J. Duke | 319a3b9 | 2007-12-01 00:00:00 +0000 | [diff] [blame^] | 1 | /* |
| 2 | * Copyright 1997-2006 Sun Microsystems, Inc. All Rights Reserved. |
| 3 | * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER. |
| 4 | * |
| 5 | * This code is free software; you can redistribute it and/or modify it |
| 6 | * under the terms of the GNU General Public License version 2 only, as |
| 7 | * published by the Free Software Foundation. Sun designates this |
| 8 | * particular file as subject to the "Classpath" exception as provided |
| 9 | * by Sun in the LICENSE file that accompanied this code. |
| 10 | * |
| 11 | * This code is distributed in the hope that it will be useful, but WITHOUT |
| 12 | * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
| 13 | * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
| 14 | * version 2 for more details (a copy is included in the LICENSE file that |
| 15 | * accompanied this code). |
| 16 | * |
| 17 | * You should have received a copy of the GNU General Public License version |
| 18 | * 2 along with this work; if not, write to the Free Software Foundation, |
| 19 | * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA. |
| 20 | * |
| 21 | * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara, |
| 22 | * CA 95054 USA or visit www.sun.com if you need additional information or |
| 23 | * have any questions. |
| 24 | */ |
| 25 | |
| 26 | package java.awt.geom; |
| 27 | |
| 28 | import java.awt.Shape; |
| 29 | import java.awt.Rectangle; |
| 30 | import java.io.Serializable; |
| 31 | import sun.awt.geom.Curve; |
| 32 | |
| 33 | /** |
| 34 | * The <code>QuadCurve2D</code> class defines a quadratic parametric curve |
| 35 | * segment in {@code (x,y)} coordinate space. |
| 36 | * <p> |
| 37 | * This class is only the abstract superclass for all objects that |
| 38 | * store a 2D quadratic curve segment. |
| 39 | * The actual storage representation of the coordinates is left to |
| 40 | * the subclass. |
| 41 | * |
| 42 | * @author Jim Graham |
| 43 | * @since 1.2 |
| 44 | */ |
| 45 | public abstract class QuadCurve2D implements Shape, Cloneable { |
| 46 | |
| 47 | /** |
| 48 | * A quadratic parametric curve segment specified with |
| 49 | * {@code float} coordinates. |
| 50 | * |
| 51 | * @since 1.2 |
| 52 | */ |
| 53 | public static class Float extends QuadCurve2D implements Serializable { |
| 54 | /** |
| 55 | * The X coordinate of the start point of the quadratic curve |
| 56 | * segment. |
| 57 | * @since 1.2 |
| 58 | * @serial |
| 59 | */ |
| 60 | public float x1; |
| 61 | |
| 62 | /** |
| 63 | * The Y coordinate of the start point of the quadratic curve |
| 64 | * segment. |
| 65 | * @since 1.2 |
| 66 | * @serial |
| 67 | */ |
| 68 | public float y1; |
| 69 | |
| 70 | /** |
| 71 | * The X coordinate of the control point of the quadratic curve |
| 72 | * segment. |
| 73 | * @since 1.2 |
| 74 | * @serial |
| 75 | */ |
| 76 | public float ctrlx; |
| 77 | |
| 78 | /** |
| 79 | * The Y coordinate of the control point of the quadratic curve |
| 80 | * segment. |
| 81 | * @since 1.2 |
| 82 | * @serial |
| 83 | */ |
| 84 | public float ctrly; |
| 85 | |
| 86 | /** |
| 87 | * The X coordinate of the end point of the quadratic curve |
| 88 | * segment. |
| 89 | * @since 1.2 |
| 90 | * @serial |
| 91 | */ |
| 92 | public float x2; |
| 93 | |
| 94 | /** |
| 95 | * The Y coordinate of the end point of the quadratic curve |
| 96 | * segment. |
| 97 | * @since 1.2 |
| 98 | * @serial |
| 99 | */ |
| 100 | public float y2; |
| 101 | |
| 102 | /** |
| 103 | * Constructs and initializes a <code>QuadCurve2D</code> with |
| 104 | * coordinates (0, 0, 0, 0, 0, 0). |
| 105 | * @since 1.2 |
| 106 | */ |
| 107 | public Float() { |
| 108 | } |
| 109 | |
| 110 | /** |
| 111 | * Constructs and initializes a <code>QuadCurve2D</code> from the |
| 112 | * specified {@code float} coordinates. |
| 113 | * |
| 114 | * @param x1 the X coordinate of the start point |
| 115 | * @param y1 the Y coordinate of the start point |
| 116 | * @param ctrlx the X coordinate of the control point |
| 117 | * @param ctrly the Y coordinate of the control point |
| 118 | * @param x2 the X coordinate of the end point |
| 119 | * @param y2 the Y coordinate of the end point |
| 120 | * @since 1.2 |
| 121 | */ |
| 122 | public Float(float x1, float y1, |
| 123 | float ctrlx, float ctrly, |
| 124 | float x2, float y2) |
| 125 | { |
| 126 | setCurve(x1, y1, ctrlx, ctrly, x2, y2); |
| 127 | } |
| 128 | |
| 129 | /** |
| 130 | * {@inheritDoc} |
| 131 | * @since 1.2 |
| 132 | */ |
| 133 | public double getX1() { |
| 134 | return (double) x1; |
| 135 | } |
| 136 | |
| 137 | /** |
| 138 | * {@inheritDoc} |
| 139 | * @since 1.2 |
| 140 | */ |
| 141 | public double getY1() { |
| 142 | return (double) y1; |
| 143 | } |
| 144 | |
| 145 | /** |
| 146 | * {@inheritDoc} |
| 147 | * @since 1.2 |
| 148 | */ |
| 149 | public Point2D getP1() { |
| 150 | return new Point2D.Float(x1, y1); |
| 151 | } |
| 152 | |
| 153 | /** |
| 154 | * {@inheritDoc} |
| 155 | * @since 1.2 |
| 156 | */ |
| 157 | public double getCtrlX() { |
| 158 | return (double) ctrlx; |
| 159 | } |
| 160 | |
| 161 | /** |
| 162 | * {@inheritDoc} |
| 163 | * @since 1.2 |
| 164 | */ |
| 165 | public double getCtrlY() { |
| 166 | return (double) ctrly; |
| 167 | } |
| 168 | |
| 169 | /** |
| 170 | * {@inheritDoc} |
| 171 | * @since 1.2 |
| 172 | */ |
| 173 | public Point2D getCtrlPt() { |
| 174 | return new Point2D.Float(ctrlx, ctrly); |
| 175 | } |
| 176 | |
| 177 | /** |
| 178 | * {@inheritDoc} |
| 179 | * @since 1.2 |
| 180 | */ |
| 181 | public double getX2() { |
| 182 | return (double) x2; |
| 183 | } |
| 184 | |
| 185 | /** |
| 186 | * {@inheritDoc} |
| 187 | * @since 1.2 |
| 188 | */ |
| 189 | public double getY2() { |
| 190 | return (double) y2; |
| 191 | } |
| 192 | |
| 193 | /** |
| 194 | * {@inheritDoc} |
| 195 | * @since 1.2 |
| 196 | */ |
| 197 | public Point2D getP2() { |
| 198 | return new Point2D.Float(x2, y2); |
| 199 | } |
| 200 | |
| 201 | /** |
| 202 | * {@inheritDoc} |
| 203 | * @since 1.2 |
| 204 | */ |
| 205 | public void setCurve(double x1, double y1, |
| 206 | double ctrlx, double ctrly, |
| 207 | double x2, double y2) |
| 208 | { |
| 209 | this.x1 = (float) x1; |
| 210 | this.y1 = (float) y1; |
| 211 | this.ctrlx = (float) ctrlx; |
| 212 | this.ctrly = (float) ctrly; |
| 213 | this.x2 = (float) x2; |
| 214 | this.y2 = (float) y2; |
| 215 | } |
| 216 | |
| 217 | /** |
| 218 | * Sets the location of the end points and control point of this curve |
| 219 | * to the specified {@code float} coordinates. |
| 220 | * |
| 221 | * @param x1 the X coordinate of the start point |
| 222 | * @param y1 the Y coordinate of the start point |
| 223 | * @param ctrlx the X coordinate of the control point |
| 224 | * @param ctrly the Y coordinate of the control point |
| 225 | * @param x2 the X coordinate of the end point |
| 226 | * @param y2 the Y coordinate of the end point |
| 227 | * @since 1.2 |
| 228 | */ |
| 229 | public void setCurve(float x1, float y1, |
| 230 | float ctrlx, float ctrly, |
| 231 | float x2, float y2) |
| 232 | { |
| 233 | this.x1 = x1; |
| 234 | this.y1 = y1; |
| 235 | this.ctrlx = ctrlx; |
| 236 | this.ctrly = ctrly; |
| 237 | this.x2 = x2; |
| 238 | this.y2 = y2; |
| 239 | } |
| 240 | |
| 241 | /** |
| 242 | * {@inheritDoc} |
| 243 | * @since 1.2 |
| 244 | */ |
| 245 | public Rectangle2D getBounds2D() { |
| 246 | float left = Math.min(Math.min(x1, x2), ctrlx); |
| 247 | float top = Math.min(Math.min(y1, y2), ctrly); |
| 248 | float right = Math.max(Math.max(x1, x2), ctrlx); |
| 249 | float bottom = Math.max(Math.max(y1, y2), ctrly); |
| 250 | return new Rectangle2D.Float(left, top, |
| 251 | right - left, bottom - top); |
| 252 | } |
| 253 | |
| 254 | /* |
| 255 | * JDK 1.6 serialVersionUID |
| 256 | */ |
| 257 | private static final long serialVersionUID = -8511188402130719609L; |
| 258 | } |
| 259 | |
| 260 | /** |
| 261 | * A quadratic parametric curve segment specified with |
| 262 | * {@code double} coordinates. |
| 263 | * |
| 264 | * @since 1.2 |
| 265 | */ |
| 266 | public static class Double extends QuadCurve2D implements Serializable { |
| 267 | /** |
| 268 | * The X coordinate of the start point of the quadratic curve |
| 269 | * segment. |
| 270 | * @since 1.2 |
| 271 | * @serial |
| 272 | */ |
| 273 | public double x1; |
| 274 | |
| 275 | /** |
| 276 | * The Y coordinate of the start point of the quadratic curve |
| 277 | * segment. |
| 278 | * @since 1.2 |
| 279 | * @serial |
| 280 | */ |
| 281 | public double y1; |
| 282 | |
| 283 | /** |
| 284 | * The X coordinate of the control point of the quadratic curve |
| 285 | * segment. |
| 286 | * @since 1.2 |
| 287 | * @serial |
| 288 | */ |
| 289 | public double ctrlx; |
| 290 | |
| 291 | /** |
| 292 | * The Y coordinate of the control point of the quadratic curve |
| 293 | * segment. |
| 294 | * @since 1.2 |
| 295 | * @serial |
| 296 | */ |
| 297 | public double ctrly; |
| 298 | |
| 299 | /** |
| 300 | * The X coordinate of the end point of the quadratic curve |
| 301 | * segment. |
| 302 | * @since 1.2 |
| 303 | * @serial |
| 304 | */ |
| 305 | public double x2; |
| 306 | |
| 307 | /** |
| 308 | * The Y coordinate of the end point of the quadratic curve |
| 309 | * segment. |
| 310 | * @since 1.2 |
| 311 | * @serial |
| 312 | */ |
| 313 | public double y2; |
| 314 | |
| 315 | /** |
| 316 | * Constructs and initializes a <code>QuadCurve2D</code> with |
| 317 | * coordinates (0, 0, 0, 0, 0, 0). |
| 318 | * @since 1.2 |
| 319 | */ |
| 320 | public Double() { |
| 321 | } |
| 322 | |
| 323 | /** |
| 324 | * Constructs and initializes a <code>QuadCurve2D</code> from the |
| 325 | * specified {@code double} coordinates. |
| 326 | * |
| 327 | * @param x1 the X coordinate of the start point |
| 328 | * @param y1 the Y coordinate of the start point |
| 329 | * @param ctrlx the X coordinate of the control point |
| 330 | * @param ctrly the Y coordinate of the control point |
| 331 | * @param x2 the X coordinate of the end point |
| 332 | * @param y2 the Y coordinate of the end point |
| 333 | * @since 1.2 |
| 334 | */ |
| 335 | public Double(double x1, double y1, |
| 336 | double ctrlx, double ctrly, |
| 337 | double x2, double y2) |
| 338 | { |
| 339 | setCurve(x1, y1, ctrlx, ctrly, x2, y2); |
| 340 | } |
| 341 | |
| 342 | /** |
| 343 | * {@inheritDoc} |
| 344 | * @since 1.2 |
| 345 | */ |
| 346 | public double getX1() { |
| 347 | return x1; |
| 348 | } |
| 349 | |
| 350 | /** |
| 351 | * {@inheritDoc} |
| 352 | * @since 1.2 |
| 353 | */ |
| 354 | public double getY1() { |
| 355 | return y1; |
| 356 | } |
| 357 | |
| 358 | /** |
| 359 | * {@inheritDoc} |
| 360 | * @since 1.2 |
| 361 | */ |
| 362 | public Point2D getP1() { |
| 363 | return new Point2D.Double(x1, y1); |
| 364 | } |
| 365 | |
| 366 | /** |
| 367 | * {@inheritDoc} |
| 368 | * @since 1.2 |
| 369 | */ |
| 370 | public double getCtrlX() { |
| 371 | return ctrlx; |
| 372 | } |
| 373 | |
| 374 | /** |
| 375 | * {@inheritDoc} |
| 376 | * @since 1.2 |
| 377 | */ |
| 378 | public double getCtrlY() { |
| 379 | return ctrly; |
| 380 | } |
| 381 | |
| 382 | /** |
| 383 | * {@inheritDoc} |
| 384 | * @since 1.2 |
| 385 | */ |
| 386 | public Point2D getCtrlPt() { |
| 387 | return new Point2D.Double(ctrlx, ctrly); |
| 388 | } |
| 389 | |
| 390 | /** |
| 391 | * {@inheritDoc} |
| 392 | * @since 1.2 |
| 393 | */ |
| 394 | public double getX2() { |
| 395 | return x2; |
| 396 | } |
| 397 | |
| 398 | /** |
| 399 | * {@inheritDoc} |
| 400 | * @since 1.2 |
| 401 | */ |
| 402 | public double getY2() { |
| 403 | return y2; |
| 404 | } |
| 405 | |
| 406 | /** |
| 407 | * {@inheritDoc} |
| 408 | * @since 1.2 |
| 409 | */ |
| 410 | public Point2D getP2() { |
| 411 | return new Point2D.Double(x2, y2); |
| 412 | } |
| 413 | |
| 414 | /** |
| 415 | * {@inheritDoc} |
| 416 | * @since 1.2 |
| 417 | */ |
| 418 | public void setCurve(double x1, double y1, |
| 419 | double ctrlx, double ctrly, |
| 420 | double x2, double y2) |
| 421 | { |
| 422 | this.x1 = x1; |
| 423 | this.y1 = y1; |
| 424 | this.ctrlx = ctrlx; |
| 425 | this.ctrly = ctrly; |
| 426 | this.x2 = x2; |
| 427 | this.y2 = y2; |
| 428 | } |
| 429 | |
| 430 | /** |
| 431 | * {@inheritDoc} |
| 432 | * @since 1.2 |
| 433 | */ |
| 434 | public Rectangle2D getBounds2D() { |
| 435 | double left = Math.min(Math.min(x1, x2), ctrlx); |
| 436 | double top = Math.min(Math.min(y1, y2), ctrly); |
| 437 | double right = Math.max(Math.max(x1, x2), ctrlx); |
| 438 | double bottom = Math.max(Math.max(y1, y2), ctrly); |
| 439 | return new Rectangle2D.Double(left, top, |
| 440 | right - left, bottom - top); |
| 441 | } |
| 442 | |
| 443 | /* |
| 444 | * JDK 1.6 serialVersionUID |
| 445 | */ |
| 446 | private static final long serialVersionUID = 4217149928428559721L; |
| 447 | } |
| 448 | |
| 449 | /** |
| 450 | * This is an abstract class that cannot be instantiated directly. |
| 451 | * Type-specific implementation subclasses are available for |
| 452 | * instantiation and provide a number of formats for storing |
| 453 | * the information necessary to satisfy the various accessor |
| 454 | * methods below. |
| 455 | * |
| 456 | * @see java.awt.geom.QuadCurve2D.Float |
| 457 | * @see java.awt.geom.QuadCurve2D.Double |
| 458 | * @since 1.2 |
| 459 | */ |
| 460 | protected QuadCurve2D() { |
| 461 | } |
| 462 | |
| 463 | /** |
| 464 | * Returns the X coordinate of the start point in |
| 465 | * <code>double</code> in precision. |
| 466 | * @return the X coordinate of the start point. |
| 467 | * @since 1.2 |
| 468 | */ |
| 469 | public abstract double getX1(); |
| 470 | |
| 471 | /** |
| 472 | * Returns the Y coordinate of the start point in |
| 473 | * <code>double</code> precision. |
| 474 | * @return the Y coordinate of the start point. |
| 475 | * @since 1.2 |
| 476 | */ |
| 477 | public abstract double getY1(); |
| 478 | |
| 479 | /** |
| 480 | * Returns the start point. |
| 481 | * @return a <code>Point2D</code> that is the start point of this |
| 482 | * <code>QuadCurve2D</code>. |
| 483 | * @since 1.2 |
| 484 | */ |
| 485 | public abstract Point2D getP1(); |
| 486 | |
| 487 | /** |
| 488 | * Returns the X coordinate of the control point in |
| 489 | * <code>double</code> precision. |
| 490 | * @return X coordinate the control point |
| 491 | * @since 1.2 |
| 492 | */ |
| 493 | public abstract double getCtrlX(); |
| 494 | |
| 495 | /** |
| 496 | * Returns the Y coordinate of the control point in |
| 497 | * <code>double</code> precision. |
| 498 | * @return the Y coordinate of the control point. |
| 499 | * @since 1.2 |
| 500 | */ |
| 501 | public abstract double getCtrlY(); |
| 502 | |
| 503 | /** |
| 504 | * Returns the control point. |
| 505 | * @return a <code>Point2D</code> that is the control point of this |
| 506 | * <code>Point2D</code>. |
| 507 | * @since 1.2 |
| 508 | */ |
| 509 | public abstract Point2D getCtrlPt(); |
| 510 | |
| 511 | /** |
| 512 | * Returns the X coordinate of the end point in |
| 513 | * <code>double</code> precision. |
| 514 | * @return the x coordiante of the end point. |
| 515 | * @since 1.2 |
| 516 | */ |
| 517 | public abstract double getX2(); |
| 518 | |
| 519 | /** |
| 520 | * Returns the Y coordinate of the end point in |
| 521 | * <code>double</code> precision. |
| 522 | * @return the Y coordinate of the end point. |
| 523 | * @since 1.2 |
| 524 | */ |
| 525 | public abstract double getY2(); |
| 526 | |
| 527 | /** |
| 528 | * Returns the end point. |
| 529 | * @return a <code>Point</code> object that is the end point |
| 530 | * of this <code>Point2D</code>. |
| 531 | * @since 1.2 |
| 532 | */ |
| 533 | public abstract Point2D getP2(); |
| 534 | |
| 535 | /** |
| 536 | * Sets the location of the end points and control point of this curve |
| 537 | * to the specified <code>double</code> coordinates. |
| 538 | * |
| 539 | * @param x1 the X coordinate of the start point |
| 540 | * @param y1 the Y coordinate of the start point |
| 541 | * @param ctrlx the X coordinate of the control point |
| 542 | * @param ctrly the Y coordinate of the control point |
| 543 | * @param x2 the X coordinate of the end point |
| 544 | * @param y2 the Y coordinate of the end point |
| 545 | * @since 1.2 |
| 546 | */ |
| 547 | public abstract void setCurve(double x1, double y1, |
| 548 | double ctrlx, double ctrly, |
| 549 | double x2, double y2); |
| 550 | |
| 551 | /** |
| 552 | * Sets the location of the end points and control points of this |
| 553 | * <code>QuadCurve2D</code> to the <code>double</code> coordinates at |
| 554 | * the specified offset in the specified array. |
| 555 | * @param coords the array containing coordinate values |
| 556 | * @param offset the index into the array from which to start |
| 557 | * getting the coordinate values and assigning them to this |
| 558 | * <code>QuadCurve2D</code> |
| 559 | * @since 1.2 |
| 560 | */ |
| 561 | public void setCurve(double[] coords, int offset) { |
| 562 | setCurve(coords[offset + 0], coords[offset + 1], |
| 563 | coords[offset + 2], coords[offset + 3], |
| 564 | coords[offset + 4], coords[offset + 5]); |
| 565 | } |
| 566 | |
| 567 | /** |
| 568 | * Sets the location of the end points and control point of this |
| 569 | * <code>QuadCurve2D</code> to the specified <code>Point2D</code> |
| 570 | * coordinates. |
| 571 | * @param p1 the start point |
| 572 | * @param cp the control point |
| 573 | * @param p2 the end point |
| 574 | * @since 1.2 |
| 575 | */ |
| 576 | public void setCurve(Point2D p1, Point2D cp, Point2D p2) { |
| 577 | setCurve(p1.getX(), p1.getY(), |
| 578 | cp.getX(), cp.getY(), |
| 579 | p2.getX(), p2.getY()); |
| 580 | } |
| 581 | |
| 582 | /** |
| 583 | * Sets the location of the end points and control points of this |
| 584 | * <code>QuadCurve2D</code> to the coordinates of the |
| 585 | * <code>Point2D</code> objects at the specified offset in |
| 586 | * the specified array. |
| 587 | * @param pts an array containing <code>Point2D</code> that define |
| 588 | * coordinate values |
| 589 | * @param offset the index into <code>pts</code> from which to start |
| 590 | * getting the coordinate values and assigning them to this |
| 591 | * <code>QuadCurve2D</code> |
| 592 | * @since 1.2 |
| 593 | */ |
| 594 | public void setCurve(Point2D[] pts, int offset) { |
| 595 | setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(), |
| 596 | pts[offset + 1].getX(), pts[offset + 1].getY(), |
| 597 | pts[offset + 2].getX(), pts[offset + 2].getY()); |
| 598 | } |
| 599 | |
| 600 | /** |
| 601 | * Sets the location of the end points and control point of this |
| 602 | * <code>QuadCurve2D</code> to the same as those in the specified |
| 603 | * <code>QuadCurve2D</code>. |
| 604 | * @param c the specified <code>QuadCurve2D</code> |
| 605 | * @since 1.2 |
| 606 | */ |
| 607 | public void setCurve(QuadCurve2D c) { |
| 608 | setCurve(c.getX1(), c.getY1(), |
| 609 | c.getCtrlX(), c.getCtrlY(), |
| 610 | c.getX2(), c.getY2()); |
| 611 | } |
| 612 | |
| 613 | /** |
| 614 | * Returns the square of the flatness, or maximum distance of a |
| 615 | * control point from the line connecting the end points, of the |
| 616 | * quadratic curve specified by the indicated control points. |
| 617 | * |
| 618 | * @param x1 the X coordinate of the start point |
| 619 | * @param y1 the Y coordinate of the start point |
| 620 | * @param ctrlx the X coordinate of the control point |
| 621 | * @param ctrly the Y coordinate of the control point |
| 622 | * @param x2 the X coordinate of the end point |
| 623 | * @param y2 the Y coordinate of the end point |
| 624 | * @return the square of the flatness of the quadratic curve |
| 625 | * defined by the specified coordinates. |
| 626 | * @since 1.2 |
| 627 | */ |
| 628 | public static double getFlatnessSq(double x1, double y1, |
| 629 | double ctrlx, double ctrly, |
| 630 | double x2, double y2) { |
| 631 | return Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx, ctrly); |
| 632 | } |
| 633 | |
| 634 | /** |
| 635 | * Returns the flatness, or maximum distance of a |
| 636 | * control point from the line connecting the end points, of the |
| 637 | * quadratic curve specified by the indicated control points. |
| 638 | * |
| 639 | * @param x1 the X coordinate of the start point |
| 640 | * @param y1 the Y coordinate of the start point |
| 641 | * @param ctrlx the X coordinate of the control point |
| 642 | * @param ctrly the Y coordinate of the control point |
| 643 | * @param x2 the X coordinate of the end point |
| 644 | * @param y2 the Y coordinate of the end point |
| 645 | * @return the flatness of the quadratic curve defined by the |
| 646 | * specified coordinates. |
| 647 | * @since 1.2 |
| 648 | */ |
| 649 | public static double getFlatness(double x1, double y1, |
| 650 | double ctrlx, double ctrly, |
| 651 | double x2, double y2) { |
| 652 | return Line2D.ptSegDist(x1, y1, x2, y2, ctrlx, ctrly); |
| 653 | } |
| 654 | |
| 655 | /** |
| 656 | * Returns the square of the flatness, or maximum distance of a |
| 657 | * control point from the line connecting the end points, of the |
| 658 | * quadratic curve specified by the control points stored in the |
| 659 | * indicated array at the indicated index. |
| 660 | * @param coords an array containing coordinate values |
| 661 | * @param offset the index into <code>coords</code> from which to |
| 662 | * to start getting the values from the array |
| 663 | * @return the flatness of the quadratic curve that is defined by the |
| 664 | * values in the specified array at the specified index. |
| 665 | * @since 1.2 |
| 666 | */ |
| 667 | public static double getFlatnessSq(double coords[], int offset) { |
| 668 | return Line2D.ptSegDistSq(coords[offset + 0], coords[offset + 1], |
| 669 | coords[offset + 4], coords[offset + 5], |
| 670 | coords[offset + 2], coords[offset + 3]); |
| 671 | } |
| 672 | |
| 673 | /** |
| 674 | * Returns the flatness, or maximum distance of a |
| 675 | * control point from the line connecting the end points, of the |
| 676 | * quadratic curve specified by the control points stored in the |
| 677 | * indicated array at the indicated index. |
| 678 | * @param coords an array containing coordinate values |
| 679 | * @param offset the index into <code>coords</code> from which to |
| 680 | * start getting the coordinate values |
| 681 | * @return the flatness of a quadratic curve defined by the |
| 682 | * specified array at the specified offset. |
| 683 | * @since 1.2 |
| 684 | */ |
| 685 | public static double getFlatness(double coords[], int offset) { |
| 686 | return Line2D.ptSegDist(coords[offset + 0], coords[offset + 1], |
| 687 | coords[offset + 4], coords[offset + 5], |
| 688 | coords[offset + 2], coords[offset + 3]); |
| 689 | } |
| 690 | |
| 691 | /** |
| 692 | * Returns the square of the flatness, or maximum distance of a |
| 693 | * control point from the line connecting the end points, of this |
| 694 | * <code>QuadCurve2D</code>. |
| 695 | * @return the square of the flatness of this |
| 696 | * <code>QuadCurve2D</code>. |
| 697 | * @since 1.2 |
| 698 | */ |
| 699 | public double getFlatnessSq() { |
| 700 | return Line2D.ptSegDistSq(getX1(), getY1(), |
| 701 | getX2(), getY2(), |
| 702 | getCtrlX(), getCtrlY()); |
| 703 | } |
| 704 | |
| 705 | /** |
| 706 | * Returns the flatness, or maximum distance of a |
| 707 | * control point from the line connecting the end points, of this |
| 708 | * <code>QuadCurve2D</code>. |
| 709 | * @return the flatness of this <code>QuadCurve2D</code>. |
| 710 | * @since 1.2 |
| 711 | */ |
| 712 | public double getFlatness() { |
| 713 | return Line2D.ptSegDist(getX1(), getY1(), |
| 714 | getX2(), getY2(), |
| 715 | getCtrlX(), getCtrlY()); |
| 716 | } |
| 717 | |
| 718 | /** |
| 719 | * Subdivides this <code>QuadCurve2D</code> and stores the resulting |
| 720 | * two subdivided curves into the <code>left</code> and |
| 721 | * <code>right</code> curve parameters. |
| 722 | * Either or both of the <code>left</code> and <code>right</code> |
| 723 | * objects can be the same as this <code>QuadCurve2D</code> or |
| 724 | * <code>null</code>. |
| 725 | * @param left the <code>QuadCurve2D</code> object for storing the |
| 726 | * left or first half of the subdivided curve |
| 727 | * @param right the <code>QuadCurve2D</code> object for storing the |
| 728 | * right or second half of the subdivided curve |
| 729 | * @since 1.2 |
| 730 | */ |
| 731 | public void subdivide(QuadCurve2D left, QuadCurve2D right) { |
| 732 | subdivide(this, left, right); |
| 733 | } |
| 734 | |
| 735 | /** |
| 736 | * Subdivides the quadratic curve specified by the <code>src</code> |
| 737 | * parameter and stores the resulting two subdivided curves into the |
| 738 | * <code>left</code> and <code>right</code> curve parameters. |
| 739 | * Either or both of the <code>left</code> and <code>right</code> |
| 740 | * objects can be the same as the <code>src</code> object or |
| 741 | * <code>null</code>. |
| 742 | * @param src the quadratic curve to be subdivided |
| 743 | * @param left the <code>QuadCurve2D</code> object for storing the |
| 744 | * left or first half of the subdivided curve |
| 745 | * @param right the <code>QuadCurve2D</code> object for storing the |
| 746 | * right or second half of the subdivided curve |
| 747 | * @since 1.2 |
| 748 | */ |
| 749 | public static void subdivide(QuadCurve2D src, |
| 750 | QuadCurve2D left, |
| 751 | QuadCurve2D right) { |
| 752 | double x1 = src.getX1(); |
| 753 | double y1 = src.getY1(); |
| 754 | double ctrlx = src.getCtrlX(); |
| 755 | double ctrly = src.getCtrlY(); |
| 756 | double x2 = src.getX2(); |
| 757 | double y2 = src.getY2(); |
| 758 | double ctrlx1 = (x1 + ctrlx) / 2.0; |
| 759 | double ctrly1 = (y1 + ctrly) / 2.0; |
| 760 | double ctrlx2 = (x2 + ctrlx) / 2.0; |
| 761 | double ctrly2 = (y2 + ctrly) / 2.0; |
| 762 | ctrlx = (ctrlx1 + ctrlx2) / 2.0; |
| 763 | ctrly = (ctrly1 + ctrly2) / 2.0; |
| 764 | if (left != null) { |
| 765 | left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx, ctrly); |
| 766 | } |
| 767 | if (right != null) { |
| 768 | right.setCurve(ctrlx, ctrly, ctrlx2, ctrly2, x2, y2); |
| 769 | } |
| 770 | } |
| 771 | |
| 772 | /** |
| 773 | * Subdivides the quadratic curve specified by the coordinates |
| 774 | * stored in the <code>src</code> array at indices |
| 775 | * <code>srcoff</code> through <code>srcoff</code> + 5 |
| 776 | * and stores the resulting two subdivided curves into the two |
| 777 | * result arrays at the corresponding indices. |
| 778 | * Either or both of the <code>left</code> and <code>right</code> |
| 779 | * arrays can be <code>null</code> or a reference to the same array |
| 780 | * and offset as the <code>src</code> array. |
| 781 | * Note that the last point in the first subdivided curve is the |
| 782 | * same as the first point in the second subdivided curve. Thus, |
| 783 | * it is possible to pass the same array for <code>left</code> and |
| 784 | * <code>right</code> and to use offsets such that |
| 785 | * <code>rightoff</code> equals <code>leftoff</code> + 4 in order |
| 786 | * to avoid allocating extra storage for this common point. |
| 787 | * @param src the array holding the coordinates for the source curve |
| 788 | * @param srcoff the offset into the array of the beginning of the |
| 789 | * the 6 source coordinates |
| 790 | * @param left the array for storing the coordinates for the first |
| 791 | * half of the subdivided curve |
| 792 | * @param leftoff the offset into the array of the beginning of the |
| 793 | * the 6 left coordinates |
| 794 | * @param right the array for storing the coordinates for the second |
| 795 | * half of the subdivided curve |
| 796 | * @param rightoff the offset into the array of the beginning of the |
| 797 | * the 6 right coordinates |
| 798 | * @since 1.2 |
| 799 | */ |
| 800 | public static void subdivide(double src[], int srcoff, |
| 801 | double left[], int leftoff, |
| 802 | double right[], int rightoff) { |
| 803 | double x1 = src[srcoff + 0]; |
| 804 | double y1 = src[srcoff + 1]; |
| 805 | double ctrlx = src[srcoff + 2]; |
| 806 | double ctrly = src[srcoff + 3]; |
| 807 | double x2 = src[srcoff + 4]; |
| 808 | double y2 = src[srcoff + 5]; |
| 809 | if (left != null) { |
| 810 | left[leftoff + 0] = x1; |
| 811 | left[leftoff + 1] = y1; |
| 812 | } |
| 813 | if (right != null) { |
| 814 | right[rightoff + 4] = x2; |
| 815 | right[rightoff + 5] = y2; |
| 816 | } |
| 817 | x1 = (x1 + ctrlx) / 2.0; |
| 818 | y1 = (y1 + ctrly) / 2.0; |
| 819 | x2 = (x2 + ctrlx) / 2.0; |
| 820 | y2 = (y2 + ctrly) / 2.0; |
| 821 | ctrlx = (x1 + x2) / 2.0; |
| 822 | ctrly = (y1 + y2) / 2.0; |
| 823 | if (left != null) { |
| 824 | left[leftoff + 2] = x1; |
| 825 | left[leftoff + 3] = y1; |
| 826 | left[leftoff + 4] = ctrlx; |
| 827 | left[leftoff + 5] = ctrly; |
| 828 | } |
| 829 | if (right != null) { |
| 830 | right[rightoff + 0] = ctrlx; |
| 831 | right[rightoff + 1] = ctrly; |
| 832 | right[rightoff + 2] = x2; |
| 833 | right[rightoff + 3] = y2; |
| 834 | } |
| 835 | } |
| 836 | |
| 837 | /** |
| 838 | * Solves the quadratic whose coefficients are in the <code>eqn</code> |
| 839 | * array and places the non-complex roots back into the same array, |
| 840 | * returning the number of roots. The quadratic solved is represented |
| 841 | * by the equation: |
| 842 | * <pre> |
| 843 | * eqn = {C, B, A}; |
| 844 | * ax^2 + bx + c = 0 |
| 845 | * </pre> |
| 846 | * A return value of <code>-1</code> is used to distinguish a constant |
| 847 | * equation, which might be always 0 or never 0, from an equation that |
| 848 | * has no zeroes. |
| 849 | * @param eqn the array that contains the quadratic coefficients |
| 850 | * @return the number of roots, or <code>-1</code> if the equation is |
| 851 | * a constant |
| 852 | * @since 1.2 |
| 853 | */ |
| 854 | public static int solveQuadratic(double eqn[]) { |
| 855 | return solveQuadratic(eqn, eqn); |
| 856 | } |
| 857 | |
| 858 | /** |
| 859 | * Solves the quadratic whose coefficients are in the <code>eqn</code> |
| 860 | * array and places the non-complex roots into the <code>res</code> |
| 861 | * array, returning the number of roots. |
| 862 | * The quadratic solved is represented by the equation: |
| 863 | * <pre> |
| 864 | * eqn = {C, B, A}; |
| 865 | * ax^2 + bx + c = 0 |
| 866 | * </pre> |
| 867 | * A return value of <code>-1</code> is used to distinguish a constant |
| 868 | * equation, which might be always 0 or never 0, from an equation that |
| 869 | * has no zeroes. |
| 870 | * @param eqn the specified array of coefficients to use to solve |
| 871 | * the quadratic equation |
| 872 | * @param res the array that contains the non-complex roots |
| 873 | * resulting from the solution of the quadratic equation |
| 874 | * @return the number of roots, or <code>-1</code> if the equation is |
| 875 | * a constant. |
| 876 | * @since 1.3 |
| 877 | */ |
| 878 | public static int solveQuadratic(double eqn[], double res[]) { |
| 879 | double a = eqn[2]; |
| 880 | double b = eqn[1]; |
| 881 | double c = eqn[0]; |
| 882 | int roots = 0; |
| 883 | if (a == 0.0) { |
| 884 | // The quadratic parabola has degenerated to a line. |
| 885 | if (b == 0.0) { |
| 886 | // The line has degenerated to a constant. |
| 887 | return -1; |
| 888 | } |
| 889 | res[roots++] = -c / b; |
| 890 | } else { |
| 891 | // From Numerical Recipes, 5.6, Quadratic and Cubic Equations |
| 892 | double d = b * b - 4.0 * a * c; |
| 893 | if (d < 0.0) { |
| 894 | // If d < 0.0, then there are no roots |
| 895 | return 0; |
| 896 | } |
| 897 | d = Math.sqrt(d); |
| 898 | // For accuracy, calculate one root using: |
| 899 | // (-b +/- d) / 2a |
| 900 | // and the other using: |
| 901 | // 2c / (-b +/- d) |
| 902 | // Choose the sign of the +/- so that b+d gets larger in magnitude |
| 903 | if (b < 0.0) { |
| 904 | d = -d; |
| 905 | } |
| 906 | double q = (b + d) / -2.0; |
| 907 | // We already tested a for being 0 above |
| 908 | res[roots++] = q / a; |
| 909 | if (q != 0.0) { |
| 910 | res[roots++] = c / q; |
| 911 | } |
| 912 | } |
| 913 | return roots; |
| 914 | } |
| 915 | |
| 916 | /** |
| 917 | * {@inheritDoc} |
| 918 | * @since 1.2 |
| 919 | */ |
| 920 | public boolean contains(double x, double y) { |
| 921 | |
| 922 | double x1 = getX1(); |
| 923 | double y1 = getY1(); |
| 924 | double xc = getCtrlX(); |
| 925 | double yc = getCtrlY(); |
| 926 | double x2 = getX2(); |
| 927 | double y2 = getY2(); |
| 928 | |
| 929 | /* |
| 930 | * We have a convex shape bounded by quad curve Pc(t) |
| 931 | * and ine Pl(t). |
| 932 | * |
| 933 | * P1 = (x1, y1) - start point of curve |
| 934 | * P2 = (x2, y2) - end point of curve |
| 935 | * Pc = (xc, yc) - control point |
| 936 | * |
| 937 | * Pq(t) = P1*(1 - t)^2 + 2*Pc*t*(1 - t) + P2*t^2 = |
| 938 | * = (P1 - 2*Pc + P2)*t^2 + 2*(Pc - P1)*t + P1 |
| 939 | * Pl(t) = P1*(1 - t) + P2*t |
| 940 | * t = [0:1] |
| 941 | * |
| 942 | * P = (x, y) - point of interest |
| 943 | * |
| 944 | * Let's look at second derivative of quad curve equation: |
| 945 | * |
| 946 | * Pq''(t) = 2 * (P1 - 2 * Pc + P2) = Pq'' |
| 947 | * It's constant vector. |
| 948 | * |
| 949 | * Let's draw a line through P to be parallel to this |
| 950 | * vector and find the intersection of the quad curve |
| 951 | * and the line. |
| 952 | * |
| 953 | * Pq(t) is point of intersection if system of equations |
| 954 | * below has the solution. |
| 955 | * |
| 956 | * L(s) = P + Pq''*s == Pq(t) |
| 957 | * Pq''*s + (P - Pq(t)) == 0 |
| 958 | * |
| 959 | * | xq''*s + (x - xq(t)) == 0 |
| 960 | * | yq''*s + (y - yq(t)) == 0 |
| 961 | * |
| 962 | * This system has the solution if rank of its matrix equals to 1. |
| 963 | * That is, determinant of the matrix should be zero. |
| 964 | * |
| 965 | * (y - yq(t))*xq'' == (x - xq(t))*yq'' |
| 966 | * |
| 967 | * Let's solve this equation with 't' variable. |
| 968 | * Also let kx = x1 - 2*xc + x2 |
| 969 | * ky = y1 - 2*yc + y2 |
| 970 | * |
| 971 | * t0q = (1/2)*((x - x1)*ky - (y - y1)*kx) / |
| 972 | * ((xc - x1)*ky - (yc - y1)*kx) |
| 973 | * |
| 974 | * Let's do the same for our line Pl(t): |
| 975 | * |
| 976 | * t0l = ((x - x1)*ky - (y - y1)*kx) / |
| 977 | * ((x2 - x1)*ky - (y2 - y1)*kx) |
| 978 | * |
| 979 | * It's easy to check that t0q == t0l. This fact means |
| 980 | * we can compute t0 only one time. |
| 981 | * |
| 982 | * In case t0 < 0 or t0 > 1, we have an intersections outside |
| 983 | * of shape bounds. So, P is definitely out of shape. |
| 984 | * |
| 985 | * In case t0 is inside [0:1], we should calculate Pq(t0) |
| 986 | * and Pl(t0). We have three points for now, and all of them |
| 987 | * lie on one line. So, we just need to detect, is our point |
| 988 | * of interest between points of intersections or not. |
| 989 | * |
| 990 | * If the denominator in the t0q and t0l equations is |
| 991 | * zero, then the points must be collinear and so the |
| 992 | * curve is degenerate and encloses no area. Thus the |
| 993 | * result is false. |
| 994 | */ |
| 995 | double kx = x1 - 2 * xc + x2; |
| 996 | double ky = y1 - 2 * yc + y2; |
| 997 | double dx = x - x1; |
| 998 | double dy = y - y1; |
| 999 | double dxl = x2 - x1; |
| 1000 | double dyl = y2 - y1; |
| 1001 | |
| 1002 | double t0 = (dx * ky - dy * kx) / (dxl * ky - dyl * kx); |
| 1003 | if (t0 < 0 || t0 > 1 || t0 != t0) { |
| 1004 | return false; |
| 1005 | } |
| 1006 | |
| 1007 | double xb = kx * t0 * t0 + 2 * (xc - x1) * t0 + x1; |
| 1008 | double yb = ky * t0 * t0 + 2 * (yc - y1) * t0 + y1; |
| 1009 | double xl = dxl * t0 + x1; |
| 1010 | double yl = dyl * t0 + y1; |
| 1011 | |
| 1012 | return (x >= xb && x < xl) || |
| 1013 | (x >= xl && x < xb) || |
| 1014 | (y >= yb && y < yl) || |
| 1015 | (y >= yl && y < yb); |
| 1016 | } |
| 1017 | |
| 1018 | /** |
| 1019 | * {@inheritDoc} |
| 1020 | * @since 1.2 |
| 1021 | */ |
| 1022 | public boolean contains(Point2D p) { |
| 1023 | return contains(p.getX(), p.getY()); |
| 1024 | } |
| 1025 | |
| 1026 | /** |
| 1027 | * Fill an array with the coefficients of the parametric equation |
| 1028 | * in t, ready for solving against val with solveQuadratic. |
| 1029 | * We currently have: |
| 1030 | * val = Py(t) = C1*(1-t)^2 + 2*CP*t*(1-t) + C2*t^2 |
| 1031 | * = C1 - 2*C1*t + C1*t^2 + 2*CP*t - 2*CP*t^2 + C2*t^2 |
| 1032 | * = C1 + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 |
| 1033 | * 0 = (C1 - val) + (2*CP - 2*C1)*t + (C1 - 2*CP + C2)*t^2 |
| 1034 | * 0 = C + Bt + At^2 |
| 1035 | * C = C1 - val |
| 1036 | * B = 2*CP - 2*C1 |
| 1037 | * A = C1 - 2*CP + C2 |
| 1038 | */ |
| 1039 | private static void fillEqn(double eqn[], double val, |
| 1040 | double c1, double cp, double c2) { |
| 1041 | eqn[0] = c1 - val; |
| 1042 | eqn[1] = cp + cp - c1 - c1; |
| 1043 | eqn[2] = c1 - cp - cp + c2; |
| 1044 | return; |
| 1045 | } |
| 1046 | |
| 1047 | /** |
| 1048 | * Evaluate the t values in the first num slots of the vals[] array |
| 1049 | * and place the evaluated values back into the same array. Only |
| 1050 | * evaluate t values that are within the range <0, 1>, including |
| 1051 | * the 0 and 1 ends of the range iff the include0 or include1 |
| 1052 | * booleans are true. If an "inflection" equation is handed in, |
| 1053 | * then any points which represent a point of inflection for that |
| 1054 | * quadratic equation are also ignored. |
| 1055 | */ |
| 1056 | private static int evalQuadratic(double vals[], int num, |
| 1057 | boolean include0, |
| 1058 | boolean include1, |
| 1059 | double inflect[], |
| 1060 | double c1, double ctrl, double c2) { |
| 1061 | int j = 0; |
| 1062 | for (int i = 0; i < num; i++) { |
| 1063 | double t = vals[i]; |
| 1064 | if ((include0 ? t >= 0 : t > 0) && |
| 1065 | (include1 ? t <= 1 : t < 1) && |
| 1066 | (inflect == null || |
| 1067 | inflect[1] + 2*inflect[2]*t != 0)) |
| 1068 | { |
| 1069 | double u = 1 - t; |
| 1070 | vals[j++] = c1*u*u + 2*ctrl*t*u + c2*t*t; |
| 1071 | } |
| 1072 | } |
| 1073 | return j; |
| 1074 | } |
| 1075 | |
| 1076 | private static final int BELOW = -2; |
| 1077 | private static final int LOWEDGE = -1; |
| 1078 | private static final int INSIDE = 0; |
| 1079 | private static final int HIGHEDGE = 1; |
| 1080 | private static final int ABOVE = 2; |
| 1081 | |
| 1082 | /** |
| 1083 | * Determine where coord lies with respect to the range from |
| 1084 | * low to high. It is assumed that low <= high. The return |
| 1085 | * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE, |
| 1086 | * or ABOVE. |
| 1087 | */ |
| 1088 | private static int getTag(double coord, double low, double high) { |
| 1089 | if (coord <= low) { |
| 1090 | return (coord < low ? BELOW : LOWEDGE); |
| 1091 | } |
| 1092 | if (coord >= high) { |
| 1093 | return (coord > high ? ABOVE : HIGHEDGE); |
| 1094 | } |
| 1095 | return INSIDE; |
| 1096 | } |
| 1097 | |
| 1098 | /** |
| 1099 | * Determine if the pttag represents a coordinate that is already |
| 1100 | * in its test range, or is on the border with either of the two |
| 1101 | * opttags representing another coordinate that is "towards the |
| 1102 | * inside" of that test range. In other words, are either of the |
| 1103 | * two "opt" points "drawing the pt inward"? |
| 1104 | */ |
| 1105 | private static boolean inwards(int pttag, int opt1tag, int opt2tag) { |
| 1106 | switch (pttag) { |
| 1107 | case BELOW: |
| 1108 | case ABOVE: |
| 1109 | default: |
| 1110 | return false; |
| 1111 | case LOWEDGE: |
| 1112 | return (opt1tag >= INSIDE || opt2tag >= INSIDE); |
| 1113 | case INSIDE: |
| 1114 | return true; |
| 1115 | case HIGHEDGE: |
| 1116 | return (opt1tag <= INSIDE || opt2tag <= INSIDE); |
| 1117 | } |
| 1118 | } |
| 1119 | |
| 1120 | /** |
| 1121 | * {@inheritDoc} |
| 1122 | * @since 1.2 |
| 1123 | */ |
| 1124 | public boolean intersects(double x, double y, double w, double h) { |
| 1125 | // Trivially reject non-existant rectangles |
| 1126 | if (w <= 0 || h <= 0) { |
| 1127 | return false; |
| 1128 | } |
| 1129 | |
| 1130 | // Trivially accept if either endpoint is inside the rectangle |
| 1131 | // (not on its border since it may end there and not go inside) |
| 1132 | // Record where they lie with respect to the rectangle. |
| 1133 | // -1 => left, 0 => inside, 1 => right |
| 1134 | double x1 = getX1(); |
| 1135 | double y1 = getY1(); |
| 1136 | int x1tag = getTag(x1, x, x+w); |
| 1137 | int y1tag = getTag(y1, y, y+h); |
| 1138 | if (x1tag == INSIDE && y1tag == INSIDE) { |
| 1139 | return true; |
| 1140 | } |
| 1141 | double x2 = getX2(); |
| 1142 | double y2 = getY2(); |
| 1143 | int x2tag = getTag(x2, x, x+w); |
| 1144 | int y2tag = getTag(y2, y, y+h); |
| 1145 | if (x2tag == INSIDE && y2tag == INSIDE) { |
| 1146 | return true; |
| 1147 | } |
| 1148 | double ctrlx = getCtrlX(); |
| 1149 | double ctrly = getCtrlY(); |
| 1150 | int ctrlxtag = getTag(ctrlx, x, x+w); |
| 1151 | int ctrlytag = getTag(ctrly, y, y+h); |
| 1152 | |
| 1153 | // Trivially reject if all points are entirely to one side of |
| 1154 | // the rectangle. |
| 1155 | if (x1tag < INSIDE && x2tag < INSIDE && ctrlxtag < INSIDE) { |
| 1156 | return false; // All points left |
| 1157 | } |
| 1158 | if (y1tag < INSIDE && y2tag < INSIDE && ctrlytag < INSIDE) { |
| 1159 | return false; // All points above |
| 1160 | } |
| 1161 | if (x1tag > INSIDE && x2tag > INSIDE && ctrlxtag > INSIDE) { |
| 1162 | return false; // All points right |
| 1163 | } |
| 1164 | if (y1tag > INSIDE && y2tag > INSIDE && ctrlytag > INSIDE) { |
| 1165 | return false; // All points below |
| 1166 | } |
| 1167 | |
| 1168 | // Test for endpoints on the edge where either the segment |
| 1169 | // or the curve is headed "inwards" from them |
| 1170 | // Note: These tests are a superset of the fast endpoint tests |
| 1171 | // above and thus repeat those tests, but take more time |
| 1172 | // and cover more cases |
| 1173 | if (inwards(x1tag, x2tag, ctrlxtag) && |
| 1174 | inwards(y1tag, y2tag, ctrlytag)) |
| 1175 | { |
| 1176 | // First endpoint on border with either edge moving inside |
| 1177 | return true; |
| 1178 | } |
| 1179 | if (inwards(x2tag, x1tag, ctrlxtag) && |
| 1180 | inwards(y2tag, y1tag, ctrlytag)) |
| 1181 | { |
| 1182 | // Second endpoint on border with either edge moving inside |
| 1183 | return true; |
| 1184 | } |
| 1185 | |
| 1186 | // Trivially accept if endpoints span directly across the rectangle |
| 1187 | boolean xoverlap = (x1tag * x2tag <= 0); |
| 1188 | boolean yoverlap = (y1tag * y2tag <= 0); |
| 1189 | if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) { |
| 1190 | return true; |
| 1191 | } |
| 1192 | if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) { |
| 1193 | return true; |
| 1194 | } |
| 1195 | |
| 1196 | // We now know that both endpoints are outside the rectangle |
| 1197 | // but the 3 points are not all on one side of the rectangle. |
| 1198 | // Therefore the curve cannot be contained inside the rectangle, |
| 1199 | // but the rectangle might be contained inside the curve, or |
| 1200 | // the curve might intersect the boundary of the rectangle. |
| 1201 | |
| 1202 | double[] eqn = new double[3]; |
| 1203 | double[] res = new double[3]; |
| 1204 | if (!yoverlap) { |
| 1205 | // Both Y coordinates for the closing segment are above or |
| 1206 | // below the rectangle which means that we can only intersect |
| 1207 | // if the curve crosses the top (or bottom) of the rectangle |
| 1208 | // in more than one place and if those crossing locations |
| 1209 | // span the horizontal range of the rectangle. |
| 1210 | fillEqn(eqn, (y1tag < INSIDE ? y : y+h), y1, ctrly, y2); |
| 1211 | return (solveQuadratic(eqn, res) == 2 && |
| 1212 | evalQuadratic(res, 2, true, true, null, |
| 1213 | x1, ctrlx, x2) == 2 && |
| 1214 | getTag(res[0], x, x+w) * getTag(res[1], x, x+w) <= 0); |
| 1215 | } |
| 1216 | |
| 1217 | // Y ranges overlap. Now we examine the X ranges |
| 1218 | if (!xoverlap) { |
| 1219 | // Both X coordinates for the closing segment are left of |
| 1220 | // or right of the rectangle which means that we can only |
| 1221 | // intersect if the curve crosses the left (or right) edge |
| 1222 | // of the rectangle in more than one place and if those |
| 1223 | // crossing locations span the vertical range of the rectangle. |
| 1224 | fillEqn(eqn, (x1tag < INSIDE ? x : x+w), x1, ctrlx, x2); |
| 1225 | return (solveQuadratic(eqn, res) == 2 && |
| 1226 | evalQuadratic(res, 2, true, true, null, |
| 1227 | y1, ctrly, y2) == 2 && |
| 1228 | getTag(res[0], y, y+h) * getTag(res[1], y, y+h) <= 0); |
| 1229 | } |
| 1230 | |
| 1231 | // The X and Y ranges of the endpoints overlap the X and Y |
| 1232 | // ranges of the rectangle, now find out how the endpoint |
| 1233 | // line segment intersects the Y range of the rectangle |
| 1234 | double dx = x2 - x1; |
| 1235 | double dy = y2 - y1; |
| 1236 | double k = y2 * x1 - x2 * y1; |
| 1237 | int c1tag, c2tag; |
| 1238 | if (y1tag == INSIDE) { |
| 1239 | c1tag = x1tag; |
| 1240 | } else { |
| 1241 | c1tag = getTag((k + dx * (y1tag < INSIDE ? y : y+h)) / dy, x, x+w); |
| 1242 | } |
| 1243 | if (y2tag == INSIDE) { |
| 1244 | c2tag = x2tag; |
| 1245 | } else { |
| 1246 | c2tag = getTag((k + dx * (y2tag < INSIDE ? y : y+h)) / dy, x, x+w); |
| 1247 | } |
| 1248 | // If the part of the line segment that intersects the Y range |
| 1249 | // of the rectangle crosses it horizontally - trivially accept |
| 1250 | if (c1tag * c2tag <= 0) { |
| 1251 | return true; |
| 1252 | } |
| 1253 | |
| 1254 | // Now we know that both the X and Y ranges intersect and that |
| 1255 | // the endpoint line segment does not directly cross the rectangle. |
| 1256 | // |
| 1257 | // We can almost treat this case like one of the cases above |
| 1258 | // where both endpoints are to one side, except that we will |
| 1259 | // only get one intersection of the curve with the vertical |
| 1260 | // side of the rectangle. This is because the endpoint segment |
| 1261 | // accounts for the other intersection. |
| 1262 | // |
| 1263 | // (Remember there is overlap in both the X and Y ranges which |
| 1264 | // means that the segment must cross at least one vertical edge |
| 1265 | // of the rectangle - in particular, the "near vertical side" - |
| 1266 | // leaving only one intersection for the curve.) |
| 1267 | // |
| 1268 | // Now we calculate the y tags of the two intersections on the |
| 1269 | // "near vertical side" of the rectangle. We will have one with |
| 1270 | // the endpoint segment, and one with the curve. If those two |
| 1271 | // vertical intersections overlap the Y range of the rectangle, |
| 1272 | // we have an intersection. Otherwise, we don't. |
| 1273 | |
| 1274 | // c1tag = vertical intersection class of the endpoint segment |
| 1275 | // |
| 1276 | // Choose the y tag of the endpoint that was not on the same |
| 1277 | // side of the rectangle as the subsegment calculated above. |
| 1278 | // Note that we can "steal" the existing Y tag of that endpoint |
| 1279 | // since it will be provably the same as the vertical intersection. |
| 1280 | c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag); |
| 1281 | |
| 1282 | // c2tag = vertical intersection class of the curve |
| 1283 | // |
| 1284 | // We have to calculate this one the straightforward way. |
| 1285 | // Note that the c2tag can still tell us which vertical edge |
| 1286 | // to test against. |
| 1287 | fillEqn(eqn, (c2tag < INSIDE ? x : x+w), x1, ctrlx, x2); |
| 1288 | int num = solveQuadratic(eqn, res); |
| 1289 | |
| 1290 | // Note: We should be able to assert(num == 2); since the |
| 1291 | // X range "crosses" (not touches) the vertical boundary, |
| 1292 | // but we pass num to evalQuadratic for completeness. |
| 1293 | evalQuadratic(res, num, true, true, null, y1, ctrly, y2); |
| 1294 | |
| 1295 | // Note: We can assert(num evals == 1); since one of the |
| 1296 | // 2 crossings will be out of the [0,1] range. |
| 1297 | c2tag = getTag(res[0], y, y+h); |
| 1298 | |
| 1299 | // Finally, we have an intersection if the two crossings |
| 1300 | // overlap the Y range of the rectangle. |
| 1301 | return (c1tag * c2tag <= 0); |
| 1302 | } |
| 1303 | |
| 1304 | /** |
| 1305 | * {@inheritDoc} |
| 1306 | * @since 1.2 |
| 1307 | */ |
| 1308 | public boolean intersects(Rectangle2D r) { |
| 1309 | return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight()); |
| 1310 | } |
| 1311 | |
| 1312 | /** |
| 1313 | * {@inheritDoc} |
| 1314 | * @since 1.2 |
| 1315 | */ |
| 1316 | public boolean contains(double x, double y, double w, double h) { |
| 1317 | if (w <= 0 || h <= 0) { |
| 1318 | return false; |
| 1319 | } |
| 1320 | // Assertion: Quadratic curves closed by connecting their |
| 1321 | // endpoints are always convex. |
| 1322 | return (contains(x, y) && |
| 1323 | contains(x + w, y) && |
| 1324 | contains(x + w, y + h) && |
| 1325 | contains(x, y + h)); |
| 1326 | } |
| 1327 | |
| 1328 | /** |
| 1329 | * {@inheritDoc} |
| 1330 | * @since 1.2 |
| 1331 | */ |
| 1332 | public boolean contains(Rectangle2D r) { |
| 1333 | return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight()); |
| 1334 | } |
| 1335 | |
| 1336 | /** |
| 1337 | * {@inheritDoc} |
| 1338 | * @since 1.2 |
| 1339 | */ |
| 1340 | public Rectangle getBounds() { |
| 1341 | return getBounds2D().getBounds(); |
| 1342 | } |
| 1343 | |
| 1344 | /** |
| 1345 | * Returns an iteration object that defines the boundary of the |
| 1346 | * shape of this <code>QuadCurve2D</code>. |
| 1347 | * The iterator for this class is not multi-threaded safe, |
| 1348 | * which means that this <code>QuadCurve2D</code> class does not |
| 1349 | * guarantee that modifications to the geometry of this |
| 1350 | * <code>QuadCurve2D</code> object do not affect any iterations of |
| 1351 | * that geometry that are already in process. |
| 1352 | * @param at an optional {@link AffineTransform} to apply to the |
| 1353 | * shape boundary |
| 1354 | * @return a {@link PathIterator} object that defines the boundary |
| 1355 | * of the shape. |
| 1356 | * @since 1.2 |
| 1357 | */ |
| 1358 | public PathIterator getPathIterator(AffineTransform at) { |
| 1359 | return new QuadIterator(this, at); |
| 1360 | } |
| 1361 | |
| 1362 | /** |
| 1363 | * Returns an iteration object that defines the boundary of the |
| 1364 | * flattened shape of this <code>QuadCurve2D</code>. |
| 1365 | * The iterator for this class is not multi-threaded safe, |
| 1366 | * which means that this <code>QuadCurve2D</code> class does not |
| 1367 | * guarantee that modifications to the geometry of this |
| 1368 | * <code>QuadCurve2D</code> object do not affect any iterations of |
| 1369 | * that geometry that are already in process. |
| 1370 | * @param at an optional <code>AffineTransform</code> to apply |
| 1371 | * to the boundary of the shape |
| 1372 | * @param flatness the maximum distance that the control points for a |
| 1373 | * subdivided curve can be with respect to a line connecting |
| 1374 | * the end points of this curve before this curve is |
| 1375 | * replaced by a straight line connecting the end points. |
| 1376 | * @return a <code>PathIterator</code> object that defines the |
| 1377 | * flattened boundary of the shape. |
| 1378 | * @since 1.2 |
| 1379 | */ |
| 1380 | public PathIterator getPathIterator(AffineTransform at, double flatness) { |
| 1381 | return new FlatteningPathIterator(getPathIterator(at), flatness); |
| 1382 | } |
| 1383 | |
| 1384 | /** |
| 1385 | * Creates a new object of the same class and with the same contents |
| 1386 | * as this object. |
| 1387 | * |
| 1388 | * @return a clone of this instance. |
| 1389 | * @exception OutOfMemoryError if there is not enough memory. |
| 1390 | * @see java.lang.Cloneable |
| 1391 | * @since 1.2 |
| 1392 | */ |
| 1393 | public Object clone() { |
| 1394 | try { |
| 1395 | return super.clone(); |
| 1396 | } catch (CloneNotSupportedException e) { |
| 1397 | // this shouldn't happen, since we are Cloneable |
| 1398 | throw new InternalError(); |
| 1399 | } |
| 1400 | } |
| 1401 | } |