0001 /*
0002 * Copyright 1997-2006 Sun Microsystems, Inc. All Rights Reserved.
0003 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
0004 *
0005 * This code is free software; you can redistribute it and/or modify it
0006 * under the terms of the GNU General Public License version 2 only, as
0007 * published by the Free Software Foundation. Sun designates this
0008 * particular file as subject to the "Classpath" exception as provided
0009 * by Sun in the LICENSE file that accompanied this code.
0010 *
0011 * This code is distributed in the hope that it will be useful, but WITHOUT
0012 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
0013 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
0014 * version 2 for more details (a copy is included in the LICENSE file that
0015 * accompanied this code).
0016 *
0017 * You should have received a copy of the GNU General Public License version
0018 * 2 along with this work; if not, write to the Free Software Foundation,
0019 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
0020 *
0021 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
0022 * CA 95054 USA or visit www.sun.com if you need additional information or
0023 * have any questions.
0024 */
0025
0026 package java.awt.geom;
0027
0028 import java.awt.Shape;
0029 import java.awt.Rectangle;
0030 import java.util.Arrays;
0031 import java.io.Serializable;
0032 import sun.awt.geom.Curve;
0033
0034 /**
0035 * The <code>CubicCurve2D</code> class defines a cubic parametric curve
0036 * segment in {@code (x,y)} coordinate space.
0037 * <p>
0038 * This class is only the abstract superclass for all objects which
0039 * store a 2D cubic curve segment.
0040 * The actual storage representation of the coordinates is left to
0041 * the subclass.
0042 *
0043 * @version 1.42, 05/05/07
0044 * @author Jim Graham
0045 * @since 1.2
0046 */
0047 public abstract class CubicCurve2D implements Shape, Cloneable {
0048
0049 /**
0050 * A cubic parametric curve segment specified with
0051 * {@code float} coordinates.
0052 * @since 1.2
0053 */
0054 public static class Float extends CubicCurve2D implements
0055 Serializable {
0056 /**
0057 * The X coordinate of the start point
0058 * of the cubic curve segment.
0059 * @since 1.2
0060 * @serial
0061 */
0062 public float x1;
0063
0064 /**
0065 * The Y coordinate of the start point
0066 * of the cubic curve segment.
0067 * @since 1.2
0068 * @serial
0069 */
0070 public float y1;
0071
0072 /**
0073 * The X coordinate of the first control point
0074 * of the cubic curve segment.
0075 * @since 1.2
0076 * @serial
0077 */
0078 public float ctrlx1;
0079
0080 /**
0081 * The Y coordinate of the first control point
0082 * of the cubic curve segment.
0083 * @since 1.2
0084 * @serial
0085 */
0086 public float ctrly1;
0087
0088 /**
0089 * The X coordinate of the second control point
0090 * of the cubic curve segment.
0091 * @since 1.2
0092 * @serial
0093 */
0094 public float ctrlx2;
0095
0096 /**
0097 * The Y coordinate of the second control point
0098 * of the cubic curve segment.
0099 * @since 1.2
0100 * @serial
0101 */
0102 public float ctrly2;
0103
0104 /**
0105 * The X coordinate of the end point
0106 * of the cubic curve segment.
0107 * @since 1.2
0108 * @serial
0109 */
0110 public float x2;
0111
0112 /**
0113 * The Y coordinate of the end point
0114 * of the cubic curve segment.
0115 * @since 1.2
0116 * @serial
0117 */
0118 public float y2;
0119
0120 /**
0121 * Constructs and initializes a CubicCurve with coordinates
0122 * (0, 0, 0, 0, 0, 0, 0, 0).
0123 * @since 1.2
0124 */
0125 public Float() {
0126 }
0127
0128 /**
0129 * Constructs and initializes a {@code CubicCurve2D} from
0130 * the specified {@code float} coordinates.
0131 *
0132 * @param x1 the X coordinate for the start point
0133 * of the resulting {@code CubicCurve2D}
0134 * @param y1 the Y coordinate for the start point
0135 * of the resulting {@code CubicCurve2D}
0136 * @param ctrlx1 the X coordinate for the first control point
0137 * of the resulting {@code CubicCurve2D}
0138 * @param ctrly1 the Y coordinate for the first control point
0139 * of the resulting {@code CubicCurve2D}
0140 * @param ctrlx2 the X coordinate for the second control point
0141 * of the resulting {@code CubicCurve2D}
0142 * @param ctrly2 the Y coordinate for the second control point
0143 * of the resulting {@code CubicCurve2D}
0144 * @param x2 the X coordinate for the end point
0145 * of the resulting {@code CubicCurve2D}
0146 * @param y2 the Y coordinate for the end point
0147 * of the resulting {@code CubicCurve2D}
0148 * @since 1.2
0149 */
0150 public Float(float x1, float y1, float ctrlx1, float ctrly1,
0151 float ctrlx2, float ctrly2, float x2, float y2) {
0152 setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
0153 }
0154
0155 /**
0156 * {@inheritDoc}
0157 * @since 1.2
0158 */
0159 public double getX1() {
0160 return (double) x1;
0161 }
0162
0163 /**
0164 * {@inheritDoc}
0165 * @since 1.2
0166 */
0167 public double getY1() {
0168 return (double) y1;
0169 }
0170
0171 /**
0172 * {@inheritDoc}
0173 * @since 1.2
0174 */
0175 public Point2D getP1() {
0176 return new Point2D.Float(x1, y1);
0177 }
0178
0179 /**
0180 * {@inheritDoc}
0181 * @since 1.2
0182 */
0183 public double getCtrlX1() {
0184 return (double) ctrlx1;
0185 }
0186
0187 /**
0188 * {@inheritDoc}
0189 * @since 1.2
0190 */
0191 public double getCtrlY1() {
0192 return (double) ctrly1;
0193 }
0194
0195 /**
0196 * {@inheritDoc}
0197 * @since 1.2
0198 */
0199 public Point2D getCtrlP1() {
0200 return new Point2D.Float(ctrlx1, ctrly1);
0201 }
0202
0203 /**
0204 * {@inheritDoc}
0205 * @since 1.2
0206 */
0207 public double getCtrlX2() {
0208 return (double) ctrlx2;
0209 }
0210
0211 /**
0212 * {@inheritDoc}
0213 * @since 1.2
0214 */
0215 public double getCtrlY2() {
0216 return (double) ctrly2;
0217 }
0218
0219 /**
0220 * {@inheritDoc}
0221 * @since 1.2
0222 */
0223 public Point2D getCtrlP2() {
0224 return new Point2D.Float(ctrlx2, ctrly2);
0225 }
0226
0227 /**
0228 * {@inheritDoc}
0229 * @since 1.2
0230 */
0231 public double getX2() {
0232 return (double) x2;
0233 }
0234
0235 /**
0236 * {@inheritDoc}
0237 * @since 1.2
0238 */
0239 public double getY2() {
0240 return (double) y2;
0241 }
0242
0243 /**
0244 * {@inheritDoc}
0245 * @since 1.2
0246 */
0247 public Point2D getP2() {
0248 return new Point2D.Float(x2, y2);
0249 }
0250
0251 /**
0252 * {@inheritDoc}
0253 * @since 1.2
0254 */
0255 public void setCurve(double x1, double y1, double ctrlx1,
0256 double ctrly1, double ctrlx2, double ctrly2, double x2,
0257 double y2) {
0258 this .x1 = (float) x1;
0259 this .y1 = (float) y1;
0260 this .ctrlx1 = (float) ctrlx1;
0261 this .ctrly1 = (float) ctrly1;
0262 this .ctrlx2 = (float) ctrlx2;
0263 this .ctrly2 = (float) ctrly2;
0264 this .x2 = (float) x2;
0265 this .y2 = (float) y2;
0266 }
0267
0268 /**
0269 * Sets the location of the end points and control points
0270 * of this curve to the specified {@code float} coordinates.
0271 *
0272 * @param x1 the X coordinate used to set the start point
0273 * of this {@code CubicCurve2D}
0274 * @param y1 the Y coordinate used to set the start point
0275 * of this {@code CubicCurve2D}
0276 * @param ctrlx1 the X coordinate used to set the first control point
0277 * of this {@code CubicCurve2D}
0278 * @param ctrly1 the Y coordinate used to set the first control point
0279 * of this {@code CubicCurve2D}
0280 * @param ctrlx2 the X coordinate used to set the second control point
0281 * of this {@code CubicCurve2D}
0282 * @param ctrly2 the Y coordinate used to set the second control point
0283 * of this {@code CubicCurve2D}
0284 * @param x2 the X coordinate used to set the end point
0285 * of this {@code CubicCurve2D}
0286 * @param y2 the Y coordinate used to set the end point
0287 * of this {@code CubicCurve2D}
0288 * @since 1.2
0289 */
0290 public void setCurve(float x1, float y1, float ctrlx1,
0291 float ctrly1, float ctrlx2, float ctrly2, float x2,
0292 float y2) {
0293 this .x1 = x1;
0294 this .y1 = y1;
0295 this .ctrlx1 = ctrlx1;
0296 this .ctrly1 = ctrly1;
0297 this .ctrlx2 = ctrlx2;
0298 this .ctrly2 = ctrly2;
0299 this .x2 = x2;
0300 this .y2 = y2;
0301 }
0302
0303 /**
0304 * {@inheritDoc}
0305 * @since 1.2
0306 */
0307 public Rectangle2D getBounds2D() {
0308 float left = Math.min(Math.min(x1, x2), Math.min(ctrlx1,
0309 ctrlx2));
0310 float top = Math.min(Math.min(y1, y2), Math.min(ctrly1,
0311 ctrly2));
0312 float right = Math.max(Math.max(x1, x2), Math.max(ctrlx1,
0313 ctrlx2));
0314 float bottom = Math.max(Math.max(y1, y2), Math.max(ctrly1,
0315 ctrly2));
0316 return new Rectangle2D.Float(left, top, right - left,
0317 bottom - top);
0318 }
0319
0320 /*
0321 * JDK 1.6 serialVersionUID
0322 */
0323 private static final long serialVersionUID = -1272015596714244385L;
0324 }
0325
0326 /**
0327 * A cubic parametric curve segment specified with
0328 * {@code double} coordinates.
0329 * @since 1.2
0330 */
0331 public static class Double extends CubicCurve2D implements
0332 Serializable {
0333 /**
0334 * The X coordinate of the start point
0335 * of the cubic curve segment.
0336 * @since 1.2
0337 * @serial
0338 */
0339 public double x1;
0340
0341 /**
0342 * The Y coordinate of the start point
0343 * of the cubic curve segment.
0344 * @since 1.2
0345 * @serial
0346 */
0347 public double y1;
0348
0349 /**
0350 * The X coordinate of the first control point
0351 * of the cubic curve segment.
0352 * @since 1.2
0353 * @serial
0354 */
0355 public double ctrlx1;
0356
0357 /**
0358 * The Y coordinate of the first control point
0359 * of the cubic curve segment.
0360 * @since 1.2
0361 * @serial
0362 */
0363 public double ctrly1;
0364
0365 /**
0366 * The X coordinate of the second control point
0367 * of the cubic curve segment.
0368 * @since 1.2
0369 * @serial
0370 */
0371 public double ctrlx2;
0372
0373 /**
0374 * The Y coordinate of the second control point
0375 * of the cubic curve segment.
0376 * @since 1.2
0377 * @serial
0378 */
0379 public double ctrly2;
0380
0381 /**
0382 * The X coordinate of the end point
0383 * of the cubic curve segment.
0384 * @since 1.2
0385 * @serial
0386 */
0387 public double x2;
0388
0389 /**
0390 * The Y coordinate of the end point
0391 * of the cubic curve segment.
0392 * @since 1.2
0393 * @serial
0394 */
0395 public double y2;
0396
0397 /**
0398 * Constructs and initializes a CubicCurve with coordinates
0399 * (0, 0, 0, 0, 0, 0, 0, 0).
0400 * @since 1.2
0401 */
0402 public Double() {
0403 }
0404
0405 /**
0406 * Constructs and initializes a {@code CubicCurve2D} from
0407 * the specified {@code double} coordinates.
0408 *
0409 * @param x1 the X coordinate for the start point
0410 * of the resulting {@code CubicCurve2D}
0411 * @param y1 the Y coordinate for the start point
0412 * of the resulting {@code CubicCurve2D}
0413 * @param ctrlx1 the X coordinate for the first control point
0414 * of the resulting {@code CubicCurve2D}
0415 * @param ctrly1 the Y coordinate for the first control point
0416 * of the resulting {@code CubicCurve2D}
0417 * @param ctrlx2 the X coordinate for the second control point
0418 * of the resulting {@code CubicCurve2D}
0419 * @param ctrly2 the Y coordinate for the second control point
0420 * of the resulting {@code CubicCurve2D}
0421 * @param x2 the X coordinate for the end point
0422 * of the resulting {@code CubicCurve2D}
0423 * @param y2 the Y coordinate for the end point
0424 * of the resulting {@code CubicCurve2D}
0425 * @since 1.2
0426 */
0427 public Double(double x1, double y1, double ctrlx1,
0428 double ctrly1, double ctrlx2, double ctrly2, double x2,
0429 double y2) {
0430 setCurve(x1, y1, ctrlx1, ctrly1, ctrlx2, ctrly2, x2, y2);
0431 }
0432
0433 /**
0434 * {@inheritDoc}
0435 * @since 1.2
0436 */
0437 public double getX1() {
0438 return x1;
0439 }
0440
0441 /**
0442 * {@inheritDoc}
0443 * @since 1.2
0444 */
0445 public double getY1() {
0446 return y1;
0447 }
0448
0449 /**
0450 * {@inheritDoc}
0451 * @since 1.2
0452 */
0453 public Point2D getP1() {
0454 return new Point2D.Double(x1, y1);
0455 }
0456
0457 /**
0458 * {@inheritDoc}
0459 * @since 1.2
0460 */
0461 public double getCtrlX1() {
0462 return ctrlx1;
0463 }
0464
0465 /**
0466 * {@inheritDoc}
0467 * @since 1.2
0468 */
0469 public double getCtrlY1() {
0470 return ctrly1;
0471 }
0472
0473 /**
0474 * {@inheritDoc}
0475 * @since 1.2
0476 */
0477 public Point2D getCtrlP1() {
0478 return new Point2D.Double(ctrlx1, ctrly1);
0479 }
0480
0481 /**
0482 * {@inheritDoc}
0483 * @since 1.2
0484 */
0485 public double getCtrlX2() {
0486 return ctrlx2;
0487 }
0488
0489 /**
0490 * {@inheritDoc}
0491 * @since 1.2
0492 */
0493 public double getCtrlY2() {
0494 return ctrly2;
0495 }
0496
0497 /**
0498 * {@inheritDoc}
0499 * @since 1.2
0500 */
0501 public Point2D getCtrlP2() {
0502 return new Point2D.Double(ctrlx2, ctrly2);
0503 }
0504
0505 /**
0506 * {@inheritDoc}
0507 * @since 1.2
0508 */
0509 public double getX2() {
0510 return x2;
0511 }
0512
0513 /**
0514 * {@inheritDoc}
0515 * @since 1.2
0516 */
0517 public double getY2() {
0518 return y2;
0519 }
0520
0521 /**
0522 * {@inheritDoc}
0523 * @since 1.2
0524 */
0525 public Point2D getP2() {
0526 return new Point2D.Double(x2, y2);
0527 }
0528
0529 /**
0530 * {@inheritDoc}
0531 * @since 1.2
0532 */
0533 public void setCurve(double x1, double y1, double ctrlx1,
0534 double ctrly1, double ctrlx2, double ctrly2, double x2,
0535 double y2) {
0536 this .x1 = x1;
0537 this .y1 = y1;
0538 this .ctrlx1 = ctrlx1;
0539 this .ctrly1 = ctrly1;
0540 this .ctrlx2 = ctrlx2;
0541 this .ctrly2 = ctrly2;
0542 this .x2 = x2;
0543 this .y2 = y2;
0544 }
0545
0546 /**
0547 * {@inheritDoc}
0548 * @since 1.2
0549 */
0550 public Rectangle2D getBounds2D() {
0551 double left = Math.min(Math.min(x1, x2), Math.min(ctrlx1,
0552 ctrlx2));
0553 double top = Math.min(Math.min(y1, y2), Math.min(ctrly1,
0554 ctrly2));
0555 double right = Math.max(Math.max(x1, x2), Math.max(ctrlx1,
0556 ctrlx2));
0557 double bottom = Math.max(Math.max(y1, y2), Math.max(ctrly1,
0558 ctrly2));
0559 return new Rectangle2D.Double(left, top, right - left,
0560 bottom - top);
0561 }
0562
0563 /*
0564 * JDK 1.6 serialVersionUID
0565 */
0566 private static final long serialVersionUID = -4202960122839707295L;
0567 }
0568
0569 /**
0570 * This is an abstract class that cannot be instantiated directly.
0571 * Type-specific implementation subclasses are available for
0572 * instantiation and provide a number of formats for storing
0573 * the information necessary to satisfy the various accessor
0574 * methods below.
0575 *
0576 * @see java.awt.geom.CubicCurve2D.Float
0577 * @see java.awt.geom.CubicCurve2D.Double
0578 * @since 1.2
0579 */
0580 protected CubicCurve2D() {
0581 }
0582
0583 /**
0584 * Returns the X coordinate of the start point in double precision.
0585 * @return the X coordinate of the start point of the
0586 * {@code CubicCurve2D}.
0587 * @since 1.2
0588 */
0589 public abstract double getX1();
0590
0591 /**
0592 * Returns the Y coordinate of the start point in double precision.
0593 * @return the Y coordinate of the start point of the
0594 * {@code CubicCurve2D}.
0595 * @since 1.2
0596 */
0597 public abstract double getY1();
0598
0599 /**
0600 * Returns the start point.
0601 * @return a {@code Point2D} that is the start point of
0602 * the {@code CubicCurve2D}.
0603 * @since 1.2
0604 */
0605 public abstract Point2D getP1();
0606
0607 /**
0608 * Returns the X coordinate of the first control point in double precision.
0609 * @return the X coordinate of the first control point of the
0610 * {@code CubicCurve2D}.
0611 * @since 1.2
0612 */
0613 public abstract double getCtrlX1();
0614
0615 /**
0616 * Returns the Y coordinate of the first control point in double precision.
0617 * @return the Y coordinate of the first control point of the
0618 * {@code CubicCurve2D}.
0619 * @since 1.2
0620 */
0621 public abstract double getCtrlY1();
0622
0623 /**
0624 * Returns the first control point.
0625 * @return a {@code Point2D} that is the first control point of
0626 * the {@code CubicCurve2D}.
0627 * @since 1.2
0628 */
0629 public abstract Point2D getCtrlP1();
0630
0631 /**
0632 * Returns the X coordinate of the second control point
0633 * in double precision.
0634 * @return the X coordinate of the second control point of the
0635 * {@code CubicCurve2D}.
0636 * @since 1.2
0637 */
0638 public abstract double getCtrlX2();
0639
0640 /**
0641 * Returns the Y coordinate of the second control point
0642 * in double precision.
0643 * @return the Y coordinate of the second control point of the
0644 * {@code CubicCurve2D}.
0645 * @since 1.2
0646 */
0647 public abstract double getCtrlY2();
0648
0649 /**
0650 * Returns the second control point.
0651 * @return a {@code Point2D} that is the second control point of
0652 * the {@code CubicCurve2D}.
0653 * @since 1.2
0654 */
0655 public abstract Point2D getCtrlP2();
0656
0657 /**
0658 * Returns the X coordinate of the end point in double precision.
0659 * @return the X coordinate of the end point of the
0660 * {@code CubicCurve2D}.
0661 * @since 1.2
0662 */
0663 public abstract double getX2();
0664
0665 /**
0666 * Returns the Y coordinate of the end point in double precision.
0667 * @return the Y coordinate of the end point of the
0668 * {@code CubicCurve2D}.
0669 * @since 1.2
0670 */
0671 public abstract double getY2();
0672
0673 /**
0674 * Returns the end point.
0675 * @return a {@code Point2D} that is the end point of
0676 * the {@code CubicCurve2D}.
0677 * @since 1.2
0678 */
0679 public abstract Point2D getP2();
0680
0681 /**
0682 * Sets the location of the end points and control points of this curve
0683 * to the specified double coordinates.
0684 *
0685 * @param x1 the X coordinate used to set the start point
0686 * of this {@code CubicCurve2D}
0687 * @param y1 the Y coordinate used to set the start point
0688 * of this {@code CubicCurve2D}
0689 * @param ctrlx1 the X coordinate used to set the first control point
0690 * of this {@code CubicCurve2D}
0691 * @param ctrly1 the Y coordinate used to set the first control point
0692 * of this {@code CubicCurve2D}
0693 * @param ctrlx2 the X coordinate used to set the second control point
0694 * of this {@code CubicCurve2D}
0695 * @param ctrly2 the Y coordinate used to set the second control point
0696 * of this {@code CubicCurve2D}
0697 * @param x2 the X coordinate used to set the end point
0698 * of this {@code CubicCurve2D}
0699 * @param y2 the Y coordinate used to set the end point
0700 * of this {@code CubicCurve2D}
0701 * @since 1.2
0702 */
0703 public abstract void setCurve(double x1, double y1, double ctrlx1,
0704 double ctrly1, double ctrlx2, double ctrly2, double x2,
0705 double y2);
0706
0707 /**
0708 * Sets the location of the end points and control points of this curve
0709 * to the double coordinates at the specified offset in the specified
0710 * array.
0711 * @param coords a double array containing coordinates
0712 * @param offset the index of <code>coords</code> from which to begin
0713 * setting the end points and control points of this curve
0714 * to the coordinates contained in <code>coords</code>
0715 * @since 1.2
0716 */
0717 public void setCurve(double[] coords, int offset) {
0718 setCurve(coords[offset + 0], coords[offset + 1],
0719 coords[offset + 2], coords[offset + 3],
0720 coords[offset + 4], coords[offset + 5],
0721 coords[offset + 6], coords[offset + 7]);
0722 }
0723
0724 /**
0725 * Sets the location of the end points and control points of this curve
0726 * to the specified <code>Point2D</code> coordinates.
0727 * @param p1 the first specified <code>Point2D</code> used to set the
0728 * start point of this curve
0729 * @param cp1 the second specified <code>Point2D</code> used to set the
0730 * first control point of this curve
0731 * @param cp2 the third specified <code>Point2D</code> used to set the
0732 * second control point of this curve
0733 * @param p2 the fourth specified <code>Point2D</code> used to set the
0734 * end point of this curve
0735 * @since 1.2
0736 */
0737 public void setCurve(Point2D p1, Point2D cp1, Point2D cp2,
0738 Point2D p2) {
0739 setCurve(p1.getX(), p1.getY(), cp1.getX(), cp1.getY(), cp2
0740 .getX(), cp2.getY(), p2.getX(), p2.getY());
0741 }
0742
0743 /**
0744 * Sets the location of the end points and control points of this curve
0745 * to the coordinates of the <code>Point2D</code> objects at the specified
0746 * offset in the specified array.
0747 * @param pts an array of <code>Point2D</code> objects
0748 * @param offset the index of <code>pts</code> from which to begin setting
0749 * the end points and control points of this curve to the
0750 * points contained in <code>pts</code>
0751 * @since 1.2
0752 */
0753 public void setCurve(Point2D[] pts, int offset) {
0754 setCurve(pts[offset + 0].getX(), pts[offset + 0].getY(),
0755 pts[offset + 1].getX(), pts[offset + 1].getY(),
0756 pts[offset + 2].getX(), pts[offset + 2].getY(),
0757 pts[offset + 3].getX(), pts[offset + 3].getY());
0758 }
0759
0760 /**
0761 * Sets the location of the end points and control points of this curve
0762 * to the same as those in the specified <code>CubicCurve2D</code>.
0763 * @param c the specified <code>CubicCurve2D</code>
0764 * @since 1.2
0765 */
0766 public void setCurve(CubicCurve2D c) {
0767 setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(), c
0768 .getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
0769 }
0770
0771 /**
0772 * Returns the square of the flatness of the cubic curve specified
0773 * by the indicated control points. The flatness is the maximum distance
0774 * of a control point from the line connecting the end points.
0775 *
0776 * @param x1 the X coordinate that specifies the start point
0777 * of a {@code CubicCurve2D}
0778 * @param y1 the Y coordinate that specifies the start point
0779 * of a {@code CubicCurve2D}
0780 * @param ctrlx1 the X coordinate that specifies the first control point
0781 * of a {@code CubicCurve2D}
0782 * @param ctrly1 the Y coordinate that specifies the first control point
0783 * of a {@code CubicCurve2D}
0784 * @param ctrlx2 the X coordinate that specifies the second control point
0785 * of a {@code CubicCurve2D}
0786 * @param ctrly2 the Y coordinate that specifies the second control point
0787 * of a {@code CubicCurve2D}
0788 * @param x2 the X coordinate that specifies the end point
0789 * of a {@code CubicCurve2D}
0790 * @param y2 the Y coordinate that specifies the end point
0791 * of a {@code CubicCurve2D}
0792 * @return the square of the flatness of the {@code CubicCurve2D}
0793 * represented by the specified coordinates.
0794 * @since 1.2
0795 */
0796 public static double getFlatnessSq(double x1, double y1,
0797 double ctrlx1, double ctrly1, double ctrlx2, double ctrly2,
0798 double x2, double y2) {
0799 return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx1,
0800 ctrly1), Line2D.ptSegDistSq(x1, y1, x2, y2, ctrlx2,
0801 ctrly2));
0802
0803 }
0804
0805 /**
0806 * Returns the flatness of the cubic curve specified
0807 * by the indicated control points. The flatness is the maximum distance
0808 * of a control point from the line connecting the end points.
0809 *
0810 * @param x1 the X coordinate that specifies the start point
0811 * of a {@code CubicCurve2D}
0812 * @param y1 the Y coordinate that specifies the start point
0813 * of a {@code CubicCurve2D}
0814 * @param ctrlx1 the X coordinate that specifies the first control point
0815 * of a {@code CubicCurve2D}
0816 * @param ctrly1 the Y coordinate that specifies the first control point
0817 * of a {@code CubicCurve2D}
0818 * @param ctrlx2 the X coordinate that specifies the second control point
0819 * of a {@code CubicCurve2D}
0820 * @param ctrly2 the Y coordinate that specifies the second control point
0821 * of a {@code CubicCurve2D}
0822 * @param x2 the X coordinate that specifies the end point
0823 * of a {@code CubicCurve2D}
0824 * @param y2 the Y coordinate that specifies the end point
0825 * of a {@code CubicCurve2D}
0826 * @return the flatness of the {@code CubicCurve2D}
0827 * represented by the specified coordinates.
0828 * @since 1.2
0829 */
0830 public static double getFlatness(double x1, double y1,
0831 double ctrlx1, double ctrly1, double ctrlx2, double ctrly2,
0832 double x2, double y2) {
0833 return Math.sqrt(getFlatnessSq(x1, y1, ctrlx1, ctrly1, ctrlx2,
0834 ctrly2, x2, y2));
0835 }
0836
0837 /**
0838 * Returns the square of the flatness of the cubic curve specified
0839 * by the control points stored in the indicated array at the
0840 * indicated index. The flatness is the maximum distance
0841 * of a control point from the line connecting the end points.
0842 * @param coords an array containing coordinates
0843 * @param offset the index of <code>coords</code> from which to begin
0844 * getting the end points and control points of the curve
0845 * @return the square of the flatness of the <code>CubicCurve2D</code>
0846 * specified by the coordinates in <code>coords</code> at
0847 * the specified offset.
0848 * @since 1.2
0849 */
0850 public static double getFlatnessSq(double coords[], int offset) {
0851 return getFlatnessSq(coords[offset + 0], coords[offset + 1],
0852 coords[offset + 2], coords[offset + 3],
0853 coords[offset + 4], coords[offset + 5],
0854 coords[offset + 6], coords[offset + 7]);
0855 }
0856
0857 /**
0858 * Returns the flatness of the cubic curve specified
0859 * by the control points stored in the indicated array at the
0860 * indicated index. The flatness is the maximum distance
0861 * of a control point from the line connecting the end points.
0862 * @param coords an array containing coordinates
0863 * @param offset the index of <code>coords</code> from which to begin
0864 * getting the end points and control points of the curve
0865 * @return the flatness of the <code>CubicCurve2D</code>
0866 * specified by the coordinates in <code>coords</code> at
0867 * the specified offset.
0868 * @since 1.2
0869 */
0870 public static double getFlatness(double coords[], int offset) {
0871 return getFlatness(coords[offset + 0], coords[offset + 1],
0872 coords[offset + 2], coords[offset + 3],
0873 coords[offset + 4], coords[offset + 5],
0874 coords[offset + 6], coords[offset + 7]);
0875 }
0876
0877 /**
0878 * Returns the square of the flatness of this curve. The flatness is the
0879 * maximum distance of a control point from the line connecting the
0880 * end points.
0881 * @return the square of the flatness of this curve.
0882 * @since 1.2
0883 */
0884 public double getFlatnessSq() {
0885 return getFlatnessSq(getX1(), getY1(), getCtrlX1(),
0886 getCtrlY1(), getCtrlX2(), getCtrlY2(), getX2(), getY2());
0887 }
0888
0889 /**
0890 * Returns the flatness of this curve. The flatness is the
0891 * maximum distance of a control point from the line connecting the
0892 * end points.
0893 * @return the flatness of this curve.
0894 * @since 1.2
0895 */
0896 public double getFlatness() {
0897 return getFlatness(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
0898 getCtrlX2(), getCtrlY2(), getX2(), getY2());
0899 }
0900
0901 /**
0902 * Subdivides this cubic curve and stores the resulting two
0903 * subdivided curves into the left and right curve parameters.
0904 * Either or both of the left and right objects may be the same
0905 * as this object or null.
0906 * @param left the cubic curve object for storing for the left or
0907 * first half of the subdivided curve
0908 * @param right the cubic curve object for storing for the right or
0909 * second half of the subdivided curve
0910 * @since 1.2
0911 */
0912 public void subdivide(CubicCurve2D left, CubicCurve2D right) {
0913 subdivide(this , left, right);
0914 }
0915
0916 /**
0917 * Subdivides the cubic curve specified by the <code>src</code> parameter
0918 * and stores the resulting two subdivided curves into the
0919 * <code>left</code> and <code>right</code> curve parameters.
0920 * Either or both of the <code>left</code> and <code>right</code> objects
0921 * may be the same as the <code>src</code> object or <code>null</code>.
0922 * @param src the cubic curve to be subdivided
0923 * @param left the cubic curve object for storing the left or
0924 * first half of the subdivided curve
0925 * @param right the cubic curve object for storing the right or
0926 * second half of the subdivided curve
0927 * @since 1.2
0928 */
0929 public static void subdivide(CubicCurve2D src, CubicCurve2D left,
0930 CubicCurve2D right) {
0931 double x1 = src.getX1();
0932 double y1 = src.getY1();
0933 double ctrlx1 = src.getCtrlX1();
0934 double ctrly1 = src.getCtrlY1();
0935 double ctrlx2 = src.getCtrlX2();
0936 double ctrly2 = src.getCtrlY2();
0937 double x2 = src.getX2();
0938 double y2 = src.getY2();
0939 double centerx = (ctrlx1 + ctrlx2) / 2.0;
0940 double centery = (ctrly1 + ctrly2) / 2.0;
0941 ctrlx1 = (x1 + ctrlx1) / 2.0;
0942 ctrly1 = (y1 + ctrly1) / 2.0;
0943 ctrlx2 = (x2 + ctrlx2) / 2.0;
0944 ctrly2 = (y2 + ctrly2) / 2.0;
0945 double ctrlx12 = (ctrlx1 + centerx) / 2.0;
0946 double ctrly12 = (ctrly1 + centery) / 2.0;
0947 double ctrlx21 = (ctrlx2 + centerx) / 2.0;
0948 double ctrly21 = (ctrly2 + centery) / 2.0;
0949 centerx = (ctrlx12 + ctrlx21) / 2.0;
0950 centery = (ctrly12 + ctrly21) / 2.0;
0951 if (left != null) {
0952 left.setCurve(x1, y1, ctrlx1, ctrly1, ctrlx12, ctrly12,
0953 centerx, centery);
0954 }
0955 if (right != null) {
0956 right.setCurve(centerx, centery, ctrlx21, ctrly21, ctrlx2,
0957 ctrly2, x2, y2);
0958 }
0959 }
0960
0961 /**
0962 * Subdivides the cubic curve specified by the coordinates
0963 * stored in the <code>src</code> array at indices <code>srcoff</code>
0964 * through (<code>srcoff</code> + 7) and stores the
0965 * resulting two subdivided curves into the two result arrays at the
0966 * corresponding indices.
0967 * Either or both of the <code>left</code> and <code>right</code>
0968 * arrays may be <code>null</code> or a reference to the same array
0969 * as the <code>src</code> array.
0970 * Note that the last point in the first subdivided curve is the
0971 * same as the first point in the second subdivided curve. Thus,
0972 * it is possible to pass the same array for <code>left</code>
0973 * and <code>right</code> and to use offsets, such as <code>rightoff</code>
0974 * equals (<code>leftoff</code> + 6), in order
0975 * to avoid allocating extra storage for this common point.
0976 * @param src the array holding the coordinates for the source curve
0977 * @param srcoff the offset into the array of the beginning of the
0978 * the 6 source coordinates
0979 * @param left the array for storing the coordinates for the first
0980 * half of the subdivided curve
0981 * @param leftoff the offset into the array of the beginning of the
0982 * the 6 left coordinates
0983 * @param right the array for storing the coordinates for the second
0984 * half of the subdivided curve
0985 * @param rightoff the offset into the array of the beginning of the
0986 * the 6 right coordinates
0987 * @since 1.2
0988 */
0989 public static void subdivide(double src[], int srcoff,
0990 double left[], int leftoff, double right[], int rightoff) {
0991 double x1 = src[srcoff + 0];
0992 double y1 = src[srcoff + 1];
0993 double ctrlx1 = src[srcoff + 2];
0994 double ctrly1 = src[srcoff + 3];
0995 double ctrlx2 = src[srcoff + 4];
0996 double ctrly2 = src[srcoff + 5];
0997 double x2 = src[srcoff + 6];
0998 double y2 = src[srcoff + 7];
0999 if (left != null) {
1000 left[leftoff + 0] = x1;
1001 left[leftoff + 1] = y1;
1002 }
1003 if (right != null) {
1004 right[rightoff + 6] = x2;
1005 right[rightoff + 7] = y2;
1006 }
1007 x1 = (x1 + ctrlx1) / 2.0;
1008 y1 = (y1 + ctrly1) / 2.0;
1009 x2 = (x2 + ctrlx2) / 2.0;
1010 y2 = (y2 + ctrly2) / 2.0;
1011 double centerx = (ctrlx1 + ctrlx2) / 2.0;
1012 double centery = (ctrly1 + ctrly2) / 2.0;
1013 ctrlx1 = (x1 + centerx) / 2.0;
1014 ctrly1 = (y1 + centery) / 2.0;
1015 ctrlx2 = (x2 + centerx) / 2.0;
1016 ctrly2 = (y2 + centery) / 2.0;
1017 centerx = (ctrlx1 + ctrlx2) / 2.0;
1018 centery = (ctrly1 + ctrly2) / 2.0;
1019 if (left != null) {
1020 left[leftoff + 2] = x1;
1021 left[leftoff + 3] = y1;
1022 left[leftoff + 4] = ctrlx1;
1023 left[leftoff + 5] = ctrly1;
1024 left[leftoff + 6] = centerx;
1025 left[leftoff + 7] = centery;
1026 }
1027 if (right != null) {
1028 right[rightoff + 0] = centerx;
1029 right[rightoff + 1] = centery;
1030 right[rightoff + 2] = ctrlx2;
1031 right[rightoff + 3] = ctrly2;
1032 right[rightoff + 4] = x2;
1033 right[rightoff + 5] = y2;
1034 }
1035 }
1036
1037 /**
1038 * Solves the cubic whose coefficients are in the <code>eqn</code>
1039 * array and places the non-complex roots back into the same array,
1040 * returning the number of roots. The solved cubic is represented
1041 * by the equation:
1042 * <pre>
1043 * eqn = {c, b, a, d}
1044 * dx^3 + ax^2 + bx + c = 0
1045 * </pre>
1046 * A return value of -1 is used to distinguish a constant equation
1047 * that might be always 0 or never 0 from an equation that has no
1048 * zeroes.
1049 * @param eqn an array containing coefficients for a cubic
1050 * @return the number of roots, or -1 if the equation is a constant.
1051 * @since 1.2
1052 */
1053 public static int solveCubic(double eqn[]) {
1054 return solveCubic(eqn, eqn);
1055 }
1056
1057 /**
1058 * Solve the cubic whose coefficients are in the <code>eqn</code>
1059 * array and place the non-complex roots into the <code>res</code>
1060 * array, returning the number of roots.
1061 * The cubic solved is represented by the equation:
1062 * eqn = {c, b, a, d}
1063 * dx^3 + ax^2 + bx + c = 0
1064 * A return value of -1 is used to distinguish a constant equation,
1065 * which may be always 0 or never 0, from an equation which has no
1066 * zeroes.
1067 * @param eqn the specified array of coefficients to use to solve
1068 * the cubic equation
1069 * @param res the array that contains the non-complex roots
1070 * resulting from the solution of the cubic equation
1071 * @return the number of roots, or -1 if the equation is a constant
1072 * @since 1.3
1073 */
1074 public static int solveCubic(double eqn[], double res[]) {
1075 // From Numerical Recipes, 5.6, Quadratic and Cubic Equations
1076 double d = eqn[3];
1077 if (d == 0.0) {
1078 // The cubic has degenerated to quadratic (or line or ...).
1079 return QuadCurve2D.solveQuadratic(eqn, res);
1080 }
1081 double a = eqn[2] / d;
1082 double b = eqn[1] / d;
1083 double c = eqn[0] / d;
1084 int roots = 0;
1085 double Q = (a * a - 3.0 * b) / 9.0;
1086 double R = (2.0 * a * a * a - 9.0 * a * b + 27.0 * c) / 54.0;
1087 double R2 = R * R;
1088 double Q3 = Q * Q * Q;
1089 a = a / 3.0;
1090 if (R2 < Q3) {
1091 double theta = Math.acos(R / Math.sqrt(Q3));
1092 Q = -2.0 * Math.sqrt(Q);
1093 if (res == eqn) {
1094 // Copy the eqn so that we don't clobber it with the
1095 // roots. This is needed so that fixRoots can do its
1096 // work with the original equation.
1097 eqn = new double[4];
1098 System.arraycopy(res, 0, eqn, 0, 4);
1099 }
1100 res[roots++] = Q * Math.cos(theta / 3.0) - a;
1101 res[roots++] = Q * Math.cos((theta + Math.PI * 2.0) / 3.0)
1102 - a;
1103 res[roots++] = Q * Math.cos((theta - Math.PI * 2.0) / 3.0)
1104 - a;
1105 fixRoots(res, eqn);
1106 } else {
1107 boolean neg = (R < 0.0);
1108 double S = Math.sqrt(R2 - Q3);
1109 if (neg) {
1110 R = -R;
1111 }
1112 double A = Math.pow(R + S, 1.0 / 3.0);
1113 if (!neg) {
1114 A = -A;
1115 }
1116 double B = (A == 0.0) ? 0.0 : (Q / A);
1117 res[roots++] = (A + B) - a;
1118 }
1119 return roots;
1120 }
1121
1122 /*
1123 * This pruning step is necessary since solveCubic uses the
1124 * cosine function to calculate the roots when there are 3
1125 * of them. Since the cosine method can have an error of
1126 * +/- 1E-14 we need to make sure that we don't make any
1127 * bad decisions due to an error.
1128 *
1129 * If the root is not near one of the endpoints, then we will
1130 * only have a slight inaccuracy in calculating the x intercept
1131 * which will only cause a slightly wrong answer for some
1132 * points very close to the curve. While the results in that
1133 * case are not as accurate as they could be, they are not
1134 * disastrously inaccurate either.
1135 *
1136 * On the other hand, if the error happens near one end of
1137 * the curve, then our processing to reject values outside
1138 * of the t=[0,1] range will fail and the results of that
1139 * failure will be disastrous since for an entire horizontal
1140 * range of test points, we will either overcount or undercount
1141 * the crossings and get a wrong answer for all of them, even
1142 * when they are clearly and obviously inside or outside the
1143 * curve.
1144 *
1145 * To work around this problem, we try a couple of Newton-Raphson
1146 * iterations to see if the true root is closer to the endpoint
1147 * or further away. If it is further away, then we can stop
1148 * since we know we are on the right side of the endpoint. If
1149 * we change direction, then either we are now being dragged away
1150 * from the endpoint in which case the first condition will cause
1151 * us to stop, or we have passed the endpoint and are headed back.
1152 * In the second case, we simply evaluate the slope at the
1153 * endpoint itself and place ourselves on the appropriate side
1154 * of it or on it depending on that result.
1155 */
1156 private static void fixRoots(double res[], double eqn[]) {
1157 final double EPSILON = 1E-5;
1158 for (int i = 0; i < 3; i++) {
1159 double t = res[i];
1160 if (Math.abs(t) < EPSILON) {
1161 res[i] = findZero(t, 0, eqn);
1162 } else if (Math.abs(t - 1) < EPSILON) {
1163 res[i] = findZero(t, 1, eqn);
1164 }
1165 }
1166 }
1167
1168 private static double solveEqn(double eqn[], int order, double t) {
1169 double v = eqn[order];
1170 while (--order >= 0) {
1171 v = v * t + eqn[order];
1172 }
1173 return v;
1174 }
1175
1176 private static double findZero(double t, double target,
1177 double eqn[]) {
1178 double slopeqn[] = { eqn[1], 2 * eqn[2], 3 * eqn[3] };
1179 double slope;
1180 double origdelta = 0;
1181 double origt = t;
1182 while (true) {
1183 slope = solveEqn(slopeqn, 2, t);
1184 if (slope == 0) {
1185 // At a local minima - must return
1186 return t;
1187 }
1188 double y = solveEqn(eqn, 3, t);
1189 if (y == 0) {
1190 // Found it! - return it
1191 return t;
1192 }
1193 // assert(slope != 0 && y != 0);
1194 double delta = -(y / slope);
1195 // assert(delta != 0);
1196 if (origdelta == 0) {
1197 origdelta = delta;
1198 }
1199 if (t < target) {
1200 if (delta < 0)
1201 return t;
1202 } else if (t > target) {
1203 if (delta > 0)
1204 return t;
1205 } else { /* t == target */
1206 return (delta > 0 ? (target + java.lang.Double.MIN_VALUE)
1207 : (target - java.lang.Double.MIN_VALUE));
1208 }
1209 double newt = t + delta;
1210 if (t == newt) {
1211 // The deltas are so small that we aren't moving...
1212 return t;
1213 }
1214 if (delta * origdelta < 0) {
1215 // We have reversed our path.
1216 int tag = (origt < t ? getTag(target, origt, t)
1217 : getTag(target, t, origt));
1218 if (tag != INSIDE) {
1219 // Local minima found away from target - return the middle
1220 return (origt + t) / 2;
1221 }
1222 // Local minima somewhere near target - move to target
1223 // and let the slope determine the resulting t.
1224 t = target;
1225 } else {
1226 t = newt;
1227 }
1228 }
1229 }
1230
1231 /**
1232 * {@inheritDoc}
1233 * @since 1.2
1234 */
1235 public boolean contains(double x, double y) {
1236 if (!(x * 0.0 + y * 0.0 == 0.0)) {
1237 /* Either x or y was infinite or NaN.
1238 * A NaN always produces a negative response to any test
1239 * and Infinity values cannot be "inside" any path so
1240 * they should return false as well.
1241 */
1242 return false;
1243 }
1244 // We count the "Y" crossings to determine if the point is
1245 // inside the curve bounded by its closing line.
1246 double x1 = getX1();
1247 double y1 = getY1();
1248 double x2 = getX2();
1249 double y2 = getY2();
1250 int crossings = (Curve.pointCrossingsForLine(x, y, x1, y1, x2,
1251 y2) + Curve.pointCrossingsForCubic(x, y, x1, y1,
1252 getCtrlX1(), getCtrlY1(), getCtrlX2(), getCtrlY2(), x2,
1253 y2, 0));
1254 return ((crossings & 1) == 1);
1255 }
1256
1257 /**
1258 * {@inheritDoc}
1259 * @since 1.2
1260 */
1261 public boolean contains(Point2D p) {
1262 return contains(p.getX(), p.getY());
1263 }
1264
1265 /*
1266 * Fill an array with the coefficients of the parametric equation
1267 * in t, ready for solving against val with solveCubic.
1268 * We currently have:
1269 * <pre>
1270 * val = P(t) = C1(1-t)^3 + 3CP1 t(1-t)^2 + 3CP2 t^2(1-t) + C2 t^3
1271 * = C1 - 3C1t + 3C1t^2 - C1t^3 +
1272 * 3CP1t - 6CP1t^2 + 3CP1t^3 +
1273 * 3CP2t^2 - 3CP2t^3 +
1274 * C2t^3
1275 * 0 = (C1 - val) +
1276 * (3CP1 - 3C1) t +
1277 * (3C1 - 6CP1 + 3CP2) t^2 +
1278 * (C2 - 3CP2 + 3CP1 - C1) t^3
1279 * 0 = C + Bt + At^2 + Dt^3
1280 * C = C1 - val
1281 * B = 3*CP1 - 3*C1
1282 * A = 3*CP2 - 6*CP1 + 3*C1
1283 * D = C2 - 3*CP2 + 3*CP1 - C1
1284 * </pre>
1285 */
1286 private static void fillEqn(double eqn[], double val, double c1,
1287 double cp1, double cp2, double c2) {
1288 eqn[0] = c1 - val;
1289 eqn[1] = (cp1 - c1) * 3.0;
1290 eqn[2] = (cp2 - cp1 - cp1 + c1) * 3.0;
1291 eqn[3] = c2 + (cp1 - cp2) * 3.0 - c1;
1292 return;
1293 }
1294
1295 /*
1296 * Evaluate the t values in the first num slots of the vals[] array
1297 * and place the evaluated values back into the same array. Only
1298 * evaluate t values that are within the range <0, 1>, including
1299 * the 0 and 1 ends of the range iff the include0 or include1
1300 * booleans are true. If an "inflection" equation is handed in,
1301 * then any points which represent a point of inflection for that
1302 * cubic equation are also ignored.
1303 */
1304 private static int evalCubic(double vals[], int num,
1305 boolean include0, boolean include1, double inflect[],
1306 double c1, double cp1, double cp2, double c2) {
1307 int j = 0;
1308 for (int i = 0; i < num; i++) {
1309 double t = vals[i];
1310 if ((include0 ? t >= 0 : t > 0)
1311 && (include1 ? t <= 1 : t < 1)
1312 && (inflect == null || inflect[1]
1313 + (2 * inflect[2] + 3 * inflect[3] * t) * t != 0)) {
1314 double u = 1 - t;
1315 vals[j++] = c1 * u * u * u + 3 * cp1 * t * u * u + 3
1316 * cp2 * t * t * u + c2 * t * t * t;
1317 }
1318 }
1319 return j;
1320 }
1321
1322 private static final int BELOW = -2;
1323 private static final int LOWEDGE = -1;
1324 private static final int INSIDE = 0;
1325 private static final int HIGHEDGE = 1;
1326 private static final int ABOVE = 2;
1327
1328 /*
1329 * Determine where coord lies with respect to the range from
1330 * low to high. It is assumed that low <= high. The return
1331 * value is one of the 5 values BELOW, LOWEDGE, INSIDE, HIGHEDGE,
1332 * or ABOVE.
1333 */
1334 private static int getTag(double coord, double low, double high) {
1335 if (coord <= low) {
1336 return (coord < low ? BELOW : LOWEDGE);
1337 }
1338 if (coord >= high) {
1339 return (coord > high ? ABOVE : HIGHEDGE);
1340 }
1341 return INSIDE;
1342 }
1343
1344 /*
1345 * Determine if the pttag represents a coordinate that is already
1346 * in its test range, or is on the border with either of the two
1347 * opttags representing another coordinate that is "towards the
1348 * inside" of that test range. In other words, are either of the
1349 * two "opt" points "drawing the pt inward"?
1350 */
1351 private static boolean inwards(int pttag, int opt1tag, int opt2tag) {
1352 switch (pttag) {
1353 case BELOW:
1354 case ABOVE:
1355 default:
1356 return false;
1357 case LOWEDGE:
1358 return (opt1tag >= INSIDE || opt2tag >= INSIDE);
1359 case INSIDE:
1360 return true;
1361 case HIGHEDGE:
1362 return (opt1tag <= INSIDE || opt2tag <= INSIDE);
1363 }
1364 }
1365
1366 /**
1367 * {@inheritDoc}
1368 * @since 1.2
1369 */
1370 public boolean intersects(double x, double y, double w, double h) {
1371 // Trivially reject non-existant rectangles
1372 if (w <= 0 || h <= 0) {
1373 return false;
1374 }
1375
1376 // Trivially accept if either endpoint is inside the rectangle
1377 // (not on its border since it may end there and not go inside)
1378 // Record where they lie with respect to the rectangle.
1379 // -1 => left, 0 => inside, 1 => right
1380 double x1 = getX1();
1381 double y1 = getY1();
1382 int x1tag = getTag(x1, x, x + w);
1383 int y1tag = getTag(y1, y, y + h);
1384 if (x1tag == INSIDE && y1tag == INSIDE) {
1385 return true;
1386 }
1387 double x2 = getX2();
1388 double y2 = getY2();
1389 int x2tag = getTag(x2, x, x + w);
1390 int y2tag = getTag(y2, y, y + h);
1391 if (x2tag == INSIDE && y2tag == INSIDE) {
1392 return true;
1393 }
1394
1395 double ctrlx1 = getCtrlX1();
1396 double ctrly1 = getCtrlY1();
1397 double ctrlx2 = getCtrlX2();
1398 double ctrly2 = getCtrlY2();
1399 int ctrlx1tag = getTag(ctrlx1, x, x + w);
1400 int ctrly1tag = getTag(ctrly1, y, y + h);
1401 int ctrlx2tag = getTag(ctrlx2, x, x + w);
1402 int ctrly2tag = getTag(ctrly2, y, y + h);
1403
1404 // Trivially reject if all points are entirely to one side of
1405 // the rectangle.
1406 if (x1tag < INSIDE && x2tag < INSIDE && ctrlx1tag < INSIDE
1407 && ctrlx2tag < INSIDE) {
1408 return false; // All points left
1409 }
1410 if (y1tag < INSIDE && y2tag < INSIDE && ctrly1tag < INSIDE
1411 && ctrly2tag < INSIDE) {
1412 return false; // All points above
1413 }
1414 if (x1tag > INSIDE && x2tag > INSIDE && ctrlx1tag > INSIDE
1415 && ctrlx2tag > INSIDE) {
1416 return false; // All points right
1417 }
1418 if (y1tag > INSIDE && y2tag > INSIDE && ctrly1tag > INSIDE
1419 && ctrly2tag > INSIDE) {
1420 return false; // All points below
1421 }
1422
1423 // Test for endpoints on the edge where either the segment
1424 // or the curve is headed "inwards" from them
1425 // Note: These tests are a superset of the fast endpoint tests
1426 // above and thus repeat those tests, but take more time
1427 // and cover more cases
1428 if (inwards(x1tag, x2tag, ctrlx1tag)
1429 && inwards(y1tag, y2tag, ctrly1tag)) {
1430 // First endpoint on border with either edge moving inside
1431 return true;
1432 }
1433 if (inwards(x2tag, x1tag, ctrlx2tag)
1434 && inwards(y2tag, y1tag, ctrly2tag)) {
1435 // Second endpoint on border with either edge moving inside
1436 return true;
1437 }
1438
1439 // Trivially accept if endpoints span directly across the rectangle
1440 boolean xoverlap = (x1tag * x2tag <= 0);
1441 boolean yoverlap = (y1tag * y2tag <= 0);
1442 if (x1tag == INSIDE && x2tag == INSIDE && yoverlap) {
1443 return true;
1444 }
1445 if (y1tag == INSIDE && y2tag == INSIDE && xoverlap) {
1446 return true;
1447 }
1448
1449 // We now know that both endpoints are outside the rectangle
1450 // but the 4 points are not all on one side of the rectangle.
1451 // Therefore the curve cannot be contained inside the rectangle,
1452 // but the rectangle might be contained inside the curve, or
1453 // the curve might intersect the boundary of the rectangle.
1454
1455 double[] eqn = new double[4];
1456 double[] res = new double[4];
1457 if (!yoverlap) {
1458 // Both y coordinates for the closing segment are above or
1459 // below the rectangle which means that we can only intersect
1460 // if the curve crosses the top (or bottom) of the rectangle
1461 // in more than one place and if those crossing locations
1462 // span the horizontal range of the rectangle.
1463 fillEqn(eqn, (y1tag < INSIDE ? y : y + h), y1, ctrly1,
1464 ctrly2, y2);
1465 int num = solveCubic(eqn, res);
1466 num = evalCubic(res, num, true, true, null, x1, ctrlx1,
1467 ctrlx2, x2);
1468 // odd counts imply the crossing was out of [0,1] bounds
1469 // otherwise there is no way for that part of the curve to
1470 // "return" to meet its endpoint
1471 return (num == 2 && getTag(res[0], x, x + w)
1472 * getTag(res[1], x, x + w) <= 0);
1473 }
1474
1475 // Y ranges overlap. Now we examine the X ranges
1476 if (!xoverlap) {
1477 // Both x coordinates for the closing segment are left of
1478 // or right of the rectangle which means that we can only
1479 // intersect if the curve crosses the left (or right) edge
1480 // of the rectangle in more than one place and if those
1481 // crossing locations span the vertical range of the rectangle.
1482 fillEqn(eqn, (x1tag < INSIDE ? x : x + w), x1, ctrlx1,
1483 ctrlx2, x2);
1484 int num = solveCubic(eqn, res);
1485 num = evalCubic(res, num, true, true, null, y1, ctrly1,
1486 ctrly2, y2);
1487 // odd counts imply the crossing was out of [0,1] bounds
1488 // otherwise there is no way for that part of the curve to
1489 // "return" to meet its endpoint
1490 return (num == 2 && getTag(res[0], y, y + h)
1491 * getTag(res[1], y, y + h) <= 0);
1492 }
1493
1494 // The X and Y ranges of the endpoints overlap the X and Y
1495 // ranges of the rectangle, now find out how the endpoint
1496 // line segment intersects the Y range of the rectangle
1497 double dx = x2 - x1;
1498 double dy = y2 - y1;
1499 double k = y2 * x1 - x2 * y1;
1500 int c1tag, c2tag;
1501 if (y1tag == INSIDE) {
1502 c1tag = x1tag;
1503 } else {
1504 c1tag = getTag(
1505 (k + dx * (y1tag < INSIDE ? y : y + h)) / dy, x, x
1506 + w);
1507 }
1508 if (y2tag == INSIDE) {
1509 c2tag = x2tag;
1510 } else {
1511 c2tag = getTag(
1512 (k + dx * (y2tag < INSIDE ? y : y + h)) / dy, x, x
1513 + w);
1514 }
1515 // If the part of the line segment that intersects the Y range
1516 // of the rectangle crosses it horizontally - trivially accept
1517 if (c1tag * c2tag <= 0) {
1518 return true;
1519 }
1520
1521 // Now we know that both the X and Y ranges intersect and that
1522 // the endpoint line segment does not directly cross the rectangle.
1523 //
1524 // We can almost treat this case like one of the cases above
1525 // where both endpoints are to one side, except that we may
1526 // get one or three intersections of the curve with the vertical
1527 // side of the rectangle. This is because the endpoint segment
1528 // accounts for the other intersection in an even pairing. Thus,
1529 // with the endpoint crossing we end up with 2 or 4 total crossings.
1530 //
1531 // (Remember there is overlap in both the X and Y ranges which
1532 // means that the segment itself must cross at least one vertical
1533 // edge of the rectangle - in particular, the "near vertical side"
1534 // - leaving an odd number of intersections for the curve.)
1535 //
1536 // Now we calculate the y tags of all the intersections on the
1537 // "near vertical side" of the rectangle. We will have one with
1538 // the endpoint segment, and one or three with the curve. If
1539 // any pair of those vertical intersections overlap the Y range
1540 // of the rectangle, we have an intersection. Otherwise, we don't.
1541
1542 // c1tag = vertical intersection class of the endpoint segment
1543 //
1544 // Choose the y tag of the endpoint that was not on the same
1545 // side of the rectangle as the subsegment calculated above.
1546 // Note that we can "steal" the existing Y tag of that endpoint
1547 // since it will be provably the same as the vertical intersection.
1548 c1tag = ((c1tag * x1tag <= 0) ? y1tag : y2tag);
1549
1550 // Now we have to calculate an array of solutions of the curve
1551 // with the "near vertical side" of the rectangle. Then we
1552 // need to sort the tags and do a pairwise range test to see
1553 // if either of the pairs of crossings spans the Y range of
1554 // the rectangle.
1555 //
1556 // Note that the c2tag can still tell us which vertical edge
1557 // to test against.
1558 fillEqn(eqn, (c2tag < INSIDE ? x : x + w), x1, ctrlx1, ctrlx2,
1559 x2);
1560 int num = solveCubic(eqn, res);
1561 num = evalCubic(res, num, true, true, null, y1, ctrly1, ctrly2,
1562 y2);
1563
1564 // Now put all of the tags into a bucket and sort them. There
1565 // is an intersection iff one of the pairs of tags "spans" the
1566 // Y range of the rectangle.
1567 int tags[] = new int[num + 1];
1568 for (int i = 0; i < num; i++) {
1569 tags[i] = getTag(res[i], y, y + h);
1570 }
1571 tags[num] = c1tag;
1572 Arrays.sort(tags);
1573 return ((num >= 1 && tags[0] * tags[1] <= 0) || (num >= 3 && tags[2]
1574 * tags[3] <= 0));
1575 }
1576
1577 /**
1578 * {@inheritDoc}
1579 * @since 1.2
1580 */
1581 public boolean intersects(Rectangle2D r) {
1582 return intersects(r.getX(), r.getY(), r.getWidth(), r
1583 .getHeight());
1584 }
1585
1586 /**
1587 * {@inheritDoc}
1588 * @since 1.2
1589 */
1590 public boolean contains(double x, double y, double w, double h) {
1591 if (w <= 0 || h <= 0) {
1592 return false;
1593 }
1594 // Assertion: Cubic curves closed by connecting their
1595 // endpoints form either one or two convex halves with
1596 // the closing line segment as an edge of both sides.
1597 if (!(contains(x, y) && contains(x + w, y)
1598 && contains(x + w, y + h) && contains(x, y + h))) {
1599 return false;
1600 }
1601 // Either the rectangle is entirely inside one of the convex
1602 // halves or it crosses from one to the other, in which case
1603 // it must intersect the closing line segment.
1604 Rectangle2D rect = new Rectangle2D.Double(x, y, w, h);
1605 return !rect.intersectsLine(getX1(), getY1(), getX2(), getY2());
1606 }
1607
1608 /**
1609 * {@inheritDoc}
1610 * @since 1.2
1611 */
1612 public boolean contains(Rectangle2D r) {
1613 return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
1614 }
1615
1616 /**
1617 * {@inheritDoc}
1618 * @since 1.2
1619 */
1620 public Rectangle getBounds() {
1621 return getBounds2D().getBounds();
1622 }
1623
1624 /**
1625 * Returns an iteration object that defines the boundary of the
1626 * shape.
1627 * The iterator for this class is not multi-threaded safe,
1628 * which means that this <code>CubicCurve2D</code> class does not
1629 * guarantee that modifications to the geometry of this
1630 * <code>CubicCurve2D</code> object do not affect any iterations of
1631 * that geometry that are already in process.
1632 * @param at an optional <code>AffineTransform</code> to be applied to the
1633 * coordinates as they are returned in the iteration, or <code>null</code>
1634 * if untransformed coordinates are desired
1635 * @return the <code>PathIterator</code> object that returns the
1636 * geometry of the outline of this <code>CubicCurve2D</code>, one
1637 * segment at a time.
1638 * @since 1.2
1639 */
1640 public PathIterator getPathIterator(AffineTransform at) {
1641 return new CubicIterator(this , at);
1642 }
1643
1644 /**
1645 * Return an iteration object that defines the boundary of the
1646 * flattened shape.
1647 * The iterator for this class is not multi-threaded safe,
1648 * which means that this <code>CubicCurve2D</code> class does not
1649 * guarantee that modifications to the geometry of this
1650 * <code>CubicCurve2D</code> object do not affect any iterations of
1651 * that geometry that are already in process.
1652 * @param at an optional <code>AffineTransform</code> to be applied to the
1653 * coordinates as they are returned in the iteration, or <code>null</code>
1654 * if untransformed coordinates are desired
1655 * @param flatness the maximum amount that the control points
1656 * for a given curve can vary from colinear before a subdivided
1657 * curve is replaced by a straight line connecting the end points
1658 * @return the <code>PathIterator</code> object that returns the
1659 * geometry of the outline of this <code>CubicCurve2D</code>,
1660 * one segment at a time.
1661 * @since 1.2
1662 */
1663 public PathIterator getPathIterator(AffineTransform at,
1664 double flatness) {
1665 return new FlatteningPathIterator(getPathIterator(at), flatness);
1666 }
1667
1668 /**
1669 * Creates a new object of the same class as this object.
1670 *
1671 * @return a clone of this instance.
1672 * @exception OutOfMemoryError if there is not enough memory.
1673 * @see java.lang.Cloneable
1674 * @since 1.2
1675 */
1676 public Object clone() {
1677 try {
1678 return super .clone();
1679 } catch (CloneNotSupportedException e) {
1680 // this shouldn't happen, since we are Cloneable
1681 throw new InternalError();
1682 }
1683 }
1684 }
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