Source for java.awt.geom.CubicCurve2D

   1: /* CubicCurve2D.java -- represents a parameterized cubic curve in 2-D space
   2:    Copyright (C) 2002, 2003, 2004 Free Software Foundation
   3: 
   4: This file is part of GNU Classpath.
   5: 
   6: GNU Classpath is free software; you can redistribute it and/or modify
   7: it under the terms of the GNU General Public License as published by
   8: the Free Software Foundation; either version 2, or (at your option)
   9: any later version.
  10: 
  11: GNU Classpath is distributed in the hope that it will be useful, but
  12: WITHOUT ANY WARRANTY; without even the implied warranty of
  13: MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
  14: General Public License for more details.
  15: 
  16: You should have received a copy of the GNU General Public License
  17: along with GNU Classpath; see the file COPYING.  If not, write to the
  18: Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
  19: 02110-1301 USA.
  20: 
  21: Linking this library statically or dynamically with other modules is
  22: making a combined work based on this library.  Thus, the terms and
  23: conditions of the GNU General Public License cover the whole
  24: combination.
  25: 
  26: As a special exception, the copyright holders of this library give you
  27: permission to link this library with independent modules to produce an
  28: executable, regardless of the license terms of these independent
  29: modules, and to copy and distribute the resulting executable under
  30: terms of your choice, provided that you also meet, for each linked
  31: independent module, the terms and conditions of the license of that
  32: module.  An independent module is a module which is not derived from
  33: or based on this library.  If you modify this library, you may extend
  34: this exception to your version of the library, but you are not
  35: obligated to do so.  If you do not wish to do so, delete this
  36: exception statement from your version. */
  37: 
  38: package java.awt.geom;
  39: 
  40: import java.awt.Rectangle;
  41: import java.awt.Shape;
  42: import java.util.NoSuchElementException;
  43: 
  44: 
  45: /**
  46:  * A two-dimensional curve that is parameterized with a cubic
  47:  * function.
  48:  *
  49:  * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
  50:  * alt="A drawing of a CubicCurve2D" />
  51:  *
  52:  * @author Eric Blake (ebb9@email.byu.edu)
  53:  * @author Graydon Hoare (graydon@redhat.com)
  54:  * @author Sascha Brawer (brawer@dandelis.ch)
  55:  * @author Sven de Marothy (sven@physto.se)
  56:  *
  57:  * @since 1.2
  58:  */
  59: public abstract class CubicCurve2D implements Shape, Cloneable
  60: {
  61:   private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0;
  62:   private static final double EPSILON = 1E-10;
  63: 
  64:   /**
  65:    * Constructs a new CubicCurve2D. Typical users will want to
  66:    * construct instances of a subclass, such as {@link
  67:    * CubicCurve2D.Float} or {@link CubicCurve2D.Double}.
  68:    */
  69:   protected CubicCurve2D()
  70:   {
  71:   }
  72: 
  73:   /**
  74:    * Returns the <i>x</i> coordinate of the curve&#x2019;s start
  75:    * point.
  76:    */
  77:   public abstract double getX1();
  78: 
  79:   /**
  80:    * Returns the <i>y</i> coordinate of the curve&#x2019;s start
  81:    * point.
  82:    */
  83:   public abstract double getY1();
  84: 
  85:   /**
  86:    * Returns the curve&#x2019;s start point.
  87:    */
  88:   public abstract Point2D getP1();
  89: 
  90:   /**
  91:    * Returns the <i>x</i> coordinate of the curve&#x2019;s first
  92:    * control point.
  93:    */
  94:   public abstract double getCtrlX1();
  95: 
  96:   /**
  97:    * Returns the <i>y</i> coordinate of the curve&#x2019;s first
  98:    * control point.
  99:    */
 100:   public abstract double getCtrlY1();
 101: 
 102:   /**
 103:    * Returns the curve&#x2019;s first control point.
 104:    */
 105:   public abstract Point2D getCtrlP1();
 106: 
 107:   /**
 108:    * Returns the <i>x</i> coordinate of the curve&#x2019;s second
 109:    * control point.
 110:    */
 111:   public abstract double getCtrlX2();
 112: 
 113:   /**
 114:    * Returns the <i>y</i> coordinate of the curve&#x2019;s second
 115:    * control point.
 116:    */
 117:   public abstract double getCtrlY2();
 118: 
 119:   /**
 120:    * Returns the curve&#x2019;s second control point.
 121:    */
 122:   public abstract Point2D getCtrlP2();
 123: 
 124:   /**
 125:    * Returns the <i>x</i> coordinate of the curve&#x2019;s end
 126:    * point.
 127:    */
 128:   public abstract double getX2();
 129: 
 130:   /**
 131:    * Returns the <i>y</i> coordinate of the curve&#x2019;s end
 132:    * point.
 133:    */
 134:   public abstract double getY2();
 135: 
 136:   /**
 137:    * Returns the curve&#x2019;s end point.
 138:    */
 139:   public abstract Point2D getP2();
 140: 
 141:   /**
 142:    * Changes the curve geometry, separately specifying each coordinate
 143:    * value.
 144:    *
 145:    * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
 146:    * alt="A drawing of a CubicCurve2D" />
 147:    *
 148:    * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new start
 149:    * point.
 150:    *
 151:    * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
 152:    * point.
 153:    *
 154:    * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s new
 155:    * first control point.
 156:    *
 157:    * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s new
 158:    * first control point.
 159:    *
 160:    * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s new
 161:    * second control point.
 162:    *
 163:    * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s new
 164:    * second control point.
 165:    *
 166:    * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
 167:    * point.
 168:    *
 169:    * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new end
 170:    * point.
 171:    */
 172:   public abstract void setCurve(double x1, double y1, double cx1, double cy1,
 173:                                 double cx2, double cy2, double x2, double y2);
 174: 
 175:   /**
 176:    * Changes the curve geometry, specifying coordinate values in an
 177:    * array.
 178:    *
 179:    * @param coords an array containing the new coordinate values.  The
 180:    * <i>x</i> coordinate of the new start point is located at
 181:    * <code>coords[offset]</code>, its <i>y</i> coordinate at
 182:    * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
 183:    * new first control point is located at <code>coords[offset +
 184:    * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
 185:    * 3]</code>.  The <i>x</i> coordinate of the new second control
 186:    * point is located at <code>coords[offset + 4]</code>, its <i>y</i>
 187:    * coordinate at <code>coords[offset + 5]</code>.  The <i>x</i>
 188:    * coordinate of the new end point is located at <code>coords[offset
 189:    * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
 190:    * 7]</code>.
 191:    *
 192:    * @param offset the offset of the first coordinate value in
 193:    * <code>coords</code>.
 194:    */
 195:   public void setCurve(double[] coords, int offset)
 196:   {
 197:     setCurve(coords[offset++], coords[offset++], coords[offset++],
 198:              coords[offset++], coords[offset++], coords[offset++],
 199:              coords[offset++], coords[offset++]);
 200:   }
 201: 
 202:   /**
 203:    * Changes the curve geometry, specifying coordinate values in
 204:    * separate Point objects.
 205:    *
 206:    * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
 207:    * alt="A drawing of a CubicCurve2D" />
 208:    *
 209:    * <p>The curve does not keep any reference to the passed point
 210:    * objects. Therefore, a later change to <code>p1</code>,
 211:    * <code>c1</code>, <code>c2</code> or <code>p2</code> will not
 212:    * affect the curve geometry.
 213:    *
 214:    * @param p1 the new start point.
 215:    * @param c1 the new first control point.
 216:    * @param c2 the new second control point.
 217:    * @param p2 the new end point.
 218:    */
 219:   public void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
 220:   {
 221:     setCurve(p1.getX(), p1.getY(), c1.getX(), c1.getY(), c2.getX(), c2.getY(),
 222:              p2.getX(), p2.getY());
 223:   }
 224: 
 225:   /**
 226:    * Changes the curve geometry, specifying coordinate values in an
 227:    * array of Point objects.
 228:    *
 229:    * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
 230:    * alt="A drawing of a CubicCurve2D" />
 231:    *
 232:    * <p>The curve does not keep references to the passed point
 233:    * objects. Therefore, a later change to the <code>pts</code> array
 234:    * or any of its elements will not affect the curve geometry.
 235:    *
 236:    * @param pts an array containing the points. The new start point
 237:    * is located at <code>pts[offset]</code>, the new first control
 238:    * point at <code>pts[offset + 1]</code>, the new second control
 239:    * point at <code>pts[offset + 2]</code>, and the new end point
 240:    * at <code>pts[offset + 3]</code>.
 241:    *
 242:    * @param offset the offset of the start point in <code>pts</code>.
 243:    */
 244:   public void setCurve(Point2D[] pts, int offset)
 245:   {
 246:     setCurve(pts[offset].getX(), pts[offset++].getY(), pts[offset].getX(),
 247:              pts[offset++].getY(), pts[offset].getX(), pts[offset++].getY(),
 248:              pts[offset].getX(), pts[offset++].getY());
 249:   }
 250: 
 251:   /**
 252:    * Changes the curve geometry to that of another curve.
 253:    *
 254:    * @param c the curve whose coordinates will be copied.
 255:    */
 256:   public void setCurve(CubicCurve2D c)
 257:   {
 258:     setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
 259:              c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
 260:   }
 261: 
 262:   /**
 263:    * Calculates the squared flatness of a cubic curve, directly
 264:    * specifying each coordinate value. The flatness is the maximal
 265:    * distance of a control point to the line between start and end
 266:    * point.
 267:    *
 268:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 269:    * alt="A drawing that illustrates the flatness" />
 270:    *
 271:    * <p>In the above drawing, the straight line connecting start point
 272:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 273:    * control point C2 is father away from the gray line. Therefore,
 274:    * the result will be the square of the distance between C2 and the
 275:    * gray line, i.e. the squared length of the red line.
 276:    *
 277:    * @param x1 the <i>x</i> coordinate of the start point P1.
 278:    * @param y1 the <i>y</i> coordinate of the start point P1.
 279:    * @param cx1 the <i>x</i> coordinate of the first control point C1.
 280:    * @param cy1 the <i>y</i> coordinate of the first control point C1.
 281:    * @param cx2 the <i>x</i> coordinate of the second control point C2.
 282:    * @param cy2 the <i>y</i> coordinate of the second control point C2.
 283:    * @param x2 the <i>x</i> coordinate of the end point P2.
 284:    * @param y2 the <i>y</i> coordinate of the end point P2.
 285:    */
 286:   public static double getFlatnessSq(double x1, double y1, double cx1,
 287:                                      double cy1, double cx2, double cy2,
 288:                                      double x2, double y2)
 289:   {
 290:     return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, cx1, cy1),
 291:                     Line2D.ptSegDistSq(x1, y1, x2, y2, cx2, cy2));
 292:   }
 293: 
 294:   /**
 295:    * Calculates the flatness of a cubic curve, directly specifying
 296:    * each coordinate value. The flatness is the maximal distance of a
 297:    * control point to the line between start and end point.
 298:    *
 299:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 300:    * alt="A drawing that illustrates the flatness" />
 301:    *
 302:    * <p>In the above drawing, the straight line connecting start point
 303:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 304:    * control point C2 is father away from the gray line. Therefore,
 305:    * the result will be the distance between C2 and the gray line,
 306:    * i.e. the length of the red line.
 307:    *
 308:    * @param x1 the <i>x</i> coordinate of the start point P1.
 309:    * @param y1 the <i>y</i> coordinate of the start point P1.
 310:    * @param cx1 the <i>x</i> coordinate of the first control point C1.
 311:    * @param cy1 the <i>y</i> coordinate of the first control point C1.
 312:    * @param cx2 the <i>x</i> coordinate of the second control point C2.
 313:    * @param cy2 the <i>y</i> coordinate of the second control point C2.
 314:    * @param x2 the <i>x</i> coordinate of the end point P2.
 315:    * @param y2 the <i>y</i> coordinate of the end point P2.
 316:    */
 317:   public static double getFlatness(double x1, double y1, double cx1,
 318:                                    double cy1, double cx2, double cy2,
 319:                                    double x2, double y2)
 320:   {
 321:     return Math.sqrt(getFlatnessSq(x1, y1, cx1, cy1, cx2, cy2, x2, y2));
 322:   }
 323: 
 324:   /**
 325:    * Calculates the squared flatness of a cubic curve, specifying the
 326:    * coordinate values in an array. The flatness is the maximal
 327:    * distance of a control point to the line between start and end
 328:    * point.
 329:    *
 330:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 331:    * alt="A drawing that illustrates the flatness" />
 332:    *
 333:    * <p>In the above drawing, the straight line connecting start point
 334:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 335:    * control point C2 is father away from the gray line. Therefore,
 336:    * the result will be the square of the distance between C2 and the
 337:    * gray line, i.e. the squared length of the red line.
 338:    *
 339:    * @param coords an array containing the coordinate values.  The
 340:    * <i>x</i> coordinate of the start point P1 is located at
 341:    * <code>coords[offset]</code>, its <i>y</i> coordinate at
 342:    * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
 343:    * first control point C1 is located at <code>coords[offset +
 344:    * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
 345:    * 3]</code>. The <i>x</i> coordinate of the second control point C2
 346:    * is located at <code>coords[offset + 4]</code>, its <i>y</i>
 347:    * coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
 348:    * coordinate of the end point P2 is located at <code>coords[offset
 349:    * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
 350:    * 7]</code>.
 351:    *
 352:    * @param offset the offset of the first coordinate value in
 353:    * <code>coords</code>.
 354:    */
 355:   public static double getFlatnessSq(double[] coords, int offset)
 356:   {
 357:     return getFlatnessSq(coords[offset++], coords[offset++], coords[offset++],
 358:                          coords[offset++], coords[offset++], coords[offset++],
 359:                          coords[offset++], coords[offset++]);
 360:   }
 361: 
 362:   /**
 363:    * Calculates the flatness of a cubic curve, specifying the
 364:    * coordinate values in an array. The flatness is the maximal
 365:    * distance of a control point to the line between start and end
 366:    * point.
 367:    *
 368:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 369:    * alt="A drawing that illustrates the flatness" />
 370:    *
 371:    * <p>In the above drawing, the straight line connecting start point
 372:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 373:    * control point C2 is father away from the gray line. Therefore,
 374:    * the result will be the distance between C2 and the gray line,
 375:    * i.e. the length of the red line.
 376:    *
 377:    * @param coords an array containing the coordinate values.  The
 378:    * <i>x</i> coordinate of the start point P1 is located at
 379:    * <code>coords[offset]</code>, its <i>y</i> coordinate at
 380:    * <code>coords[offset + 1]</code>.  The <i>x</i> coordinate of the
 381:    * first control point C1 is located at <code>coords[offset +
 382:    * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
 383:    * 3]</code>. The <i>x</i> coordinate of the second control point C2
 384:    * is located at <code>coords[offset + 4]</code>, its <i>y</i>
 385:    * coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
 386:    * coordinate of the end point P2 is located at <code>coords[offset
 387:    * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
 388:    * 7]</code>.
 389:    *
 390:    * @param offset the offset of the first coordinate value in
 391:    * <code>coords</code>.
 392:    */
 393:   public static double getFlatness(double[] coords, int offset)
 394:   {
 395:     return Math.sqrt(getFlatnessSq(coords[offset++], coords[offset++],
 396:                                    coords[offset++], coords[offset++],
 397:                                    coords[offset++], coords[offset++],
 398:                                    coords[offset++], coords[offset++]));
 399:   }
 400: 
 401:   /**
 402:    * Calculates the squared flatness of this curve.  The flatness is
 403:    * the maximal distance of a control point to the line between start
 404:    * and end point.
 405:    *
 406:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 407:    * alt="A drawing that illustrates the flatness" />
 408:    *
 409:    * <p>In the above drawing, the straight line connecting start point
 410:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 411:    * control point C2 is father away from the gray line. Therefore,
 412:    * the result will be the square of the distance between C2 and the
 413:    * gray line, i.e. the squared length of the red line.
 414:    */
 415:   public double getFlatnessSq()
 416:   {
 417:     return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
 418:                          getCtrlX2(), getCtrlY2(), getX2(), getY2());
 419:   }
 420: 
 421:   /**
 422:    * Calculates the flatness of this curve.  The flatness is the
 423:    * maximal distance of a control point to the line between start and
 424:    * end point.
 425:    *
 426:    * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
 427:    * alt="A drawing that illustrates the flatness" />
 428:    *
 429:    * <p>In the above drawing, the straight line connecting start point
 430:    * P1 and end point P2 is depicted in gray.  In comparison to C1,
 431:    * control point C2 is father away from the gray line. Therefore,
 432:    * the result will be the distance between C2 and the gray line,
 433:    * i.e. the length of the red line.
 434:    */
 435:   public double getFlatness()
 436:   {
 437:     return Math.sqrt(getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
 438:                                    getCtrlX2(), getCtrlY2(), getX2(), getY2()));
 439:   }
 440: 
 441:   /**
 442:    * Subdivides this curve into two halves.
 443:    *
 444:    * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
 445:    * height="180" alt="A drawing that illustrates the effects of
 446:    * subdividing a CubicCurve2D" />
 447:    *
 448:    * @param left a curve whose geometry will be set to the left half
 449:    * of this curve, or <code>null</code> if the caller is not
 450:    * interested in the left half.
 451:    *
 452:    * @param right a curve whose geometry will be set to the right half
 453:    * of this curve, or <code>null</code> if the caller is not
 454:    * interested in the right half.
 455:    */
 456:   public void subdivide(CubicCurve2D left, CubicCurve2D right)
 457:   {
 458:     // Use empty slots at end to share single array.
 459:     double[] d = new double[]
 460:                  {
 461:                    getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(),
 462:                    getCtrlY2(), getX2(), getY2(), 0, 0, 0, 0, 0, 0
 463:                  };
 464:     subdivide(d, 0, d, 0, d, 6);
 465:     if (left != null)
 466:       left.setCurve(d, 0);
 467:     if (right != null)
 468:       right.setCurve(d, 6);
 469:   }
 470: 
 471:   /**
 472:    * Subdivides a cubic curve into two halves.
 473:    *
 474:    * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
 475:    * height="180" alt="A drawing that illustrates the effects of
 476:    * subdividing a CubicCurve2D" />
 477:    *
 478:    * @param src the curve to be subdivided.
 479:    *
 480:    * @param left a curve whose geometry will be set to the left half
 481:    * of <code>src</code>, or <code>null</code> if the caller is not
 482:    * interested in the left half.
 483:    *
 484:    * @param right a curve whose geometry will be set to the right half
 485:    * of <code>src</code>, or <code>null</code> if the caller is not
 486:    * interested in the right half.
 487:    */
 488:   public static void subdivide(CubicCurve2D src, CubicCurve2D left,
 489:                                CubicCurve2D right)
 490:   {
 491:     src.subdivide(left, right);
 492:   }
 493: 
 494:   /**
 495:    * Subdivides a cubic curve into two halves, passing all coordinates
 496:    * in an array.
 497:    *
 498:    * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
 499:    * height="180" alt="A drawing that illustrates the effects of
 500:    * subdividing a CubicCurve2D" />
 501:    *
 502:    * <p>The left end point and the right start point will always be
 503:    * identical. Memory-concious programmers thus may want to pass the
 504:    * same array for both <code>left</code> and <code>right</code>, and
 505:    * set <code>rightOff</code> to <code>leftOff + 6</code>.
 506:    *
 507:    * @param src an array containing the coordinates of the curve to be
 508:    * subdivided.  The <i>x</i> coordinate of the start point P1 is
 509:    * located at <code>src[srcOff]</code>, its <i>y</i> at
 510:    * <code>src[srcOff + 1]</code>.  The <i>x</i> coordinate of the
 511:    * first control point C1 is located at <code>src[srcOff +
 512:    * 2]</code>, its <i>y</i> at <code>src[srcOff + 3]</code>.  The
 513:    * <i>x</i> coordinate of the second control point C2 is located at
 514:    * <code>src[srcOff + 4]</code>, its <i>y</i> at <code>src[srcOff +
 515:    * 5]</code>. The <i>x</i> coordinate of the end point is located at
 516:    * <code>src[srcOff + 6]</code>, its <i>y</i> at <code>src[srcOff +
 517:    * 7]</code>.
 518:    *
 519:    * @param srcOff an offset into <code>src</code>, specifying
 520:    * the index of the start point&#x2019;s <i>x</i> coordinate.
 521:    *
 522:    * @param left an array that will receive the coordinates of the
 523:    * left half of <code>src</code>. It is acceptable to pass
 524:    * <code>src</code>. A caller who is not interested in the left half
 525:    * can pass <code>null</code>.
 526:    *
 527:    * @param leftOff an offset into <code>left</code>, specifying the
 528:    * index where the start point&#x2019;s <i>x</i> coordinate will be
 529:    * stored.
 530:    *
 531:    * @param right an array that will receive the coordinates of the
 532:    * right half of <code>src</code>. It is acceptable to pass
 533:    * <code>src</code> or <code>left</code>. A caller who is not
 534:    * interested in the right half can pass <code>null</code>.
 535:    *
 536:    * @param rightOff an offset into <code>right</code>, specifying the
 537:    * index where the start point&#x2019;s <i>x</i> coordinate will be
 538:    * stored.
 539:    */
 540:   public static void subdivide(double[] src, int srcOff, double[] left,
 541:                                int leftOff, double[] right, int rightOff)
 542:   {
 543:     // To understand this code, please have a look at the image
 544:     // "CubicCurve2D-3.png" in the sub-directory "doc-files".
 545:     double src_C1_x;
 546:     double src_C1_y;
 547:     double src_C2_x;
 548:     double src_C2_y;
 549:     double left_P1_x;
 550:     double left_P1_y;
 551:     double left_C1_x;
 552:     double left_C1_y;
 553:     double left_C2_x;
 554:     double left_C2_y;
 555:     double right_C1_x;
 556:     double right_C1_y;
 557:     double right_C2_x;
 558:     double right_C2_y;
 559:     double right_P2_x;
 560:     double right_P2_y;
 561:     double Mid_x; // Mid = left.P2 = right.P1
 562:     double Mid_y; // Mid = left.P2 = right.P1
 563: 
 564:     left_P1_x = src[srcOff];
 565:     left_P1_y = src[srcOff + 1];
 566:     src_C1_x = src[srcOff + 2];
 567:     src_C1_y = src[srcOff + 3];
 568:     src_C2_x = src[srcOff + 4];
 569:     src_C2_y = src[srcOff + 5];
 570:     right_P2_x = src[srcOff + 6];
 571:     right_P2_y = src[srcOff + 7];
 572: 
 573:     left_C1_x = (left_P1_x + src_C1_x) / 2;
 574:     left_C1_y = (left_P1_y + src_C1_y) / 2;
 575:     right_C2_x = (right_P2_x + src_C2_x) / 2;
 576:     right_C2_y = (right_P2_y + src_C2_y) / 2;
 577:     Mid_x = (src_C1_x + src_C2_x) / 2;
 578:     Mid_y = (src_C1_y + src_C2_y) / 2;
 579:     left_C2_x = (left_C1_x + Mid_x) / 2;
 580:     left_C2_y = (left_C1_y + Mid_y) / 2;
 581:     right_C1_x = (Mid_x + right_C2_x) / 2;
 582:     right_C1_y = (Mid_y + right_C2_y) / 2;
 583:     Mid_x = (left_C2_x + right_C1_x) / 2;
 584:     Mid_y = (left_C2_y + right_C1_y) / 2;
 585: 
 586:     if (left != null)
 587:       {
 588:         left[leftOff] = left_P1_x;
 589:         left[leftOff + 1] = left_P1_y;
 590:         left[leftOff + 2] = left_C1_x;
 591:         left[leftOff + 3] = left_C1_y;
 592:         left[leftOff + 4] = left_C2_x;
 593:         left[leftOff + 5] = left_C2_y;
 594:         left[leftOff + 6] = Mid_x;
 595:         left[leftOff + 7] = Mid_y;
 596:       }
 597: 
 598:     if (right != null)
 599:       {
 600:         right[rightOff] = Mid_x;
 601:         right[rightOff + 1] = Mid_y;
 602:         right[rightOff + 2] = right_C1_x;
 603:         right[rightOff + 3] = right_C1_y;
 604:         right[rightOff + 4] = right_C2_x;
 605:         right[rightOff + 5] = right_C2_y;
 606:         right[rightOff + 6] = right_P2_x;
 607:         right[rightOff + 7] = right_P2_y;
 608:       }
 609:   }
 610: 
 611:   /**
 612:    * Finds the non-complex roots of a cubic equation, placing the
 613:    * results into the same array as the equation coefficients. The
 614:    * following equation is being solved:
 615:    *
 616:    * <blockquote><code>eqn[3]</code> &#xb7; <i>x</i><sup>3</sup>
 617:    * + <code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
 618:    * + <code>eqn[1]</code> &#xb7; <i>x</i>
 619:    * + <code>eqn[0]</code>
 620:    * = 0
 621:    * </blockquote>
 622:    *
 623:    * <p>For some background about solving cubic equations, see the
 624:    * article <a
 625:    * href="http://planetmath.org/encyclopedia/CubicFormula.html"
 626:    * >&#x201c;Cubic Formula&#x201d;</a> in <a
 627:    * href="http://planetmath.org/" >PlanetMath</a>.  For an extensive
 628:    * library of numerical algorithms written in the C programming
 629:    * language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
 630:    * Scientific Library</a>, from which this implementation was
 631:    * adapted.
 632:    *
 633:    * @param eqn an array with the coefficients of the equation. When
 634:    * this procedure has returned, <code>eqn</code> will contain the
 635:    * non-complex solutions of the equation, in no particular order.
 636:    *
 637:    * @return the number of non-complex solutions. A result of 0
 638:    * indicates that the equation has no non-complex solutions. A
 639:    * result of -1 indicates that the equation is constant (i.e.,
 640:    * always or never zero).
 641:    *
 642:    * @see #solveCubic(double[], double[])
 643:    * @see QuadCurve2D#solveQuadratic(double[],double[])
 644:    *
 645:    * @author Brian Gough (bjg@network-theory.com)
 646:    * (original C implementation in the <a href=
 647:    * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
 648:    *
 649:    * @author Sascha Brawer (brawer@dandelis.ch)
 650:    * (adaptation to Java)
 651:    */
 652:   public static int solveCubic(double[] eqn)
 653:   {
 654:     return solveCubic(eqn, eqn);
 655:   }
 656: 
 657:   /**
 658:    * Finds the non-complex roots of a cubic equation. The following
 659:    * equation is being solved:
 660:    *
 661:    * <blockquote><code>eqn[3]</code> &#xb7; <i>x</i><sup>3</sup>
 662:    * + <code>eqn[2]</code> &#xb7; <i>x</i><sup>2</sup>
 663:    * + <code>eqn[1]</code> &#xb7; <i>x</i>
 664:    * + <code>eqn[0]</code>
 665:    * = 0
 666:    * </blockquote>
 667:    *
 668:    * <p>For some background about solving cubic equations, see the
 669:    * article <a
 670:    * href="http://planetmath.org/encyclopedia/CubicFormula.html"
 671:    * >&#x201c;Cubic Formula&#x201d;</a> in <a
 672:    * href="http://planetmath.org/" >PlanetMath</a>.  For an extensive
 673:    * library of numerical algorithms written in the C programming
 674:    * language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
 675:    * Scientific Library</a>, from which this implementation was
 676:    * adapted.
 677:    *
 678:    * @see QuadCurve2D#solveQuadratic(double[],double[])
 679:    *
 680:    * @param eqn an array with the coefficients of the equation.
 681:    *
 682:    * @param res an array into which the non-complex roots will be
 683:    * stored.  The results may be in an arbitrary order. It is safe to
 684:    * pass the same array object reference for both <code>eqn</code>
 685:    * and <code>res</code>.
 686:    *
 687:    * @return the number of non-complex solutions. A result of 0
 688:    * indicates that the equation has no non-complex solutions. A
 689:    * result of -1 indicates that the equation is constant (i.e.,
 690:    * always or never zero).
 691:    *
 692:    * @author Brian Gough (bjg@network-theory.com)
 693:    * (original C implementation in the <a href=
 694:    * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
 695:    *
 696:    * @author Sascha Brawer (brawer@dandelis.ch)
 697:    * (adaptation to Java)
 698:    */
 699:   public static int solveCubic(double[] eqn, double[] res)
 700:   {
 701:     // Adapted from poly/solve_cubic.c in the GNU Scientific Library
 702:     // (GSL), revision 1.7 of 2003-07-26. For the original source, see
 703:     // http://www.gnu.org/software/gsl/
 704:     //
 705:     // Brian Gough, the author of that code, has granted the
 706:     // permission to use it in GNU Classpath under the GNU Classpath
 707:     // license, and has assigned the copyright to the Free Software
 708:     // Foundation.
 709:     //
 710:     // The Java implementation is very similar to the GSL code, but
 711:     // not a strict one-to-one copy. For example, GSL would sort the
 712:     // result.
 713: 
 714:     double a;
 715:     double b;
 716:     double c;
 717:     double q;
 718:     double r;
 719:     double Q;
 720:     double R;
 721:     double c3;
 722:     double Q3;
 723:     double R2;
 724:     double CR2;
 725:     double CQ3;
 726: 
 727:     // If the cubic coefficient is zero, we have a quadratic equation.
 728:     c3 = eqn[3];
 729:     if (c3 == 0)
 730:       return QuadCurve2D.solveQuadratic(eqn, res);
 731: 
 732:     // Divide the equation by the cubic coefficient.
 733:     c = eqn[0] / c3;
 734:     b = eqn[1] / c3;
 735:     a = eqn[2] / c3;
 736: 
 737:     // We now need to solve x^3 + ax^2 + bx + c = 0.
 738:     q = a * a - 3 * b;
 739:     r = 2 * a * a * a - 9 * a * b + 27 * c;
 740: 
 741:     Q = q / 9;
 742:     R = r / 54;
 743: 
 744:     Q3 = Q * Q * Q;
 745:     R2 = R * R;
 746: 
 747:     CR2 = 729 * r * r;
 748:     CQ3 = 2916 * q * q * q;
 749: 
 750:     if (R == 0 && Q == 0)
 751:       {
 752:         // The GNU Scientific Library would return three identical
 753:         // solutions in this case.
 754:         res[0] = -a / 3;
 755:         return 1;
 756:       }
 757: 
 758:     if (CR2 == CQ3)
 759:       {
 760:         /* this test is actually R2 == Q3, written in a form suitable
 761:            for exact computation with integers */
 762:         /* Due to finite precision some double roots may be missed, and
 763:            considered to be a pair of complex roots z = x +/- epsilon i
 764:            close to the real axis. */
 765:         double sqrtQ = Math.sqrt(Q);
 766: 
 767:         if (R > 0)
 768:           {
 769:             res[0] = -2 * sqrtQ - a / 3;
 770:             res[1] = sqrtQ - a / 3;
 771:           }
 772:         else
 773:           {
 774:             res[0] = -sqrtQ - a / 3;
 775:             res[1] = 2 * sqrtQ - a / 3;
 776:           }
 777:         return 2;
 778:       }
 779: 
 780:     if (CR2 < CQ3) /* equivalent to R2 < Q3 */
 781:       {
 782:         double sqrtQ = Math.sqrt(Q);
 783:         double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ;
 784:         double theta = Math.acos(R / sqrtQ3);
 785:         double norm = -2 * sqrtQ;
 786:         res[0] = norm * Math.cos(theta / 3) - a / 3;
 787:         res[1] = norm * Math.cos((theta + 2.0 * Math.PI) / 3) - a / 3;
 788:         res[2] = norm * Math.cos((theta - 2.0 * Math.PI) / 3) - a / 3;
 789: 
 790:         // The GNU Scientific Library sorts the results. We don't.
 791:         return 3;
 792:       }
 793: 
 794:     double sgnR = (R >= 0 ? 1 : -1);
 795:     double A = -sgnR * Math.pow(Math.abs(R) + Math.sqrt(R2 - Q3), 1.0 / 3.0);
 796:     double B = Q / A;
 797:     res[0] = A + B - a / 3;
 798:     return 1;
 799:   }
 800: 
 801:   /**
 802:    * Determines whether a position lies inside the area bounded
 803:    * by the curve and the straight line connecting its end points.
 804:    *
 805:    * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
 806:    * alt="A drawing of the area spanned by the curve" />
 807:    *
 808:    * <p>The above drawing illustrates in which area points are
 809:    * considered &#x201c;inside&#x201d; a CubicCurve2D.
 810:    */
 811:   public boolean contains(double x, double y)
 812:   {
 813:     if (! getBounds2D().contains(x, y))
 814:       return false;
 815: 
 816:     return ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0);
 817:   }
 818: 
 819:   /**
 820:    * Determines whether a point lies inside the area bounded
 821:    * by the curve and the straight line connecting its end points.
 822:    *
 823:    * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
 824:    * alt="A drawing of the area spanned by the curve" />
 825:    *
 826:    * <p>The above drawing illustrates in which area points are
 827:    * considered &#x201c;inside&#x201d; a CubicCurve2D.
 828:    */
 829:   public boolean contains(Point2D p)
 830:   {
 831:     return contains(p.getX(), p.getY());
 832:   }
 833: 
 834:   /**
 835:    * Determines whether any part of a rectangle is inside the area bounded
 836:    * by the curve and the straight line connecting its end points.
 837:    *
 838:    * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
 839:    * alt="A drawing of the area spanned by the curve" />
 840:    *
 841:    * <p>The above drawing illustrates in which area points are
 842:    * considered &#x201c;inside&#x201d; in a CubicCurve2D.
 843:    * @see #contains(double, double)
 844:    */
 845:   public boolean intersects(double x, double y, double w, double h)
 846:   {
 847:     if (! getBounds2D().contains(x, y, w, h))
 848:       return false;
 849: 
 850:     /* Does any edge intersect? */
 851:     if (getAxisIntersections(x, y, true, w) != 0 /* top */
 852:         || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
 853:         || getAxisIntersections(x + w, y, false, h) != 0 /* right */
 854:         || getAxisIntersections(x, y, false, h) != 0) /* left */
 855:       return true;
 856: 
 857:     /* No intersections, is any point inside? */
 858:     if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
 859:       return true;
 860: 
 861:     return false;
 862:   }
 863: 
 864:   /**
 865:    * Determines whether any part of a Rectangle2D is inside the area bounded
 866:    * by the curve and the straight line connecting its end points.
 867:    * @see #intersects(double, double, double, double)
 868:    */
 869:   public boolean intersects(Rectangle2D r)
 870:   {
 871:     return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
 872:   }
 873: 
 874:   /**
 875:    * Determine whether a rectangle is entirely inside the area that is bounded
 876:    * by the curve and the straight line connecting its end points.
 877:    *
 878:    * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
 879:    * alt="A drawing of the area spanned by the curve" />
 880:    *
 881:    * <p>The above drawing illustrates in which area points are
 882:    * considered &#x201c;inside&#x201d; a CubicCurve2D.
 883:    * @see #contains(double, double)
 884:    */
 885:   public boolean contains(double x, double y, double w, double h)
 886:   {
 887:     if (! getBounds2D().intersects(x, y, w, h))
 888:       return false;
 889: 
 890:     /* Does any edge intersect? */
 891:     if (getAxisIntersections(x, y, true, w) != 0 /* top */
 892:         || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
 893:         || getAxisIntersections(x + w, y, false, h) != 0 /* right */
 894:         || getAxisIntersections(x, y, false, h) != 0) /* left */
 895:       return false;
 896: 
 897:     /* No intersections, is any point inside? */
 898:     if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
 899:       return true;
 900: 
 901:     return false;
 902:   }
 903: 
 904:   /**
 905:    * Determine whether a Rectangle2D is entirely inside the area that is
 906:    * bounded by the curve and the straight line connecting its end points.
 907:    *
 908:    * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
 909:    * alt="A drawing of the area spanned by the curve" />
 910:    *
 911:    * <p>The above drawing illustrates in which area points are
 912:    * considered &#x201c;inside&#x201d; a CubicCurve2D.
 913:    * @see #contains(double, double)
 914:    */
 915:   public boolean contains(Rectangle2D r)
 916:   {
 917:     return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
 918:   }
 919: 
 920:   /**
 921:    * Determines the smallest rectangle that encloses the
 922:    * curve&#x2019;s start, end and control points.
 923:    */
 924:   public Rectangle getBounds()
 925:   {
 926:     return getBounds2D().getBounds();
 927:   }
 928: 
 929:   public PathIterator getPathIterator(final AffineTransform at)
 930:   {
 931:     return new PathIterator()
 932:       {
 933:         /** Current coordinate. */
 934:         private int current = 0;
 935: 
 936:         public int getWindingRule()
 937:         {
 938:           return WIND_NON_ZERO;
 939:         }
 940: 
 941:         public boolean isDone()
 942:         {
 943:           return current >= 2;
 944:         }
 945: 
 946:         public void next()
 947:         {
 948:           current++;
 949:         }
 950: 
 951:         public int currentSegment(float[] coords)
 952:         {
 953:           int result;
 954:           switch (current)
 955:             {
 956:             case 0:
 957:               coords[0] = (float) getX1();
 958:               coords[1] = (float) getY1();
 959:               result = SEG_MOVETO;
 960:               break;
 961:             case 1:
 962:               coords[0] = (float) getCtrlX1();
 963:               coords[1] = (float) getCtrlY1();
 964:               coords[2] = (float) getCtrlX2();
 965:               coords[3] = (float) getCtrlY2();
 966:               coords[4] = (float) getX2();
 967:               coords[5] = (float) getY2();
 968:               result = SEG_CUBICTO;
 969:               break;
 970:             default:
 971:               throw new NoSuchElementException("cubic iterator out of bounds");
 972:             }
 973:           if (at != null)
 974:             at.transform(coords, 0, coords, 0, 3);
 975:           return result;
 976:         }
 977: 
 978:         public int currentSegment(double[] coords)
 979:         {
 980:           int result;
 981:           switch (current)
 982:             {
 983:             case 0:
 984:               coords[0] = getX1();
 985:               coords[1] = getY1();
 986:               result = SEG_MOVETO;
 987:               break;
 988:             case 1:
 989:               coords[0] = getCtrlX1();
 990:               coords[1] = getCtrlY1();
 991:               coords[2] = getCtrlX2();
 992:               coords[3] = getCtrlY2();
 993:               coords[4] = getX2();
 994:               coords[5] = getY2();
 995:               result = SEG_CUBICTO;
 996:               break;
 997:             default:
 998:               throw new NoSuchElementException("cubic iterator out of bounds");
 999:             }
1000:           if (at != null)
1001:             at.transform(coords, 0, coords, 0, 3);
1002:           return result;
1003:         }
1004:       };
1005:   }
1006: 
1007:   public PathIterator getPathIterator(AffineTransform at, double flatness)
1008:   {
1009:     return new FlatteningPathIterator(getPathIterator(at), flatness);
1010:   }
1011: 
1012:   /**
1013:    * Create a new curve with the same contents as this one.
1014:    *
1015:    * @return the clone.
1016:    */
1017:   public Object clone()
1018:   {
1019:     try
1020:       {
1021:         return super.clone();
1022:       }
1023:     catch (CloneNotSupportedException e)
1024:       {
1025:         throw (Error) new InternalError().initCause(e); // Impossible
1026:       }
1027:   }
1028: 
1029:   /**
1030:    * Helper method used by contains() and intersects() methods, that
1031:    * returns the number of curve/line intersections on a given axis
1032:    * extending from a certain point.
1033:    *
1034:    * @param x x coordinate of the origin point
1035:    * @param y y coordinate of the origin point
1036:    * @param useYaxis axis used, if true the positive Y axis is used,
1037:    * false uses the positive X axis.
1038:    *
1039:    * This is an implementation of the line-crossings algorithm,
1040:    * Detailed in an article on Eric Haines' page:
1041:    * http://www.acm.org/tog/editors/erich/ptinpoly/
1042:    *
1043:    * A special-case not adressed in this code is self-intersections
1044:    * of the curve, e.g. if the axis intersects the self-itersection,
1045:    * the degenerate roots of the polynomial will erroneously count as
1046:    * a single intersection of the curve, and not two.
1047:    */
1048:   private int getAxisIntersections(double x, double y, boolean useYaxis,
1049:                                    double distance)
1050:   {
1051:     int nCrossings = 0;
1052:     double a0;
1053:     double a1;
1054:     double a2;
1055:     double a3;
1056:     double b0;
1057:     double b1;
1058:     double b2;
1059:     double b3;
1060:     double[] r = new double[4];
1061:     int nRoots;
1062: 
1063:     a0 = a3 = 0.0;
1064: 
1065:     if (useYaxis)
1066:       {
1067:         a0 = getY1() - y;
1068:         a1 = getCtrlY1() - y;
1069:         a2 = getCtrlY2() - y;
1070:         a3 = getY2() - y;
1071:         b0 = getX1() - x;
1072:         b1 = getCtrlX1() - x;
1073:         b2 = getCtrlX2() - x;
1074:         b3 = getX2() - x;
1075:       }
1076:     else
1077:       {
1078:         a0 = getX1() - x;
1079:         a1 = getCtrlX1() - x;
1080:         a2 = getCtrlX2() - x;
1081:         a3 = getX2() - x;
1082:         b0 = getY1() - y;
1083:         b1 = getCtrlY1() - y;
1084:         b2 = getCtrlY2() - y;
1085:         b3 = getY2() - y;
1086:       }
1087: 
1088:     /* If the axis intersects a start/endpoint, shift it up by some small
1089:        amount to guarantee the line is 'inside'
1090:        If this is not done, bad behaviour may result for points on that axis.*/
1091:     if (a0 == 0.0 || a3 == 0.0)
1092:       {
1093:         double small = getFlatness() * EPSILON;
1094:         if (a0 == 0.0)
1095:           a0 -= small;
1096:         if (a3 == 0.0)
1097:           a3 -= small;
1098:       }
1099: 
1100:     if (useYaxis)
1101:       {
1102:         if (Line2D.linesIntersect(b0, a0, b3, a3, EPSILON, 0.0, distance, 0.0))
1103:           nCrossings++;
1104:       }
1105:     else
1106:       {
1107:         if (Line2D.linesIntersect(a0, b0, a3, b3, 0.0, EPSILON, 0.0, distance))
1108:           nCrossings++;
1109:       }
1110: 
1111:     r[0] = a0;
1112:     r[1] = 3 * (a1 - a0);
1113:     r[2] = 3 * (a2 + a0 - 2 * a1);
1114:     r[3] = a3 - 3 * a2 + 3 * a1 - a0;
1115: 
1116:     if ((nRoots = solveCubic(r)) != 0)
1117:       for (int i = 0; i < nRoots; i++)
1118:         {
1119:           double t = r[i];
1120:           if (t >= 0.0 && t <= 1.0)
1121:             {
1122:               double crossing = -(t * t * t) * (b0 - 3 * b1 + 3 * b2 - b3)
1123:                                 + 3 * t * t * (b0 - 2 * b1 + b2)
1124:                                 + 3 * t * (b1 - b0) + b0;
1125:               if (crossing > 0.0 && crossing <= distance)
1126:                 nCrossings++;
1127:             }
1128:         }
1129: 
1130:     return (nCrossings);
1131:   }
1132: 
1133:   /**
1134:    * A two-dimensional curve that is parameterized with a cubic
1135:    * function and stores coordinate values in double-precision
1136:    * floating-point format.
1137:    *
1138:    * @see CubicCurve2D.Float
1139:    *
1140:    * @author Eric Blake (ebb9@email.byu.edu)
1141:    * @author Sascha Brawer (brawer@dandelis.ch)
1142:    */
1143:   public static class Double extends CubicCurve2D
1144:   {
1145:     /**
1146:      * The <i>x</i> coordinate of the curve&#x2019;s start point.
1147:      */
1148:     public double x1;
1149: 
1150:     /**
1151:      * The <i>y</i> coordinate of the curve&#x2019;s start point.
1152:      */
1153:     public double y1;
1154: 
1155:     /**
1156:      * The <i>x</i> coordinate of the curve&#x2019;s first control point.
1157:      */
1158:     public double ctrlx1;
1159: 
1160:     /**
1161:      * The <i>y</i> coordinate of the curve&#x2019;s first control point.
1162:      */
1163:     public double ctrly1;
1164: 
1165:     /**
1166:      * The <i>x</i> coordinate of the curve&#x2019;s second control point.
1167:      */
1168:     public double ctrlx2;
1169: 
1170:     /**
1171:      * The <i>y</i> coordinate of the curve&#x2019;s second control point.
1172:      */
1173:     public double ctrly2;
1174: 
1175:     /**
1176:      * The <i>x</i> coordinate of the curve&#x2019;s end point.
1177:      */
1178:     public double x2;
1179: 
1180:     /**
1181:      * The <i>y</i> coordinate of the curve&#x2019;s end point.
1182:      */
1183:     public double y2;
1184: 
1185:     /**
1186:      * Constructs a new CubicCurve2D that stores its coordinate values
1187:      * in double-precision floating-point format. All points are
1188:      * initially at position (0, 0).
1189:      */
1190:     public Double()
1191:     {
1192:     }
1193: 
1194:     /**
1195:      * Constructs a new CubicCurve2D that stores its coordinate values
1196:      * in double-precision floating-point format, specifying the
1197:      * initial position of each point.
1198:      *
1199:      * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1200:      * alt="A drawing of a CubicCurve2D" />
1201:      *
1202:      * @param x1 the <i>x</i> coordinate of the curve&#x2019;s start
1203:      * point.
1204:      *
1205:      * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
1206:      * point.
1207:      *
1208:      * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s first
1209:      * control point.
1210:      *
1211:      * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s first
1212:      * control point.
1213:      *
1214:      * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s second
1215:      * control point.
1216:      *
1217:      * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s second
1218:      * control point.
1219:      *
1220:      * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
1221:      * point.
1222:      *
1223:      * @param y2 the <i>y</i> coordinate of the curve&#x2019;s end
1224:      * point.
1225:      */
1226:     public Double(double x1, double y1, double cx1, double cy1, double cx2,
1227:                   double cy2, double x2, double y2)
1228:     {
1229:       this.x1 = x1;
1230:       this.y1 = y1;
1231:       ctrlx1 = cx1;
1232:       ctrly1 = cy1;
1233:       ctrlx2 = cx2;
1234:       ctrly2 = cy2;
1235:       this.x2 = x2;
1236:       this.y2 = y2;
1237:     }
1238: 
1239:     /**
1240:      * Returns the <i>x</i> coordinate of the curve&#x2019;s start
1241:      * point.
1242:      */
1243:     public double getX1()
1244:     {
1245:       return x1;
1246:     }
1247: 
1248:     /**
1249:      * Returns the <i>y</i> coordinate of the curve&#x2019;s start
1250:      * point.
1251:      */
1252:     public double getY1()
1253:     {
1254:       return y1;
1255:     }
1256: 
1257:     /**
1258:      * Returns the curve&#x2019;s start point.
1259:      */
1260:     public Point2D getP1()
1261:     {
1262:       return new Point2D.Double(x1, y1);
1263:     }
1264: 
1265:     /**
1266:      * Returns the <i>x</i> coordinate of the curve&#x2019;s first
1267:      * control point.
1268:      */
1269:     public double getCtrlX1()
1270:     {
1271:       return ctrlx1;
1272:     }
1273: 
1274:     /**
1275:      * Returns the <i>y</i> coordinate of the curve&#x2019;s first
1276:      * control point.
1277:      */
1278:     public double getCtrlY1()
1279:     {
1280:       return ctrly1;
1281:     }
1282: 
1283:     /**
1284:      * Returns the curve&#x2019;s first control point.
1285:      */
1286:     public Point2D getCtrlP1()
1287:     {
1288:       return new Point2D.Double(ctrlx1, ctrly1);
1289:     }
1290: 
1291:     /**
1292:      * Returns the <i>x</i> coordinate of the curve&#x2019;s second
1293:      * control point.
1294:      */
1295:     public double getCtrlX2()
1296:     {
1297:       return ctrlx2;
1298:     }
1299: 
1300:     /**
1301:      * Returns the <i>y</i> coordinate of the curve&#x2019;s second
1302:      * control point.
1303:      */
1304:     public double getCtrlY2()
1305:     {
1306:       return ctrly2;
1307:     }
1308: 
1309:     /**
1310:      * Returns the curve&#x2019;s second control point.
1311:      */
1312:     public Point2D getCtrlP2()
1313:     {
1314:       return new Point2D.Double(ctrlx2, ctrly2);
1315:     }
1316: 
1317:     /**
1318:      * Returns the <i>x</i> coordinate of the curve&#x2019;s end
1319:      * point.
1320:      */
1321:     public double getX2()
1322:     {
1323:       return x2;
1324:     }
1325: 
1326:     /**
1327:      * Returns the <i>y</i> coordinate of the curve&#x2019;s end
1328:      * point.
1329:      */
1330:     public double getY2()
1331:     {
1332:       return y2;
1333:     }
1334: 
1335:     /**
1336:      * Returns the curve&#x2019;s end point.
1337:      */
1338:     public Point2D getP2()
1339:     {
1340:       return new Point2D.Double(x2, y2);
1341:     }
1342: 
1343:     /**
1344:      * Changes the curve geometry, separately specifying each coordinate
1345:      * value.
1346:      *
1347:      * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1348:      * alt="A drawing of a CubicCurve2D" />
1349:      *
1350:      * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new start
1351:      * point.
1352:      *
1353:      * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
1354:      * point.
1355:      *
1356:      * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s new
1357:      * first control point.
1358:      *
1359:      * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s new
1360:      * first control point.
1361:      *
1362:      * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s new
1363:      * second control point.
1364:      *
1365:      * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s new
1366:      * second control point.
1367:      *
1368:      * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
1369:      * point.
1370:      *
1371:      * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new end
1372:      * point.
1373:      */
1374:     public void setCurve(double x1, double y1, double cx1, double cy1,
1375:                          double cx2, double cy2, double x2, double y2)
1376:     {
1377:       this.x1 = x1;
1378:       this.y1 = y1;
1379:       ctrlx1 = cx1;
1380:       ctrly1 = cy1;
1381:       ctrlx2 = cx2;
1382:       ctrly2 = cy2;
1383:       this.x2 = x2;
1384:       this.y2 = y2;
1385:     }
1386: 
1387:     /**
1388:      * Determines the smallest rectangle that encloses the
1389:      * curve&#x2019;s start, end and control points. As the
1390:      * illustration below shows, the invisible control points may cause
1391:      * the bounds to be much larger than the area that is actually
1392:      * covered by the curve.
1393:      *
1394:      * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
1395:      * alt="An illustration of the bounds of a CubicCurve2D" />
1396:      */
1397:     public Rectangle2D getBounds2D()
1398:     {
1399:       double nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
1400:       double ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
1401:       double nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
1402:       double ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
1403:       return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1);
1404:     }
1405:   }
1406: 
1407:   /**
1408:    * A two-dimensional curve that is parameterized with a cubic
1409:    * function and stores coordinate values in single-precision
1410:    * floating-point format.
1411:    *
1412:    * @see CubicCurve2D.Float
1413:    *
1414:    * @author Eric Blake (ebb9@email.byu.edu)
1415:    * @author Sascha Brawer (brawer@dandelis.ch)
1416:    */
1417:   public static class Float extends CubicCurve2D
1418:   {
1419:     /**
1420:      * The <i>x</i> coordinate of the curve&#x2019;s start point.
1421:      */
1422:     public float x1;
1423: 
1424:     /**
1425:      * The <i>y</i> coordinate of the curve&#x2019;s start point.
1426:      */
1427:     public float y1;
1428: 
1429:     /**
1430:      * The <i>x</i> coordinate of the curve&#x2019;s first control point.
1431:      */
1432:     public float ctrlx1;
1433: 
1434:     /**
1435:      * The <i>y</i> coordinate of the curve&#x2019;s first control point.
1436:      */
1437:     public float ctrly1;
1438: 
1439:     /**
1440:      * The <i>x</i> coordinate of the curve&#x2019;s second control point.
1441:      */
1442:     public float ctrlx2;
1443: 
1444:     /**
1445:      * The <i>y</i> coordinate of the curve&#x2019;s second control point.
1446:      */
1447:     public float ctrly2;
1448: 
1449:     /**
1450:      * The <i>x</i> coordinate of the curve&#x2019;s end point.
1451:      */
1452:     public float x2;
1453: 
1454:     /**
1455:      * The <i>y</i> coordinate of the curve&#x2019;s end point.
1456:      */
1457:     public float y2;
1458: 
1459:     /**
1460:      * Constructs a new CubicCurve2D that stores its coordinate values
1461:      * in single-precision floating-point format. All points are
1462:      * initially at position (0, 0).
1463:      */
1464:     public Float()
1465:     {
1466:     }
1467: 
1468:     /**
1469:      * Constructs a new CubicCurve2D that stores its coordinate values
1470:      * in single-precision floating-point format, specifying the
1471:      * initial position of each point.
1472:      *
1473:      * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1474:      * alt="A drawing of a CubicCurve2D" />
1475:      *
1476:      * @param x1 the <i>x</i> coordinate of the curve&#x2019;s start
1477:      * point.
1478:      *
1479:      * @param y1 the <i>y</i> coordinate of the curve&#x2019;s start
1480:      * point.
1481:      *
1482:      * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s first
1483:      * control point.
1484:      *
1485:      * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s first
1486:      * control point.
1487:      *
1488:      * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s second
1489:      * control point.
1490:      *
1491:      * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s second
1492:      * control point.
1493:      *
1494:      * @param x2 the <i>x</i> coordinate of the curve&#x2019;s end
1495:      * point.
1496:      *
1497:      * @param y2 the <i>y</i> coordinate of the curve&#x2019;s end
1498:      * point.
1499:      */
1500:     public Float(float x1, float y1, float cx1, float cy1, float cx2,
1501:                  float cy2, float x2, float y2)
1502:     {
1503:       this.x1 = x1;
1504:       this.y1 = y1;
1505:       ctrlx1 = cx1;
1506:       ctrly1 = cy1;
1507:       ctrlx2 = cx2;
1508:       ctrly2 = cy2;
1509:       this.x2 = x2;
1510:       this.y2 = y2;
1511:     }
1512: 
1513:     /**
1514:      * Returns the <i>x</i> coordinate of the curve&#x2019;s start
1515:      * point.
1516:      */
1517:     public double getX1()
1518:     {
1519:       return x1;
1520:     }
1521: 
1522:     /**
1523:      * Returns the <i>y</i> coordinate of the curve&#x2019;s start
1524:      * point.
1525:      */
1526:     public double getY1()
1527:     {
1528:       return y1;
1529:     }
1530: 
1531:     /**
1532:      * Returns the curve&#x2019;s start point.
1533:      */
1534:     public Point2D getP1()
1535:     {
1536:       return new Point2D.Float(x1, y1);
1537:     }
1538: 
1539:     /**
1540:      * Returns the <i>x</i> coordinate of the curve&#x2019;s first
1541:      * control point.
1542:      */
1543:     public double getCtrlX1()
1544:     {
1545:       return ctrlx1;
1546:     }
1547: 
1548:     /**
1549:      * Returns the <i>y</i> coordinate of the curve&#x2019;s first
1550:      * control point.
1551:      */
1552:     public double getCtrlY1()
1553:     {
1554:       return ctrly1;
1555:     }
1556: 
1557:     /**
1558:      * Returns the curve&#x2019;s first control point.
1559:      */
1560:     public Point2D getCtrlP1()
1561:     {
1562:       return new Point2D.Float(ctrlx1, ctrly1);
1563:     }
1564: 
1565:     /**
1566:      * Returns the <i>s</i> coordinate of the curve&#x2019;s second
1567:      * control point.
1568:      */
1569:     public double getCtrlX2()
1570:     {
1571:       return ctrlx2;
1572:     }
1573: 
1574:     /**
1575:      * Returns the <i>y</i> coordinate of the curve&#x2019;s second
1576:      * control point.
1577:      */
1578:     public double getCtrlY2()
1579:     {
1580:       return ctrly2;
1581:     }
1582: 
1583:     /**
1584:      * Returns the curve&#x2019;s second control point.
1585:      */
1586:     public Point2D getCtrlP2()
1587:     {
1588:       return new Point2D.Float(ctrlx2, ctrly2);
1589:     }
1590: 
1591:     /**
1592:      * Returns the <i>x</i> coordinate of the curve&#x2019;s end
1593:      * point.
1594:      */
1595:     public double getX2()
1596:     {
1597:       return x2;
1598:     }
1599: 
1600:     /**
1601:      * Returns the <i>y</i> coordinate of the curve&#x2019;s end
1602:      * point.
1603:      */
1604:     public double getY2()
1605:     {
1606:       return y2;
1607:     }
1608: 
1609:     /**
1610:      * Returns the curve&#x2019;s end point.
1611:      */
1612:     public Point2D getP2()
1613:     {
1614:       return new Point2D.Float(x2, y2);
1615:     }
1616: 
1617:     /**
1618:      * Changes the curve geometry, separately specifying each coordinate
1619:      * value as a double-precision floating-point number.
1620:      *
1621:      * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1622:      * alt="A drawing of a CubicCurve2D" />
1623:      *
1624:      * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new start
1625:      * point.
1626:      *
1627:      * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
1628:      * point.
1629:      *
1630:      * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s new
1631:      * first control point.
1632:      *
1633:      * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s new
1634:      * first control point.
1635:      *
1636:      * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s new
1637:      * second control point.
1638:      *
1639:      * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s new
1640:      * second control point.
1641:      *
1642:      * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
1643:      * point.
1644:      *
1645:      * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new end
1646:      * point.
1647:      */
1648:     public void setCurve(double x1, double y1, double cx1, double cy1,
1649:                          double cx2, double cy2, double x2, double y2)
1650:     {
1651:       this.x1 = (float) x1;
1652:       this.y1 = (float) y1;
1653:       ctrlx1 = (float) cx1;
1654:       ctrly1 = (float) cy1;
1655:       ctrlx2 = (float) cx2;
1656:       ctrly2 = (float) cy2;
1657:       this.x2 = (float) x2;
1658:       this.y2 = (float) y2;
1659:     }
1660: 
1661:     /**
1662:      * Changes the curve geometry, separately specifying each coordinate
1663:      * value as a single-precision floating-point number.
1664:      *
1665:      * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1666:      * alt="A drawing of a CubicCurve2D" />
1667:      *
1668:      * @param x1 the <i>x</i> coordinate of the curve&#x2019;s new start
1669:      * point.
1670:      *
1671:      * @param y1 the <i>y</i> coordinate of the curve&#x2019;s new start
1672:      * point.
1673:      *
1674:      * @param cx1 the <i>x</i> coordinate of the curve&#x2019;s new
1675:      * first control point.
1676:      *
1677:      * @param cy1 the <i>y</i> coordinate of the curve&#x2019;s new
1678:      * first control point.
1679:      *
1680:      * @param cx2 the <i>x</i> coordinate of the curve&#x2019;s new
1681:      * second control point.
1682:      *
1683:      * @param cy2 the <i>y</i> coordinate of the curve&#x2019;s new
1684:      * second control point.
1685:      *
1686:      * @param x2 the <i>x</i> coordinate of the curve&#x2019;s new end
1687:      * point.
1688:      *
1689:      * @param y2 the <i>y</i> coordinate of the curve&#x2019;s new end
1690:      * point.
1691:      */
1692:     public void setCurve(float x1, float y1, float cx1, float cy1, float cx2,
1693:                          float cy2, float x2, float y2)
1694:     {
1695:       this.x1 = x1;
1696:       this.y1 = y1;
1697:       ctrlx1 = cx1;
1698:       ctrly1 = cy1;
1699:       ctrlx2 = cx2;
1700:       ctrly2 = cy2;
1701:       this.x2 = x2;
1702:       this.y2 = y2;
1703:     }
1704: 
1705:     /**
1706:      * Determines the smallest rectangle that encloses the
1707:      * curve&#x2019;s start, end and control points. As the
1708:      * illustration below shows, the invisible control points may cause
1709:      * the bounds to be much larger than the area that is actually
1710:      * covered by the curve.
1711:      *
1712:      * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
1713:      * alt="An illustration of the bounds of a CubicCurve2D" />
1714:      */
1715:     public Rectangle2D getBounds2D()
1716:     {
1717:       float nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
1718:       float ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
1719:       float nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
1720:       float ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
1721:       return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
1722:     }
1723:   }
1724: }