/* AffineTransform.java -- transform coordinates between two 2-D spaces
   Copyright (C) 2000, 2001, 2002, 2004 Free Software Foundation

This file is part of GNU Classpath.

GNU Classpath is free software; you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
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02111-1307 USA.

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permission to link this library with independent modules to produce an
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package java.awt.geom;

import java.awt.Shape;
import java.io.IOException;
import java.io.ObjectInputStream;
import java.io.Serializable;

/**
 * This class represents an affine transformation between two coordinate
 * spaces in 2 dimensions. Such a transform preserves the "straightness"
 * and "parallelness" of lines. The transform is built from a sequence of
 * translations, scales, flips, rotations, and shears.
 *
 * <p>The transformation can be represented using matrix math on a 3x3 array.
 * Given (x,y), the transformation (x',y') can be found by:
 * <pre>
 * [ x']   [ m00 m01 m02 ] [ x ]   [ m00*x + m01*y + m02 ]
 * [ y'] = [ m10 m11 m12 ] [ y ] = [ m10*x + m11*y + m12 ]
 * [ 1 ]   [  0   0   1  ] [ 1 ]   [          1          ]
 * </pre>
 * The bottom row of the matrix is constant, so a transform can be uniquely
 * represented (as in {@link #toString()}) by 
 * "[[m00, m01, m02], [m10, m11, m12]]".
 *
 * @author Tom Tromey (tromey@cygnus.com)
 * @author Eric Blake (ebb9@email.byu.edu)
 * @since 1.2
 * @status partially updated to 1.4, still has some problems
 */
public class AffineTransform implements Cloneable, Serializable
{
  /**
   * Compatible with JDK 1.2+.
   */
  private static final long serialVersionUID = 1330973210523860834L;

  /**
   * The transformation is the identity (x' = x, y' = y). All other transforms
   * have either a combination of the appropriate transform flag bits for
   * their type, or the type GENERAL_TRANSFORM.
   *
   * @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;

  /**
   * The transformation includes a translation - shifting in the x or y
   * direction without changing length or angles.
   *
   * @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;

  /**
   * The transformation includes a uniform scale - length is scaled in both
   * the x and y directions by the same amount, without affecting angles.
   * This is mutually exclusive with TYPE_GENERAL_SCALE.
   *
   * @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 #TYPE_MASK_SCALE
   * @see #getType()
   */
  public static final int TYPE_UNIFORM_SCALE = 2;

  /**
   * The transformation includes a general scale - length is scaled in either
   * or both the x and y directions, but by different amounts; without
   * affecting angles. This is mutually exclusive with TYPE_UNIFORM_SCALE.
   *
   * @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 #TYPE_MASK_SCALE
   * @see #getType()
   */
  public static final int TYPE_GENERAL_SCALE = 4;

  /**
   * This constant checks if either variety of scale transform is performed.
   *
   * @see #TYPE_UNIFORM_SCALE
   * @see #TYPE_GENERAL_SCALE
   */
  public static final int TYPE_MASK_SCALE = 6;

  /**
   * The transformation includes a flip about an axis, swapping between
   * right-handed and left-handed coordinate systems. In a right-handed
   * system, the positive x-axis rotates counter-clockwise to the positive
   * y-axis; in a left-handed system it rotates clockwise.
   *
   * @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;

  /**
   * The transformation includes a rotation of a multiple of 90 degrees (PI/2
   * radians). Angles are rotated, but length is preserved. This is mutually
   * exclusive with TYPE_GENERAL_ROTATION.
   *
   * @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 #TYPE_MASK_ROTATION
   * @see #getType()
   */
  public static final int TYPE_QUADRANT_ROTATION = 8;

  /**
   * The transformation includes a rotation by an arbitrary angle. Angles are
   * rotated, but length is preserved. This is mutually exclusive with
   * TYPE_QUADRANT_ROTATION.
   *
   * @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 #TYPE_MASK_ROTATION
   * @see #getType()
   */
  public static final int TYPE_GENERAL_ROTATION = 16;

  /**
   * This constant checks if either variety of rotation is performed.
   *
   * @see #TYPE_QUADRANT_ROTATION
   * @see #TYPE_GENERAL_ROTATION
   */
  public static final int TYPE_MASK_ROTATION = 24;

  /**
   * The transformation is an arbitrary conversion of coordinates which
   * could not be decomposed into the other TYPEs.
   *
   * @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;

  /**
   * The X coordinate scaling element of the transform matrix.
   *
   * @serial matrix[0,0]
   */
  private double m00;

  /**
   * The Y coordinate shearing element of the transform matrix.
   *
   * @serial matrix[1,0]
   */
  private double m10;

  /**
   * The X coordinate shearing element of the transform matrix.
   *
   * @serial matrix[0,1]
   */
  private double m01;

  /**
   * The Y coordinate scaling element of the transform matrix.
   *
   * @serial matrix[1,1]
   */
  private double m11;

  /**
   * The X coordinate translation element of the transform matrix.
   *
   * @serial matrix[0,2]
   */
  private double m02;

  /**
   * The Y coordinate translation element of the transform matrix.
   *
   * @serial matrix[1,2]
   */
  private double m12;

  /** The type of this transform. */
  private transient int type;

  /**
   * Construct a new identity transform:
   * <pre>
   * [ 1 0 0 ]
   * [ 0 1 0 ]
   * [ 0 0 1 ]
   * </pre>
   */
  public AffineTransform()
  {
    m00 = m11 = 1;
  }

  /**
   * Create a new transform which copies the given one.
   *
   * @param tx the transform to copy
   * @throws NullPointerException if tx is null
   */
  public AffineTransform(AffineTransform tx)
  {
    setTransform(tx);
  }

  /**
   * Construct a transform with the given matrix entries:
   * <pre>
   * [ m00 m01 m02 ]
   * [ m10 m11 m12 ]
   * [  0   0   1  ]
   * </pre>
   *
   * @param m00 the x scaling component
   * @param m10 the y shearing component
   * @param m01 the x shearing component
   * @param m11 the y scaling component
   * @param m02 the x translation component
   * @param m12 the y translation component
   */
  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;
    updateType();
  }

  /**
   * Construct a transform from a sequence of float entries. The array must
   * have at least 4 entries, which has a translation factor of 0; or 6
   * entries, for specifying all parameters:
   * <pre>
   * [ f[0] f[2] (f[4]) ]
   * [ f[1] f[3] (f[5]) ]
   * [  0     0    1    ]
   * </pre>
   *
   * @param f the matrix to copy from, with at least 4 (6) entries
   * @throws NullPointerException if f is null
   * @throws ArrayIndexOutOfBoundsException if f is too small
   */
  public AffineTransform(float[] f)
  {
    m00 = f[0];
    m10 = f[1];
    m01 = f[2];
    m11 = f[3];
    if (f.length >= 6)
      {
        m02 = f[4];
        m12 = f[5];
      }
    updateType();
  }

  /**
   * Construct a transform with the given matrix entries:
   * <pre>
   * [ m00 m01 m02 ]
   * [ m10 m11 m12 ]
   * [  0   0   1  ]
   * </pre>
   *
   * @param m00 the x scaling component
   * @param m10 the y shearing component
   * @param m01 the x shearing component
   * @param m11 the y scaling component
   * @param m02 the x translation component
   * @param m12 the y translation component
   */
  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;
    updateType();
  }

  /**
   * Construct a transform from a sequence of double entries. The array must
   * have at least 4 entries, which has a translation factor of 0; or 6
   * entries, for specifying all parameters:
   * <pre>
   * [ d[0] d[2] (d[4]) ]
   * [ d[1] d[3] (d[5]) ]
   * [  0     0    1    ]
   * </pre>
   *
   * @param d the matrix to copy from, with at least 4 (6) entries
   * @throws NullPointerException if d is null
   * @throws ArrayIndexOutOfBoundsException if d is too small
   */
  public AffineTransform(double[] d)
  {
    m00 = d[0];
    m10 = d[1];
    m01 = d[2];
    m11 = d[3];
    if (d.length >= 6)
      {
        m02 = d[4];
        m12 = d[5];
      }
    updateType();
  }

  /**
   * Returns a translation transform:
   * <pre>
   * [ 1 0 tx ]
   * [ 0 1 ty ]
   * [ 0 0 1  ]
   * </pre>
   *
   * @param tx the x translation distance
   * @param ty the y translation distance
   * @return the translating transform
   */
  public static AffineTransform getTranslateInstance(double tx, double ty)
  {
    AffineTransform t = new AffineTransform();
    t.setToTranslation(tx, ty);
    return t;
  }

  /**
   * Returns a rotation transform. A positive angle (in radians) rotates
   * the positive x-axis to the positive y-axis:
   * <pre>
   * [ cos(theta) -sin(theta) 0 ]
   * [ sin(theta)  cos(theta) 0 ]
   * [     0           0      1 ]
   * </pre>
   *
   * @param theta the rotation angle
   * @return the rotating transform
   */
  public static AffineTransform getRotateInstance(double theta)
  {
    AffineTransform t = new AffineTransform();
    t.setToRotation(theta);
    return t;
  }

  /**
   * Returns a rotation transform about a point. A positive angle (in radians)
   * rotates the positive x-axis to the positive y-axis. This is the same
   * as calling:
   * <pre>
   * AffineTransform tx = new AffineTransform();
   * tx.setToTranslation(x, y);
   * tx.rotate(theta);
   * tx.translate(-x, -y);
   * </pre>
   *
   * <p>The resulting matrix is: 
   * <pre>
   * [ cos(theta) -sin(theta) x-x*cos+y*sin ]
   * [ sin(theta)  cos(theta) y-x*sin-y*cos ]
   * [     0           0            1       ]
   * </pre>
   *
   * @param theta the rotation angle
   * @param x the x coordinate of the pivot point
   * @param y the y coordinate of the pivot point
   * @return the rotating transform
   */
  public static AffineTransform getRotateInstance(double theta,
                                                  double x, double y)
  {
    AffineTransform t = new AffineTransform();
    t.setToTranslation(x, y);
    t.rotate(theta);
    t.translate(-x, -y);
    return t;
  }

  /**
   * Returns a scaling transform:
   * <pre>
   * [ sx 0  0 ]
   * [ 0  sy 0 ]
   * [ 0  0  1 ]
   * </pre>
   *
   * @param sx the x scaling factor
   * @param sy the y scaling factor
   * @return the scaling transform
   */
  public static AffineTransform getScaleInstance(double sx, double sy)
  {
    AffineTransform t = new AffineTransform();
    t.setToScale(sx, sy);
    return t;
  }

  /**
   * Returns a shearing transform (points are shifted in the x direction based
   * on a factor of their y coordinate, and in the y direction as a factor of
   * their x coordinate):
   * <pre>
   * [  1  shx 0 ]
   * [ shy  1  0 ]
   * [  0   0  1 ]
   * </pre>
   *
   * @param shx the x shearing factor
   * @param shy the y shearing factor
   * @return the shearing transform
   */
  public static AffineTransform getShearInstance(double shx, double shy)
  {
    AffineTransform t = new AffineTransform();
    t.setToShear(shx, shy);
    return t;
  }

  /**
   * Returns the type of this transform. The result is always valid, although
   * it may not be the simplest interpretation (in other words, there are
   * sequences of transforms which reduce to something simpler, which this
   * does not always detect). The result is either TYPE_GENERAL_TRANSFORM,
   * or a bit-wise combination of TYPE_TRANSLATION, the mutually exclusive
   * TYPE_*_ROTATIONs, and the mutually exclusive TYPE_*_SCALEs.
   *
   * @return The type.
   * 
   * @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()
  {
    return type;
  }

  /**
   * Return the determinant of this transform matrix. If the determinant is
   * non-zero, the transform is invertible; otherwise operations which require
   * an inverse throw a NoninvertibleTransformException. A result very near
   * zero, due to rounding errors, may indicate that inversion results do not
   * carry enough precision to be meaningful.
   *
   * <p>If this is a uniform scale transformation, the determinant also
   * represents the squared value of the scale. Otherwise, it carries little
   * additional meaning. The determinant is calculated as:
   * <pre>
   * | m00 m01 m02 |
   * | m10 m11 m12 | = m00 * m11 - m01 * m10
   * |  0   0   1  |
   * </pre>
   *
   * @return the determinant
   * @see #createInverse()
   */
  public double getDeterminant()
  {
    return m00 * m11 - m01 * m10;
  }

  /**
   * Return the matrix of values used in this transform. If the matrix has
   * fewer than 6 entries, only the scale and shear factors are returned;
   * otherwise the translation factors are copied as well. The resulting
   * values are:
   * <pre>
   * [ d[0] d[2] (d[4]) ]
   * [ d[1] d[3] (d[5]) ]
   * [  0     0    1    ]
   * </pre>
   *
   * @param d the matrix to store the results into; with 4 (6) entries
   * @throws NullPointerException if d is null
   * @throws ArrayIndexOutOfBoundsException if d is too small
   */
  public void getMatrix(double[] d)
  {
    d[0] = m00;
    d[1] = m10;
    d[2] = m01;
    d[3] = m11;
    if (d.length >= 6)
      {
        d[4] = m02;
        d[5] = m12;
      }
  }

  /**
   * Returns the X coordinate scaling factor of the matrix.
   *
   * @return m00
   * @see #getMatrix(double[])
   */
  public double getScaleX()
  {
    return m00;
  }

  /**
   * Returns the Y coordinate scaling factor of the matrix.
   *
   * @return m11
   * @see #getMatrix(double[])
   */
  public double getScaleY()
  {
    return m11;
  }

  /**
   * Returns the X coordinate shearing factor of the matrix.
   *
   * @return m01
   * @see #getMatrix(double[])
   */
  public double getShearX()
  {
    return m01;
  }

  /**
   * Returns the Y coordinate shearing factor of the matrix.
   *
   * @return m10
   * @see #getMatrix(double[])
   */
  public double getShearY()
  {
    return m10;
  }

  /**
   * Returns the X coordinate translation factor of the matrix.
   *
   * @return m02
   * @see #getMatrix(double[])
   */
  public double getTranslateX()
  {
    return m02;
  }

  /**
   * Returns the Y coordinate translation factor of the matrix.
   *
   * @return m12
   * @see #getMatrix(double[])
   */
  public double getTranslateY()
  {
    return m12;
  }

  /**
   * Concatenate a translation onto this transform. This is equivalent, but
   * more efficient than
   * <code>concatenate(AffineTransform.getTranslateInstance(tx, ty))</code>.
   *
   * @param tx the x translation distance
   * @param ty the y translation distance
   * @see #getTranslateInstance(double, double)
   * @see #concatenate(AffineTransform)
   */
  public void translate(double tx, double ty)
  {
    m02 += tx * m00 + ty * m01;
    m12 += tx * m10 + ty * m11;
    updateType();
  }

  /**
   * Concatenate a rotation onto this transform. This is equivalent, but
   * more efficient than
   * <code>concatenate(AffineTransform.getRotateInstance(theta))</code>.
   *
   * @param theta the rotation angle
   * @see #getRotateInstance(double)
   * @see #concatenate(AffineTransform)
   */
  public void rotate(double theta)
  {
    double c = Math.cos(theta);
    double s = Math.sin(theta);
    double n00 = m00 *  c + m01 * s;
    double n01 = m00 * -s + m01 * c;
    double n10 = m10 *  c + m11 * s;
    double n11 = m10 * -s + m11 * c;
    m00 = n00;
    m01 = n01;
    m10 = n10;
    m11 = n11;
    updateType();
  }

  /**
   * Concatenate a rotation about a point onto this transform. This is
   * equivalent, but more efficient than
   * <code>concatenate(AffineTransform.getRotateInstance(theta, x, y))</code>.
   *
   * @param theta the rotation angle
   * @param x the x coordinate of the pivot point
   * @param y the y coordinate of the pivot point
   * @see #getRotateInstance(double, double, double)
   * @see #concatenate(AffineTransform)
   */
  public void rotate(double theta, double x, double y)
  {
    translate(x, y);
    rotate(theta);
    translate(-x, -y);
  }

  /**
   * Concatenate a scale onto this transform. This is equivalent, but more
   * efficient than
   * <code>concatenate(AffineTransform.getScaleInstance(sx, sy))</code>.
   *
   * @param sx the x scaling factor
   * @param sy the y scaling factor
   * @see #getScaleInstance(double, double)
   * @see #concatenate(AffineTransform)
   */
  public void scale(double sx, double sy)
  {
    m00 *= sx;
    m01 *= sy;
    m10 *= sx;
    m11 *= sy;
    updateType();
  }

  /**
   * Concatenate a shearing onto this transform. This is equivalent, but more
   * efficient than
   * <code>concatenate(AffineTransform.getShearInstance(sx, sy))</code>.
   *
   * @param shx the x shearing factor
   * @param shy the y shearing factor
   * @see #getShearInstance(double, double)
   * @see #concatenate(AffineTransform)
   */
  public void shear(double shx, double shy)
  {
    double n00 = m00 + (shy * m01);
    double n01 = m01 + (shx * m00);
    double n10 = m10 + (shy * m11);
    double n11 = m11 + (shx * m10);
    m00 = n00;
    m01 = n01;
    m10 = n10;
    m11 = n11;
    updateType();
  }

  /**
   * Reset this transform to the identity (no transformation):
   * <pre>
   * [ 1 0 0 ]
   * [ 0 1 0 ]
   * [ 0 0 1 ]
   * </pre>
   */
  public void setToIdentity()
  {
    m00 = m11 = 1;
    m01 = m02 = m10 = m12 = 0;
    type = TYPE_IDENTITY;
  }

  /**
   * Set this transform to a translation:
   * <pre>
   * [ 1 0 tx ]
   * [ 0 1 ty ]
   * [ 0 0 1  ]
   * </pre>
   *
   * @param tx the x translation distance
   * @param ty the y translation distance
   */
  public void setToTranslation(double tx, double ty)
  {
    m00 = m11 = 1;
    m01 = m10 = 0;
    m02 = tx;
    m12 = ty;
    type = (tx == 0 && ty == 0) ? TYPE_UNIFORM_SCALE : TYPE_TRANSLATION;
  }

  /**
   * Set this transform to a rotation. A positive angle (in radians) rotates
   * the positive x-axis to the positive y-axis:
   * <pre>
   * [ cos(theta) -sin(theta) 0 ]
   * [ sin(theta)  cos(theta) 0 ]
   * [     0           0      1 ]
   * </pre>
   *
   * @param theta the rotation angle
   */
  public void setToRotation(double theta)
  {
    double c = Math.cos(theta);
    double s = Math.sin(theta);
    m00 = c;
    m01 = -s;
    m02 = 0;
    m10 = s;
    m11 = c;
    m12 = 0;
    type = (c == 1 ? TYPE_IDENTITY
            : c == 0 || c == -1 ? TYPE_QUADRANT_ROTATION
            : TYPE_GENERAL_ROTATION);
  }

  /**
   * Set this transform to a rotation about a point. A positive angle (in
   * radians) rotates the positive x-axis to the positive y-axis. This is the
   * same as calling:
   * <pre>
   * tx.setToTranslation(x, y);
   * tx.rotate(theta);
   * tx.translate(-x, -y);
   * </pre>
   *
   * <p>The resulting matrix is: 
   * <pre>
   * [ cos(theta) -sin(theta) x-x*cos+y*sin ]
   * [ sin(theta)  cos(theta) y-x*sin-y*cos ]
   * [     0           0            1       ]
   * </pre>
   *
   * @param theta the rotation angle
   * @param x the x coordinate of the pivot point
   * @param y the y coordinate of the pivot point
   */
  public void setToRotation(double theta, double x, double y)
  {
    double c = Math.cos(theta);
    double s = Math.sin(theta);
    m00 = c;
    m01 = -s;
    m02 = x - x * c + y * s;
    m10 = s;
    m11 = c;
    m12 = y - x * s - y * c;
    updateType();
  }

  /**
   * Set this transform to a scale:
   * <pre>
   * [ sx 0  0 ]
   * [ 0  sy 0 ]
   * [ 0  0  1 ]
   * </pre>
   *
   * @param sx the x scaling factor
   * @param sy the y scaling factor
   */
  public void setToScale(double sx, double sy)
  {
    m00 = sx;
    m01 = m02 = m10 = m12 = 0;
    m11 = sy;
    type = (sx != sy ? TYPE_GENERAL_SCALE
            : sx == 1 ? TYPE_IDENTITY : TYPE_UNIFORM_SCALE);
  }

  /**
   * Set this transform to a shear (points are shifted in the x direction based
   * on a factor of their y coordinate, and in the y direction as a factor of
   * their x coordinate):
   * <pre>
   * [  1  shx 0 ]
   * [ shy  1  0 ]
   * [  0   0  1 ]
   * </pre>
   *
   * @param shx the x shearing factor
   * @param shy the y shearing factor
   */
  public void setToShear(double shx, double shy)
  {
    m00 = m11 = 1;
    m01 = shx;
    m10 = shy;
    m02 = m12 = 0;
    updateType();
  }

  /**
   * Set this transform to a copy of the given one.
   *
   * @param tx the transform to copy
   * @throws NullPointerException if tx is null
   */
  public void setTransform(AffineTransform tx)
  {
    m00 = tx.m00;
    m01 = tx.m01;
    m02 = tx.m02;
    m10 = tx.m10;
    m11 = tx.m11;
    m12 = tx.m12;
    type = tx.type;
  }

  /**
   * Set this transform to the given values:
   * <pre>
   * [ m00 m01 m02 ]
   * [ m10 m11 m12 ]
   * [  0   0   1  ]
   * </pre>
   *
   * @param m00 the x scaling component
   * @param m10 the y shearing component
   * @param m01 the x shearing component
   * @param m11 the y scaling component
   * @param m02 the x translation component
   * @param m12 the y translation component
   */
  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;
    updateType();
  }

  /**
   * Set this transform to the result of performing the original version of
   * this followed by tx. This is commonly used when chaining transformations
   * from one space to another. In matrix form:
   * <pre>
   * [ this ] = [ this ] x [ tx ]
   * </pre>
   *
   * @param tx the transform to concatenate
   * @throws NullPointerException if tx is null
   * @see #preConcatenate(AffineTransform)
   */
  public void concatenate(AffineTransform tx)
  {
    double n00 = m00 * tx.m00 + m01 * tx.m10;
    double n01 = m00 * tx.m01 + m01 * tx.m11;
    double n02 = m00 * tx.m02 + m01 * tx.m12 + m02;
    double n10 = m10 * tx.m00 + m11 * tx.m10;
    double n11 = m10 * tx.m01 + m11 * tx.m11;
    double n12 = m10 * tx.m02 + m11 * tx.m12 + m12;
    m00 = n00;
    m01 = n01;
    m02 = n02;
    m10 = n10;
    m11 = n11;
    m12 = n12;
    updateType();
  }

  /**
   * Set this transform to the result of performing tx followed by the
   * original version of this. This is less common than normal concatenation,
   * but can still be used to chain transformations from one space to another.
   * In matrix form:
   * <pre>
   * [ this ] = [ tx ] x [ this ]
   * </pre>
   *
   * @param tx the transform to concatenate
   * @throws NullPointerException if tx is null
   * @see #concatenate(AffineTransform)
   */
  public void preConcatenate(AffineTransform tx)
  {
    double n00 = tx.m00 * m00 + tx.m01 * m10;
    double n01 = tx.m00 * m01 + tx.m01 * m11;
    double n02 = tx.m00 * m02 + tx.m01 * m12 + tx.m02;
    double n10 = tx.m10 * m00 + tx.m11 * m10;
    double n11 = tx.m10 * m01 + tx.m11 * m11;
    double n12 = tx.m10 * m02 + tx.m11 * m12 + tx.m12;
    m00 = n00;
    m01 = n01;
    m02 = n02;
    m10 = n10;
    m11 = n11;
    m12 = n12;
    updateType();
  }

  /**
   * Returns a transform, which if concatenated to this one, will result in
   * the identity transform. This is useful for undoing transformations, but
   * is only possible if the original transform has an inverse (ie. does not
   * map multiple points to the same line or point). A transform exists only
   * if getDeterminant() has a non-zero value.
   *
   * The inverse is calculated as:
   * 
   * <pre>
   *
   * Let A be the matrix for which we want to find the inverse:
   *
   * A = [ m00 m01 m02 ]
   *     [ m10 m11 m12 ]
   *     [ 0   0   1   ] 
   *
   *
   *                 1    
   * inverse (A) =  ---   x  adjoint(A) 
   *                det 
   *
   *
   *
   *             =   1       [  m11  -m01   m01*m12-m02*m11  ]
   *                ---   x  [ -m10   m00  -m00*m12+m10*m02  ]
   *                det      [  0     0     m00*m11-m10*m01  ]
   *
   *
   *
   *             = [  m11/det  -m01/det   m01*m12-m02*m11/det ]
   *               [ -m10/det   m00/det  -m00*m12+m10*m02/det ]
   *               [   0           0          1               ]
   *
   *
   * </pre>
   *
   *
   *
   * @return a new inverse transform
   * @throws NoninvertibleTransformException if inversion is not possible
   * @see #getDeterminant()
   */
  public AffineTransform createInverse()
    throws NoninvertibleTransformException
  {
    double det = getDeterminant();
    if (det == 0)
      throw new NoninvertibleTransformException("can't invert transform");
    
    double im00 = m11 / det;
    double im10 = -m10 / det;
    double im01 = -m01 / det;
    double im11 = m00 / det;
    double im02 = (m01 * m12 - m02 * m11) / det;
    double im12 = (-m00 * m12 + m10 * m02) / det;
    
    return new AffineTransform (im00, im10, im01, im11, im02, im12);
  }

  /**
   * Perform this transformation on the given source point, and store the
   * result in the destination (creating it if necessary). It is safe for
   * src and dst to be the same.
   *
   * @param src the source point
   * @param dst the destination, or null
   * @return the transformation of src, in dst if it was non-null
   * @throws NullPointerException if src is null
   */
  public Point2D transform(Point2D src, Point2D dst)
  {
    if (dst == null)
      dst = new Point2D.Double();
    double x = src.getX();
    double y = src.getY();
    double nx = m00 * x + m01 * y + m02;
    double ny = m10 * x + m11 * y + m12;
    dst.setLocation(nx, ny);
    return dst;
  }

  /**
   * Perform this transformation on an array of points, storing the results
   * in another (possibly same) array. This will not create a destination
   * array, but will create points for the null entries of the destination.
   * The transformation is done sequentially. While having a single source
   * and destination point be the same is safe, you should be aware that
   * duplicate references to the same point in the source, and having the
   * source overlap the destination, may result in your source points changing
   * from a previous transform before it is their turn to be evaluated.
   *
   * @param src the array of source points
   * @param srcOff the starting offset into src
   * @param dst the array of destination points (may have null entries)
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null, or src has null
   *         entries
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   * @throws ArrayStoreException if new points are incompatible with dst
   */
  public void transform(Point2D[] src, int srcOff,
                        Point2D[] dst, int dstOff, int num)
  {
    while (--num >= 0)
      dst[dstOff] = transform(src[srcOff++], dst[dstOff++]);
  }

  /**
   * Perform this transformation on an array of points, in (x,y) pairs,
   * storing the results in another (possibly same) array. This will not
   * create a destination array. All sources are copied before the
   * transformation, so that no result will overwrite a point that has not yet
   * been evaluated.
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   */
  public void transform(float[] srcPts, int srcOff,
                        float[] dstPts, int dstOff, int num)
  {
    if (srcPts == dstPts && dstOff > srcOff
        && num > 1 && srcOff + 2 * num > dstOff)
      {
        float[] f = new float[2 * num];
        System.arraycopy(srcPts, srcOff, f, 0, 2 * num);
        srcPts = f;
      }
    while (--num >= 0)
      {
        float x = srcPts[srcOff++];
        float y = srcPts[srcOff++];
        dstPts[dstOff++] = (float) (m00 * x + m01 * y + m02);
        dstPts[dstOff++] = (float) (m10 * x + m11 * y + m12);
      }
  }

  /**
   * Perform this transformation on an array of points, in (x,y) pairs,
   * storing the results in another (possibly same) array. This will not
   * create a destination array. All sources are copied before the
   * transformation, so that no result will overwrite a point that has not yet
   * been evaluated.
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   */
  public void transform(double[] srcPts, int srcOff,
                        double[] dstPts, int dstOff, int num)
  {
    if (srcPts == dstPts && dstOff > srcOff
        && num > 1 && srcOff + 2 * num > dstOff)
      {
        double[] d = new double[2 * num];
        System.arraycopy(srcPts, srcOff, d, 0, 2 * num);
        srcPts = d;
      }
    while (--num >= 0)
      {
        double x = srcPts[srcOff++];
        double y = srcPts[srcOff++];
        dstPts[dstOff++] = m00 * x + m01 * y + m02;
        dstPts[dstOff++] = m10 * x + m11 * y + m12;
      }
  }

  /**
   * Perform this transformation on an array of points, in (x,y) pairs,
   * storing the results in another array. This will not create a destination
   * array.
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   */
  public void transform(float[] srcPts, int srcOff,
                        double[] dstPts, int dstOff, int num)
  {
    while (--num >= 0)
      {
        float x = srcPts[srcOff++];
        float y = srcPts[srcOff++];
        dstPts[dstOff++] = m00 * x + m01 * y + m02;
        dstPts[dstOff++] = m10 * x + m11 * y + m12;
      }
  }

  /**
   * Perform this transformation on an array of points, in (x,y) pairs,
   * storing the results in another array. This will not create a destination
   * array.
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   */
  public void transform(double[] srcPts, int srcOff,
                        float[] dstPts, int dstOff, int num)
  {
    while (--num >= 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);
      }
  }

  /**
   * Perform the inverse of this transformation on the given source point,
   * and store the result in the destination (creating it if necessary). It
   * is safe for src and dst to be the same.
   *
   * @param src the source point
   * @param dst the destination, or null
   * @return the inverse transformation of src, in dst if it was non-null
   * @throws NullPointerException if src is null
   * @throws NoninvertibleTransformException if the inverse does not exist
   * @see #getDeterminant()
   */
  public Point2D inverseTransform(Point2D src, Point2D dst)
    throws NoninvertibleTransformException
  {
    return createInverse().transform(src, dst);
  }

  /**
   * Perform the inverse of this transformation on an array of points, in
   * (x,y) pairs, storing the results in another (possibly same) array. This
   * will not create a destination array. All sources are copied before the
   * transformation, so that no result will overwrite a point that has not yet
   * been evaluated.
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   * @throws NoninvertibleTransformException if the inverse does not exist
   * @see #getDeterminant()
   */
  public void inverseTransform(double[] srcPts, int srcOff,
                               double[] dstPts, int dstOff, int num)
    throws NoninvertibleTransformException
  {
    createInverse().transform(srcPts, srcOff, dstPts, dstOff, num);
  }

  /**
   * Perform this transformation, less any translation, on the given source
   * point, and store the result in the destination (creating it if
   * necessary). It is safe for src and dst to be the same. The reduced
   * transform is equivalent to:
   * <pre>
   * [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
   * [ y' ]   [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
   * </pre>
   *
   * @param src the source point
   * @param dst the destination, or null
   * @return the delta transformation of src, in dst if it was non-null
   * @throws NullPointerException if src is null
   */
  public Point2D deltaTransform(Point2D src, Point2D dst)
  {
    if (dst == null)
      dst = new Point2D.Double();
    double x = src.getX();
    double y = src.getY();
    double nx = m00 * x + m01 * y;
    double ny = m10 * x + m11 * y;
    dst.setLocation(nx, ny);
    return dst;
  }

  /**
   * Perform this transformation, less any translation, on an array of points,
   * in (x,y) pairs, storing the results in another (possibly same) array.
   * This will not create a destination array. All sources are copied before
   * the transformation, so that no result will overwrite a point that has
   * not yet been evaluated. The reduced transform is equivalent to:
   * <pre>
   * [ x' ] = [ m00 m01 ] [ x ] = [ m00 * x + m01 * y ]
   * [ y' ]   [ m10 m11 ] [ y ] = [ m10 * x + m11 * y ]
   * </pre>
   *
   * @param srcPts the array of source points
   * @param srcOff the starting offset into src
   * @param dstPts the array of destination points
   * @param dstOff the starting offset into dst
   * @param num the number of points to transform
   * @throws NullPointerException if src or dst is null
   * @throws ArrayIndexOutOfBoundsException if array bounds are exceeded
   */
  public void deltaTransform(double[] srcPts, int srcOff,
                              double[] dstPts, int dstOff,
                              int num)
  {
    if (srcPts == dstPts && dstOff > srcOff
        && num > 1 && srcOff + 2 * num > dstOff)
      {
        double[] d = new double[2 * num];
        System.arraycopy(srcPts, srcOff, d, 0, 2 * num);
        srcPts = d;
      }
    while (--num >= 0)
      {
        double x = srcPts[srcOff++];
        double y = srcPts[srcOff++];
        dstPts[dstOff++] = m00 * x + m01 * y;
        dstPts[dstOff++] = m10 * x + m11 * y;
      }
  }

  /**
   * Return a new Shape, based on the given one, where the path of the shape
   * has been transformed by this transform. Notice that this uses GeneralPath,
   * which only stores points in float precision.
   *
   * @param src the shape source to transform
   * @return the shape, transformed by this, <code>null</code> if src is 
   * <code>null</code>.
   * @see GeneralPath#transform(AffineTransform)
   */
  public Shape createTransformedShape(Shape src)
  {
    if(src == null) 
      return null;
    GeneralPath p = new GeneralPath(src);
    p.transform(this);
    return p;
  }

  /**
   * Returns a string representation of the transform, in the format:
   * <code>"AffineTransform[[" + m00 + ", " + m01 + ", " + m02 + "], ["
   *   + m10 + ", " + m11 + ", " + m12 + "]]"</code>.
   *
   * @return the string representation
   */
  public String toString()
  {
    return "AffineTransform[[" + m00 + ", " + m01 + ", " + m02 + "], ["
      + m10 + ", " + m11 + ", " + m12 + "]]";
  }

  /**
   * Tests if this transformation is the identity:
   * <pre>
   * [ 1 0 0 ]
   * [ 0 1 0 ]
   * [ 0 0 1 ]
   * </pre>
   *
   * @return true if this is the identity transform
   */
  public boolean isIdentity()
  {
    // Rather than rely on type, check explicitly.
    return (m00 == 1 && m01 == 0 && m02 == 0
            && m10 == 0 && m11 == 1 && m12 == 0);
  }

  /**
   * Create a new transform of the same run-time type, with the same
   * transforming properties as this one.
   *
   * @return the clone
   */
  public Object clone()
  {
    try
      {
        return super.clone();
      }
    catch (CloneNotSupportedException e)
      {
        throw (Error) new InternalError().initCause(e); // Impossible
      }
  }

  /**
   * Return the hashcode for this transformation. The formula is not
   * documented, but appears to be the same as:
   * <pre>
   * long l = Double.doubleToLongBits(getScaleX());
   * l = l * 31 + Double.doubleToLongBits(getShearY());
   * l = l * 31 + Double.doubleToLongBits(getShearX());
   * l = l * 31 + Double.doubleToLongBits(getScaleY());
   * l = l * 31 + Double.doubleToLongBits(getTranslateX());
   * l = l * 31 + Double.doubleToLongBits(getTranslateY());
   * return (int) ((l >> 32) ^ l);
   * </pre>
   *
   * @return the hashcode
   */
  public int hashCode()
  {
    long l = Double.doubleToLongBits(m00);
    l = l * 31 + Double.doubleToLongBits(m10);
    l = l * 31 + Double.doubleToLongBits(m01);
    l = l * 31 + Double.doubleToLongBits(m11);
    l = l * 31 + Double.doubleToLongBits(m02);
    l = l * 31 + Double.doubleToLongBits(m12);
    return (int) ((l >> 32) ^ l);
  }

  /**
   * Compares two transforms for equality. This returns true if they have the
   * same matrix values.
   *
   * @param obj the transform to compare
   * @return true if it is equal
   */
  public boolean equals(Object obj)
  {
    if (! (obj instanceof AffineTransform))
      return false;
    AffineTransform t = (AffineTransform) obj;
    return (m00 == t.m00 && m01 == t.m01 && m02 == t.m02
            && m10 == t.m10 && m11 == t.m11 && m12 == t.m12);
  }

  /**
   * Helper to decode the type from the matrix. This is not guaranteed
   * to find the optimal type, but at least it will be valid.
   */
  private void updateType()
  {
    double det = getDeterminant();
    if (det == 0)
      {
        type = TYPE_GENERAL_TRANSFORM;
        return;
      }
    // Scale (includes rotation by PI) or translation.
    if (m01 == 0 && m10 == 0)
      {
        if (m00 == m11)
          type = m00 == 1 ? TYPE_IDENTITY : TYPE_UNIFORM_SCALE;
        else
          type = TYPE_GENERAL_SCALE;
        if (m02 != 0 || m12 != 0)
          type |= TYPE_TRANSLATION;
      }
    // Rotation.
    else if (m00 == m11 && m01 == -m10)
      {
        type = m00 == 0 ? TYPE_QUADRANT_ROTATION : TYPE_GENERAL_ROTATION;
        if (det != 1)
          type |= TYPE_UNIFORM_SCALE;
        if (m02 != 0 || m12 != 0)
          type |= TYPE_TRANSLATION;
      }
    else
      type = TYPE_GENERAL_TRANSFORM;
  }

  /**
   * Reads a transform from an object stream.
   *
   * @param s the stream to read from
   * @throws ClassNotFoundException if there is a problem deserializing
   * @throws IOException if there is a problem deserializing
   */
  private void readObject(ObjectInputStream s)
    throws ClassNotFoundException, IOException
  {
    s.defaultReadObject();
    updateType();
  }
} // class AffineTransform