GeneralPath.java 26.4 KB
Newer Older
Tom Tromey committed
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376 377 378 379 380 381 382 383 384 385 386 387 388 389 390 391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479 480 481 482 483 484 485 486 487 488 489 490 491 492 493 494 495 496 497 498 499 500 501 502 503 504 505 506 507 508 509 510 511 512 513 514 515 516 517 518 519 520 521 522 523 524 525 526 527 528 529 530 531 532 533 534 535 536 537 538 539 540 541 542 543 544 545 546 547 548 549 550 551 552 553 554 555 556 557 558 559 560
/* GeneralPath.java -- represents a shape built from subpaths
   Copyright (C) 2002, 2003, 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
the Free Software Foundation; either version 2, or (at your option)
any later version.

GNU Classpath is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
General Public License for more details.

You should have received a copy of the GNU General Public License
along with GNU Classpath; see the file COPYING.  If not, write to the
Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
02110-1301 USA.

Linking this library statically or dynamically with other modules is
making a combined work based on this library.  Thus, the terms and
conditions of the GNU General Public License cover the whole
combination.

As a special exception, the copyright holders of this library give you
permission to link this library with independent modules to produce an
executable, regardless of the license terms of these independent
modules, and to copy and distribute the resulting executable under
terms of your choice, provided that you also meet, for each linked
independent module, the terms and conditions of the license of that
module.  An independent module is a module which is not derived from
or based on this library.  If you modify this library, you may extend
this exception to your version of the library, but you are not
obligated to do so.  If you do not wish to do so, delete this
exception statement from your version. */


package java.awt.geom;

import java.awt.Rectangle;
import java.awt.Shape;


/**
 * A general geometric path, consisting of any number of subpaths
 * constructed out of straight lines and cubic or quadratic Bezier
 * curves.
 *
 * <p>The inside of the curve is defined for drawing purposes by a winding
 * rule. Either the WIND_EVEN_ODD or WIND_NON_ZERO winding rule can be chosen.
 *
 * <p><img src="doc-files/GeneralPath-1.png" width="300" height="210"
 * alt="A drawing of a GeneralPath" />
 * <p>The EVEN_ODD winding rule defines a point as inside a path if:
 * A ray from the point towards infinity in an arbitrary direction
 * intersects the path an odd number of times. Points <b>A</b> and
 * <b>C</b> in the image are considered to be outside the path.
 * (both intersect twice)
 * Point <b>B</b> intersects once, and is inside.
 *
 * <p>The NON_ZERO winding rule defines a point as inside a path if:
 * The path intersects the ray in an equal number of opposite directions.
 * Point <b>A</b> in the image is outside (one intersection in the 
 * &#x2019;up&#x2019;
 * direction, one in the &#x2019;down&#x2019; direction) Point <b>B</b> in 
 * the image is inside (one intersection &#x2019;down&#x2019;)
 * Point <b>C</b> in the image is outside (two intersections 
 * &#x2019;down&#x2019;)
 *
 * @see Line2D
 * @see CubicCurve2D
 * @see QuadCurve2D
 *
 * @author Sascha Brawer (brawer@dandelis.ch)
 * @author Sven de Marothy (sven@physto.se)
 *
 * @since 1.2
 */
public final class GeneralPath implements Shape, Cloneable
{
  public static final int WIND_EVEN_ODD = PathIterator.WIND_EVEN_ODD;
  public static final int WIND_NON_ZERO = PathIterator.WIND_NON_ZERO;

  /** Initial size if not specified. */
  private static final int INIT_SIZE = 10;

  /** A big number, but not so big it can't survive a few float operations */
  private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0;

  /** The winding rule.
   * This is package-private to avoid an accessor method.
   */
  int rule;

  /**
   * The path type in points. Note that xpoints[index] and ypoints[index] maps
   * to types[index]; the control points of quad and cubic paths map as
   * well but are ignored.
   * This is package-private to avoid an accessor method.
   */
  byte[] types;

  /**
   * The list of all points seen. Since you can only append floats, it makes
   * sense for these to be float[]. I have no idea why Sun didn't choose to
   * allow a general path of double precision points.
   * Note: Storing x and y coords seperately makes for a slower transforms,
   * But it speeds up and simplifies box-intersection checking a lot.
   * These are package-private to avoid accessor methods.
   */
  float[] xpoints;
  float[] ypoints;

  /** The index of the most recent moveto point, or null. */
  private int subpath = -1;

  /** The next available index into points.
   * This is package-private to avoid an accessor method.
   */
  int index;

  /**
   * Constructs a GeneralPath with the default (NON_ZERO)
   * winding rule and initial capacity (20).
   */
  public GeneralPath()
  {
    this(WIND_NON_ZERO, INIT_SIZE);
  }

  /**
   * Constructs a GeneralPath with a specific winding rule
   * and the default initial capacity (20).
   * @param rule the winding rule (WIND_NON_ZERO or WIND_EVEN_ODD)
   */
  public GeneralPath(int rule)
  {
    this(rule, INIT_SIZE);
  }

  /**
   * Constructs a GeneralPath with a specific winding rule
   * and the initial capacity. The initial capacity should be
   * the approximate number of path segments to be used.
   * @param rule the winding rule (WIND_NON_ZERO or WIND_EVEN_ODD)
   * @param capacity the inital capacity, in path segments
   */
  public GeneralPath(int rule, int capacity)
  {
    if (rule != WIND_EVEN_ODD && rule != WIND_NON_ZERO)
      throw new IllegalArgumentException();
    this.rule = rule;
    if (capacity < INIT_SIZE)
      capacity = INIT_SIZE;
    types = new byte[capacity];
    xpoints = new float[capacity];
    ypoints = new float[capacity];
  }

  /**
   * Constructs a GeneralPath from an arbitrary shape object.
   * The Shapes PathIterator path and winding rule will be used.
   * @param s the shape
   */
  public GeneralPath(Shape s)
  {
    types = new byte[INIT_SIZE];
    xpoints = new float[INIT_SIZE];
    ypoints = new float[INIT_SIZE];
    PathIterator pi = s.getPathIterator(null);
    setWindingRule(pi.getWindingRule());
    append(pi, false);
  }

  /**
   * Adds a new point to a path.
   */
  public void moveTo(float x, float y)
  {
    subpath = index;
    ensureSize(index + 1);
    types[index] = PathIterator.SEG_MOVETO;
    xpoints[index] = x;
    ypoints[index++] = y;
  }

  /**
   * Appends a straight line to the current path.
   * @param x x coordinate of the line endpoint.
   * @param y y coordinate of the line endpoint.
   */
  public void lineTo(float x, float y)
  {
    ensureSize(index + 1);
    types[index] = PathIterator.SEG_LINETO;
    xpoints[index] = x;
    ypoints[index++] = y;
  }

  /**
   * Appends a quadratic Bezier curve to the current path.
   * @param x1 x coordinate of the control point
   * @param y1 y coordinate of the control point
   * @param x2 x coordinate of the curve endpoint.
   * @param y2 y coordinate of the curve endpoint.
   */
  public void quadTo(float x1, float y1, float x2, float y2)
  {
    ensureSize(index + 2);
    types[index] = PathIterator.SEG_QUADTO;
    xpoints[index] = x1;
    ypoints[index++] = y1;
    xpoints[index] = x2;
    ypoints[index++] = y2;
  }

  /**
   * Appends a cubic Bezier curve to the current path.
   * @param x1 x coordinate of the first control point
   * @param y1 y coordinate of the first control point
   * @param x2 x coordinate of the second control point
   * @param y2 y coordinate of the second control point
   * @param x3 x coordinate of the curve endpoint.
   * @param y3 y coordinate of the curve endpoint.
   */
  public void curveTo(float x1, float y1, float x2, float y2, float x3,
                      float y3)
  {
    ensureSize(index + 3);
    types[index] = PathIterator.SEG_CUBICTO;
    xpoints[index] = x1;
    ypoints[index++] = y1;
    xpoints[index] = x2;
    ypoints[index++] = y2;
    xpoints[index] = x3;
    ypoints[index++] = y3;
  }

  /**
   * Closes the current subpath by drawing a line
   * back to the point of the last moveTo.
   */
  public void closePath()
  {
    ensureSize(index + 1);
    types[index] = PathIterator.SEG_CLOSE;
    xpoints[index] = xpoints[subpath];
    ypoints[index++] = ypoints[subpath];
  }

  /**
   * Appends the segments of a Shape to the path. If <code>connect</code> is 
   * true, the new path segments are connected to the existing one with a line.
   * The winding rule of the Shape is ignored.
   */
  public void append(Shape s, boolean connect)
  {
    append(s.getPathIterator(null), connect);
  }

  /**
   * Appends the segments of a PathIterator to this GeneralPath.
   * Optionally, the initial {@link PathIterator#SEG_MOVETO} segment
   * of the appended path is changed into a {@link
   * PathIterator#SEG_LINETO} segment.
   *
   * @param iter the PathIterator specifying which segments shall be
   * appended.
   *
   * @param connect <code>true</code> for substituting the initial
   * {@link PathIterator#SEG_MOVETO} segment by a {@link
   * PathIterator#SEG_LINETO}, or <code>false</code> for not
   * performing any substitution. If this GeneralPath is currently
   * empty, <code>connect</code> is assumed to be <code>false</code>,
   * thus leaving the initial {@link PathIterator#SEG_MOVETO}
   * unchanged.
   */
  public void append(PathIterator iter, boolean connect)
  {
    // A bad implementation of this method had caused Classpath bug #6076.
    float[] f = new float[6];
    while (! iter.isDone())
      {
	switch (iter.currentSegment(f))
	  {
	  case PathIterator.SEG_MOVETO:
	    if (! connect || (index == 0))
	      {
		moveTo(f[0], f[1]);
		break;
	      }
	    if ((index >= 1) && (types[index - 1] == PathIterator.SEG_CLOSE)
	        && (f[0] == xpoints[index - 1])
	        && (f[1] == ypoints[index - 1]))
	      break;

	  // Fall through.
	  case PathIterator.SEG_LINETO:
	    lineTo(f[0], f[1]);
	    break;
	  case PathIterator.SEG_QUADTO:
	    quadTo(f[0], f[1], f[2], f[3]);
	    break;
	  case PathIterator.SEG_CUBICTO:
	    curveTo(f[0], f[1], f[2], f[3], f[4], f[5]);
	    break;
	  case PathIterator.SEG_CLOSE:
	    closePath();
	    break;
	  }

	connect = false;
	iter.next();
      }
  }

  /**
   * Returns the path&#x2019;s current winding rule.
   */
  public int getWindingRule()
  {
    return rule;
  }

  /**
   * Sets the path&#x2019;s winding rule, which controls which areas are 
   * considered &#x2019;inside&#x2019; or &#x2019;outside&#x2019; the path 
   * on drawing. Valid rules are WIND_EVEN_ODD for an even-odd winding rule, 
   * or WIND_NON_ZERO for a non-zero winding rule.
   */
  public void setWindingRule(int rule)
  {
    if (rule != WIND_EVEN_ODD && rule != WIND_NON_ZERO)
      throw new IllegalArgumentException();
    this.rule = rule;
  }

  /**
   * Returns the current appending point of the path.
   */
  public Point2D getCurrentPoint()
  {
    if (subpath < 0)
      return null;
    return new Point2D.Float(xpoints[index - 1], ypoints[index - 1]);
  }

  /**
   * Resets the path. All points and segments are destroyed.
   */
  public void reset()
  {
    subpath = -1;
    index = 0;
  }

  /**
   * Applies a transform to the path.
   */
  public void transform(AffineTransform xform)
  {
    double nx;
    double ny;
    double[] m = new double[6];
    xform.getMatrix(m);
    for (int i = 0; i < index; i++)
      {
	nx = m[0] * xpoints[i] + m[2] * ypoints[i] + m[4];
	ny = m[1] * xpoints[i] + m[3] * ypoints[i] + m[5];
	xpoints[i] = (float) nx;
	ypoints[i] = (float) ny;
      }
  }

  /**
   * Creates a transformed version of the path.
   * @param xform the transform to apply
   * @return a new transformed GeneralPath
   */
  public Shape createTransformedShape(AffineTransform xform)
  {
    GeneralPath p = new GeneralPath(this);
    p.transform(xform);
    return p;
  }

  /**
   * Returns the path&#x2019;s bounding box.
   */
  public Rectangle getBounds()
  {
    return getBounds2D().getBounds();
  }

  /**
   * Returns the path&#x2019;s bounding box, in <code>float</code> precision
   */
  public Rectangle2D getBounds2D()
  {
    float x1;
    float y1;
    float x2;
    float y2;

    if (index > 0)
      {
	x1 = x2 = xpoints[0];
	y1 = y2 = ypoints[0];
      }
    else
      x1 = x2 = y1 = y2 = 0.0f;

    for (int i = 0; i < index; i++)
      {
	x1 = Math.min(xpoints[i], x1);
	y1 = Math.min(ypoints[i], y1);
	x2 = Math.max(xpoints[i], x2);
	y2 = Math.max(ypoints[i], y2);
      }
    return (new Rectangle2D.Float(x1, y1, x2 - x1, y2 - y1));
  }

  /**
   * Evaluates if a point is within the GeneralPath,
   * The NON_ZERO winding rule is used, regardless of the
   * set winding rule.
   * @param x x coordinate of the point to evaluate
   * @param y y coordinate of the point to evaluate
   * @return true if the point is within the path, false otherwise
   */
  public boolean contains(double x, double y)
  {
    return (getWindingNumber(x, y) != 0);
  }

  /**
   * Evaluates if a Point2D is within the GeneralPath,
   * The NON_ZERO winding rule is used, regardless of the
   * set winding rule.
   * @param p The Point2D to evaluate
   * @return true if the point is within the path, false otherwise
   */
  public boolean contains(Point2D p)
  {
    return contains(p.getX(), p.getY());
  }

  /**
   * Evaluates if a rectangle is completely contained within the path.
   * This method will return false in the cases when the box
   * intersects an inner segment of the path.
   * (i.e.: The method is accurate for the EVEN_ODD winding rule)
   */
  public boolean contains(double x, double y, double w, double h)
  {
    if (! getBounds2D().intersects(x, y, w, h))
      return false;

    /* Does any edge intersect? */
    if (getAxisIntersections(x, y, false, w) != 0 /* top */
        || getAxisIntersections(x, y + h, false, w) != 0 /* bottom */
        || getAxisIntersections(x + w, y, true, h) != 0 /* right */
        || getAxisIntersections(x, y, true, h) != 0) /* left */
      return false;

    /* No intersections, is any point inside? */
    if (getWindingNumber(x, y) != 0)
      return true;

    return false;
  }

  /**
   * Evaluates if a rectangle is completely contained within the path.
   * This method will return false in the cases when the box
   * intersects an inner segment of the path.
   * (i.e.: The method is accurate for the EVEN_ODD winding rule)
   * @param r the rectangle
   * @return <code>true</code> if the rectangle is completely contained
   * within the path, <code>false</code> otherwise
   */
  public boolean contains(Rectangle2D r)
  {
    return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * Evaluates if a rectangle intersects the path.
   * @param x x coordinate of the rectangle
   * @param y y coordinate of the rectangle
   * @param w width of the rectangle
   * @param h height of the rectangle
   * @return <code>true</code> if the rectangle intersects the path,
   * <code>false</code> otherwise
   */
  public boolean intersects(double x, double y, double w, double h)
  {
    /* Does any edge intersect? */
    if (getAxisIntersections(x, y, false, w) != 0 /* top */
        || getAxisIntersections(x, y + h, false, w) != 0 /* bottom */
        || getAxisIntersections(x + w, y, true, h) != 0 /* right */
        || getAxisIntersections(x, y, true, h) != 0) /* left */
      return true;

    /* No intersections, is any point inside? */
    if (getWindingNumber(x, y) != 0)
      return true;

    return false;
  }

  /**
   * Evaluates if a Rectangle2D intersects the path.
   * @param r The rectangle
   * @return <code>true</code> if the rectangle intersects the path,
   * <code>false</code> otherwise
   */
  public boolean intersects(Rectangle2D r)
  {
    return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
  }

  /**
   * A PathIterator that iterates over the segments of a GeneralPath.
   *
   * @author Sascha Brawer (brawer@dandelis.ch)
   */
  private static class GeneralPathIterator implements PathIterator
  {
    /**
     * The number of coordinate values for each segment type.
     */
    private static final int[] NUM_COORDS = { 
                                            /* 0: SEG_MOVETO */ 1, 
                                            /* 1: SEG_LINETO */ 1, 
                                            /* 2: SEG_QUADTO */ 2, 
                                            /* 3: SEG_CUBICTO */ 3, 
                                            /* 4: SEG_CLOSE */ 0};

    /**
     * The GeneralPath whose segments are being iterated.
     * This is package-private to avoid an accessor method.
     */
    final GeneralPath path;

    /**
     * The affine transformation used to transform coordinates.
     */
    private final AffineTransform transform;

    /**
     * The current position of the iterator.
     */
    private int pos;

    /**
     * Constructs a new iterator for enumerating the segments of a
     * GeneralPath.
     *
561 562
     * @param path the path to enumerate
     * @param transform an affine transformation for projecting the returned
Tom Tromey committed
563 564 565 566 567 568 569 570 571 572 573 574 575 576 577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618 619 620 621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641 642 643 644 645 646 647 648 649 650 651 652 653 654 655 656 657 658 659 660 661 662 663 664 665 666 667 668 669 670 671 672 673 674 675 676 677 678 679 680 681 682 683 684 685 686 687 688 689 690 691 692 693 694 695 696 697 698 699 700 701 702 703 704 705 706 707 708 709 710 711 712 713 714 715 716 717 718 719 720 721 722 723 724 725 726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751 752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792 793 794 795 796 797 798 799 800 801 802 803 804 805 806 807 808 809 810 811 812 813 814 815 816 817 818 819 820 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858 859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886 887 888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923 924 925 926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949 950 951 952 953 954 955 956 957 958 959
     * points, or <code>null</code> to return the original points
     * without any mapping.
     */
    GeneralPathIterator(GeneralPath path, AffineTransform transform)
    {
      this.path = path;
      this.transform = transform;
    }

    /**
     * Returns the current winding rule of the GeneralPath.
     */
    public int getWindingRule()
    {
      return path.rule;
    }

    /**
     * Determines whether the iterator has reached the last segment in
     * the path.
     */
    public boolean isDone()
    {
      return pos >= path.index;
    }

    /**
     * Advances the iterator position by one segment.
     */
    public void next()
    {
      int seg;

      /*
       * Increment pos by the number of coordinate pairs.
       */
      seg = path.types[pos];
      if (seg == SEG_CLOSE)
	pos++;
      else
	pos += NUM_COORDS[seg];
    }

    /**
     * Returns the current segment in float coordinates.
     */
    public int currentSegment(float[] coords)
    {
      int seg;
      int numCoords;

      seg = path.types[pos];
      numCoords = NUM_COORDS[seg];
      if (numCoords > 0)
        {
	  for (int i = 0; i < numCoords; i++)
	    {
	      coords[i << 1] = path.xpoints[pos + i];
	      coords[(i << 1) + 1] = path.ypoints[pos + i];
	    }

	  if (transform != null)
	    transform.transform( /* src */
	    coords, /* srcOffset */
	    0, /* dest */ coords, /* destOffset */
	    0, /* numPoints */ numCoords);
        }
      return seg;
    }

    /**
     * Returns the current segment in double coordinates.
     */
    public int currentSegment(double[] coords)
    {
      int seg;
      int numCoords;

      seg = path.types[pos];
      numCoords = NUM_COORDS[seg];
      if (numCoords > 0)
        {
	  for (int i = 0; i < numCoords; i++)
	    {
	      coords[i << 1] = (double) path.xpoints[pos + i];
	      coords[(i << 1) + 1] = (double) path.ypoints[pos + i];
	    }
	  if (transform != null)
	    transform.transform( /* src */
	    coords, /* srcOffset */
	    0, /* dest */ coords, /* destOffset */
	    0, /* numPoints */ numCoords);
        }
      return seg;
    }
  }

  /**
   * Creates a PathIterator for iterating along the segments of the path.
   *
   * @param at an affine transformation for projecting the returned
   * points, or <code>null</code> to let the created iterator return
   * the original points without any mapping.
   */
  public PathIterator getPathIterator(AffineTransform at)
  {
    return new GeneralPathIterator(this, at);
  }

  /**
   * Creates a new FlatteningPathIterator for the path
   */
  public PathIterator getPathIterator(AffineTransform at, double flatness)
  {
    return new FlatteningPathIterator(getPathIterator(at), flatness);
  }

  /**
   * Creates a new shape of the same run-time type with the same contents 
   * as this one.
   *
   * @return the clone
   *
   * @exception OutOfMemoryError If there is not enough memory available.
   *
   * @since 1.2
   */
  public Object clone()
  {
    // This class is final; no need to use super.clone().
    return new GeneralPath(this);
  }

  /**
   * Helper method - ensure the size of the data arrays,
   * otherwise, reallocate new ones twice the size
   */
  private void ensureSize(int size)
  {
    if (subpath < 0)
      throw new IllegalPathStateException("need initial moveto");
    if (size <= xpoints.length)
      return;
    byte[] b = new byte[types.length << 1];
    System.arraycopy(types, 0, b, 0, index);
    types = b;
    float[] f = new float[xpoints.length << 1];
    System.arraycopy(xpoints, 0, f, 0, index);
    xpoints = f;
    f = new float[ypoints.length << 1];
    System.arraycopy(ypoints, 0, f, 0, index);
    ypoints = f;
  }

  /**
   * Helper method - Get the total number of intersections from (x,y) along 
   * a given axis, within a given distance.
   */
  private int getAxisIntersections(double x, double y, boolean useYaxis,
                                   double distance)
  {
    return (evaluateCrossings(x, y, false, useYaxis, distance));
  }

  /**
   * Helper method - returns the winding number of a point.
   */
  private int getWindingNumber(double x, double y)
  {
    /* Evaluate the crossings from x,y to infinity on the y axis (arbitrary 
       choice). Note that we don't actually use Double.INFINITY, since that's 
       slower, and may cause problems. */
    return (evaluateCrossings(x, y, true, true, BIG_VALUE));
  }

  /**
   * Helper method - evaluates the number of intersections on an axis from 
   * the point (x,y) to the point (x,y+distance) or (x+distance,y).
   * @param x x coordinate.
   * @param y y coordinate.
   * @param neg True if opposite-directed intersections should cancel, 
   * false to sum all intersections.
   * @param useYaxis Use the Y axis, false uses the X axis.
   * @param distance Interval from (x,y) on the selected axis to find 
   * intersections.
   */
  private int evaluateCrossings(double x, double y, boolean neg,
                                boolean useYaxis, double distance)
  {
    float cx = 0.0f;
    float cy = 0.0f;
    float firstx = 0.0f;
    float firsty = 0.0f;

    int negative = (neg) ? -1 : 1;
    double x0;
    double x1;
    double x2;
    double x3;
    double y0;
    double y1;
    double y2;
    double y3;
    double[] r = new double[4];
    int nRoots;
    double epsilon = 0.0;
    int pos = 0;
    int windingNumber = 0;
    boolean pathStarted = false;

    if (index == 0)
      return (0);
    if (useYaxis)
      {
	float[] swap1;
	swap1 = ypoints;
	ypoints = xpoints;
	xpoints = swap1;
	double swap2;
	swap2 = y;
	y = x;
	x = swap2;
      }

    /* Get a value which is hopefully small but not insignificant relative
     the path. */
    epsilon = ypoints[0] * 1E-7;

    if(epsilon == 0) 
      epsilon = 1E-7;

    pos = 0;
    while (pos < index)
      {
	switch (types[pos])
	  {
	  case PathIterator.SEG_MOVETO:
	    if (pathStarted) // close old path
	      {
		x0 = cx;
		y0 = cy;
		x1 = firstx;
		y1 = firsty;

		if (y0 == 0.0)
		  y0 -= epsilon;
		if (y1 == 0.0)
		  y1 -= epsilon;
		if (Line2D.linesIntersect(x0, y0, x1, y1, 
					  epsilon, 0.0, distance, 0.0))
		  windingNumber += (y1 < y0) ? 1 : negative;

		cx = firstx;
		cy = firsty;
	      }
	    cx = firstx = xpoints[pos] - (float) x;
	    cy = firsty = ypoints[pos++] - (float) y;
	    pathStarted = true;
	    break;
	  case PathIterator.SEG_CLOSE:
	    x0 = cx;
	    y0 = cy;
	    x1 = firstx;
	    y1 = firsty;

	    if (y0 == 0.0)
	      y0 -= epsilon;
	    if (y1 == 0.0)
	      y1 -= epsilon;
	    if (Line2D.linesIntersect(x0, y0, x1, y1, 
				      epsilon, 0.0, distance, 0.0))
	      windingNumber += (y1 < y0) ? 1 : negative;

	    cx = firstx;
	    cy = firsty;
	    pos++;
	    pathStarted = false;
	    break;
	  case PathIterator.SEG_LINETO:
	    x0 = cx;
	    y0 = cy;
	    x1 = xpoints[pos] - (float) x;
	    y1 = ypoints[pos++] - (float) y;

	    if (y0 == 0.0)
	      y0 -= epsilon;
	    if (y1 == 0.0)
	      y1 -= epsilon;
	    if (Line2D.linesIntersect(x0, y0, x1, y1, 
				      epsilon, 0.0, distance, 0.0))
	      windingNumber += (y1 < y0) ? 1 : negative;

	    cx = xpoints[pos - 1] - (float) x;
	    cy = ypoints[pos - 1] - (float) y;
	    break;
	  case PathIterator.SEG_QUADTO:
	    x0 = cx;
	    y0 = cy;
	    x1 = xpoints[pos] - x;
	    y1 = ypoints[pos++] - y;
	    x2 = xpoints[pos] - x;
	    y2 = ypoints[pos++] - y;

	    /* check if curve may intersect X+ axis. */
	    if ((x0 > 0.0 || x1 > 0.0 || x2 > 0.0)
	        && (y0 * y1 <= 0 || y1 * y2 <= 0))
	      {
		if (y0 == 0.0)
		  y0 -= epsilon;
		if (y2 == 0.0)
		  y2 -= epsilon;

		r[0] = y0;
		r[1] = 2 * (y1 - y0);
		r[2] = (y2 - 2 * y1 + y0);

		/* degenerate roots (=tangent points) do not
		   contribute to the winding number. */
		if ((nRoots = QuadCurve2D.solveQuadratic(r)) == 2)
		  for (int i = 0; i < nRoots; i++)
		    {
		      float t = (float) r[i];
		      if (t > 0.0f && t < 1.0f)
		        {
			  double crossing = t * t * (x2 - 2 * x1 + x0)
			                    + 2 * t * (x1 - x0) + x0;
			  if (crossing >= 0.0 && crossing <= distance)
			    windingNumber += (2 * t * (y2 - 2 * y1 + y0)
			                   + 2 * (y1 - y0) < 0) ? 1 : negative;
		        }
		    }
	      }

	    cx = xpoints[pos - 1] - (float) x;
	    cy = ypoints[pos - 1] - (float) y;
	    break;
	  case PathIterator.SEG_CUBICTO:
	    x0 = cx;
	    y0 = cy;
	    x1 = xpoints[pos] - x;
	    y1 = ypoints[pos++] - y;
	    x2 = xpoints[pos] - x;
	    y2 = ypoints[pos++] - y;
	    x3 = xpoints[pos] - x;
	    y3 = ypoints[pos++] - y;

	    /* check if curve may intersect X+ axis. */
	    if ((x0 > 0.0 || x1 > 0.0 || x2 > 0.0 || x3 > 0.0)
	        && (y0 * y1 <= 0 || y1 * y2 <= 0 || y2 * y3 <= 0))
	      {
		if (y0 == 0.0)
		  y0 -= epsilon;
		if (y3 == 0.0)
		  y3 -= epsilon;

		r[0] = y0;
		r[1] = 3 * (y1 - y0);
		r[2] = 3 * (y2 + y0 - 2 * y1);
		r[3] = y3 - 3 * y2 + 3 * y1 - y0;

		if ((nRoots = CubicCurve2D.solveCubic(r)) != 0)
		  for (int i = 0; i < nRoots; i++)
		    {
		      float t = (float) r[i];
		      if (t > 0.0 && t < 1.0)
		        {
			  double crossing = -(t * t * t) * (x0 - 3 * x1
			                    + 3 * x2 - x3)
			                    + 3 * t * t * (x0 - 2 * x1 + x2)
			                    + 3 * t * (x1 - x0) + x0;
			  if (crossing >= 0 && crossing <= distance)
			    windingNumber += (3 * t * t * (y3 + 3 * y1
			                     - 3 * y2 - y0)
			                     + 6 * t * (y0 - 2 * y1 + y2)
			                   + 3 * (y1 - y0) < 0) ? 1 : negative;
		        }
		    }
	      }

	    cx = xpoints[pos - 1] - (float) x;
	    cy = ypoints[pos - 1] - (float) y;
	    break;
	  }
      }

    // swap coordinates back
    if (useYaxis)
      {
	float[] swap;
	swap = ypoints;
	ypoints = xpoints;
	xpoints = swap;
      }
    return (windingNumber);
  }
} // class GeneralPath