	    return;
	case (HI_TRANSLATE | APPLY_SHEAR | APPLY_TRANSLATE):
	    m02 = Tx.m12 * m01 + m02;
	    m12 = Tx.m02 * m10 + m12;
	    return;
	case (HI_TRANSLATE | APPLY_SHEAR):
	    m02 = Tx.m12 * m01;
	    m12 = Tx.m02 * m10;
	    state = APPLY_SHEAR | APPLY_TRANSLATE;
	    return;
	case (HI_TRANSLATE | APPLY_SCALE | APPLY_TRANSLATE):
	    m02 = Tx.m02 * m00 + m02;
	    m12 = Tx.m12 * m11 + m12;
	    return;
	case (HI_TRANSLATE | APPLY_SCALE):
	    m02 = Tx.m02 * m00;
	    m12 = Tx.m12 * m11;
	    state = APPLY_SCALE | APPLY_TRANSLATE;
	    return;
	case (HI_TRANSLATE | APPLY_TRANSLATE):
	    m02 = Tx.m02 + m02;
	    m12 = Tx.m12 + m12;
	    return;

	    /* ---------- Tx == SCALE cases ---------- */
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR | APPLY_SCALE):
	    T00 = Tx.m00; T11 = Tx.m11;
	    m00 *= T00;
	    m11 *= T11;
	    m01 *= T11;
	    m10 *= T00;
	    return;
	case (HI_SCALE | APPLY_SHEAR | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SHEAR):
	    m01 *= Tx.m11;
	    m10 *= Tx.m00;
	    return;
	case (HI_SCALE | APPLY_SCALE | APPLY_TRANSLATE):
	case (HI_SCALE | APPLY_SCALE):
	    m00 *= Tx.m00;
	    m11 *= Tx.m11;
	    return;
	case (HI_SCALE | APPLY_TRANSLATE):
	    m00 = Tx.m00;
	    m11 = Tx.m11;
	    state = APPLY_SCALE | APPLY_TRANSLATE;
	    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;
	    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);
	    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);
	    return;
	case (HI_SHEAR | APPLY_TRANSLATE):
	    m00 = 0.0;
	    m01 = Tx.m01;
	    m10 = Tx.m10;
	    m11 = 0.0;
	    state = APPLY_TRANSLATE | APPLY_SHEAR;
	    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;
	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;
	    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;
	    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
     */
    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;
	    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;
	    }
	    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;
	    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;
	    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.
     */
    public AffineTransform createInverse()
	throws NoninvertibleTransformException
    {
	double det;
	switch (state) {
	default:
	    stateError();
	    /* NOTREACHED */
	case (APPLY_SHEAR | APPLY_SCALE | APPLY_TRANSLATE):
	    det = m00 * m11 - m01 * m10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    return new AffineTransform( m11 / det, -m10 / det,
				       -m01 / det,  m00 / det,
				       (m01 * m12 - m11 * m02) / det,
				       (m10 * m02 - m00 * m12) / det,
				       (APPLY_SHEAR |
					APPLY_SCALE |
					APPLY_TRANSLATE));
	case (APPLY_SHEAR | APPLY_SCALE):
	    det = m00 * m11 - m01 * m10;
	    if (Math.abs(det) <= Double.MIN_VALUE) {
		throw new NoninvertibleTransformException("Determinant is "+
							  det);
	    }
	    return new AffineTransform( m11 / det, -m10 / det,
				       -m01 / det,  m00 / det,
				        0.0,        0.0,
				       (APPLY_SHEAR | APPLY_SCALE));
	case (APPLY_SHEAR | APPLY_TRANSLATE):
	    if (m01 == 0.0 || m10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform( 0.0,        1.0 / m01,
				        1.0 / m10,  0.0,
				       -m12 / m10, -m02 / m01,
				       (APPLY_SHEAR | APPLY_TRANSLATE));
	case (APPLY_SHEAR):
	    if (m01 == 0.0 || m10 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform(0.0,       1.0 / m01,
				       1.0 / m10, 0.0,
				       0.0,       0.0,
				       (APPLY_SHEAR));
	case (APPLY_SCALE | APPLY_TRANSLATE):
	    if (m00 == 0.0 || m11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform( 1.0 / m00,  0.0,
				        0.0,        1.0 / m11,
				       -m02 / m00, -m12 / m11,
				       (APPLY_SCALE | APPLY_TRANSLATE));
	case (APPLY_SCALE):
	    if (m00 == 0.0 || m11 == 0.0) {
		throw new NoninvertibleTransformException("Determinant is 0");
	    }
	    return new AffineTransform(1.0 / m00, 0.0,
				       0.0,       1.0 / m11,
				       0.0,       0.0,
				       (APPLY_SCALE));
	case (APPLY_TRANSLATE):
	    return new AffineTransform( 1.0,  0.0,
				        0.0,  1.0,
				       -m02, -m12,
				       (APPLY_TRANSLATE));
	case (APPLY_IDENTITY):
	    return new AffineTransform();
	}

	/* NOTREACHED */
    }

    /**
     * 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