001 /* CubicCurve2D.java -- represents a parameterized cubic curve in 2-D space
002 Copyright (C) 2002, 2003, 2004 Free Software Foundation
003
004 This file is part of GNU Classpath.
005
006 GNU Classpath is free software; you can redistribute it and/or modify
007 it under the terms of the GNU General Public License as published by
008 the Free Software Foundation; either version 2, or (at your option)
009 any later version.
010
011 GNU Classpath is distributed in the hope that it will be useful, but
012 WITHOUT ANY WARRANTY; without even the implied warranty of
013 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
014 General Public License for more details.
015
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017 along with GNU Classpath; see the file COPYING. If not, write to the
018 Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
019 02110-1301 USA.
020
021 Linking this library statically or dynamically with other modules is
022 making a combined work based on this library. Thus, the terms and
023 conditions of the GNU General Public License cover the whole
024 combination.
025
026 As a special exception, the copyright holders of this library give you
027 permission to link this library with independent modules to produce an
028 executable, regardless of the license terms of these independent
029 modules, and to copy and distribute the resulting executable under
030 terms of your choice, provided that you also meet, for each linked
031 independent module, the terms and conditions of the license of that
032 module. An independent module is a module which is not derived from
033 or based on this library. If you modify this library, you may extend
034 this exception to your version of the library, but you are not
035 obligated to do so. If you do not wish to do so, delete this
036 exception statement from your version. */
037
038 package java.awt.geom;
039
040 import java.awt.Rectangle;
041 import java.awt.Shape;
042 import java.util.NoSuchElementException;
043
044
045 /**
046 * A two-dimensional curve that is parameterized with a cubic
047 * function.
048 *
049 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
050 * alt="A drawing of a CubicCurve2D" />
051 *
052 * @author Eric Blake (ebb9@email.byu.edu)
053 * @author Graydon Hoare (graydon@redhat.com)
054 * @author Sascha Brawer (brawer@dandelis.ch)
055 * @author Sven de Marothy (sven@physto.se)
056 *
057 * @since 1.2
058 */
059 public abstract class CubicCurve2D implements Shape, Cloneable
060 {
061 private static final double BIG_VALUE = java.lang.Double.MAX_VALUE / 10.0;
062 private static final double EPSILON = 1E-10;
063
064 /**
065 * Constructs a new CubicCurve2D. Typical users will want to
066 * construct instances of a subclass, such as {@link
067 * CubicCurve2D.Float} or {@link CubicCurve2D.Double}.
068 */
069 protected CubicCurve2D()
070 {
071 }
072
073 /**
074 * Returns the <i>x</i> coordinate of the curve’s start
075 * point.
076 */
077 public abstract double getX1();
078
079 /**
080 * Returns the <i>y</i> coordinate of the curve’s start
081 * point.
082 */
083 public abstract double getY1();
084
085 /**
086 * Returns the curve’s start point.
087 */
088 public abstract Point2D getP1();
089
090 /**
091 * Returns the <i>x</i> coordinate of the curve’s first
092 * control point.
093 */
094 public abstract double getCtrlX1();
095
096 /**
097 * Returns the <i>y</i> coordinate of the curve’s first
098 * control point.
099 */
100 public abstract double getCtrlY1();
101
102 /**
103 * Returns the curve’s first control point.
104 */
105 public abstract Point2D getCtrlP1();
106
107 /**
108 * Returns the <i>x</i> coordinate of the curve’s second
109 * control point.
110 */
111 public abstract double getCtrlX2();
112
113 /**
114 * Returns the <i>y</i> coordinate of the curve’s second
115 * control point.
116 */
117 public abstract double getCtrlY2();
118
119 /**
120 * Returns the curve’s second control point.
121 */
122 public abstract Point2D getCtrlP2();
123
124 /**
125 * Returns the <i>x</i> coordinate of the curve’s end
126 * point.
127 */
128 public abstract double getX2();
129
130 /**
131 * Returns the <i>y</i> coordinate of the curve’s end
132 * point.
133 */
134 public abstract double getY2();
135
136 /**
137 * Returns the curve’s end point.
138 */
139 public abstract Point2D getP2();
140
141 /**
142 * Changes the curve geometry, separately specifying each coordinate
143 * value.
144 *
145 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
146 * alt="A drawing of a CubicCurve2D" />
147 *
148 * @param x1 the <i>x</i> coordinate of the curve’s new start
149 * point.
150 *
151 * @param y1 the <i>y</i> coordinate of the curve’s new start
152 * point.
153 *
154 * @param cx1 the <i>x</i> coordinate of the curve’s new
155 * first control point.
156 *
157 * @param cy1 the <i>y</i> coordinate of the curve’s new
158 * first control point.
159 *
160 * @param cx2 the <i>x</i> coordinate of the curve’s new
161 * second control point.
162 *
163 * @param cy2 the <i>y</i> coordinate of the curve’s new
164 * second control point.
165 *
166 * @param x2 the <i>x</i> coordinate of the curve’s new end
167 * point.
168 *
169 * @param y2 the <i>y</i> coordinate of the curve’s new end
170 * point.
171 */
172 public abstract void setCurve(double x1, double y1, double cx1, double cy1,
173 double cx2, double cy2, double x2, double y2);
174
175 /**
176 * Changes the curve geometry, specifying coordinate values in an
177 * array.
178 *
179 * @param coords an array containing the new coordinate values. The
180 * <i>x</i> coordinate of the new start point is located at
181 * <code>coords[offset]</code>, its <i>y</i> coordinate at
182 * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
183 * new first control point is located at <code>coords[offset +
184 * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
185 * 3]</code>. The <i>x</i> coordinate of the new second control
186 * point is located at <code>coords[offset + 4]</code>, its <i>y</i>
187 * coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
188 * coordinate of the new end point is located at <code>coords[offset
189 * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
190 * 7]</code>.
191 *
192 * @param offset the offset of the first coordinate value in
193 * <code>coords</code>.
194 */
195 public void setCurve(double[] coords, int offset)
196 {
197 setCurve(coords[offset++], coords[offset++], coords[offset++],
198 coords[offset++], coords[offset++], coords[offset++],
199 coords[offset++], coords[offset++]);
200 }
201
202 /**
203 * Changes the curve geometry, specifying coordinate values in
204 * separate Point objects.
205 *
206 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
207 * alt="A drawing of a CubicCurve2D" />
208 *
209 * <p>The curve does not keep any reference to the passed point
210 * objects. Therefore, a later change to <code>p1</code>,
211 * <code>c1</code>, <code>c2</code> or <code>p2</code> will not
212 * affect the curve geometry.
213 *
214 * @param p1 the new start point.
215 * @param c1 the new first control point.
216 * @param c2 the new second control point.
217 * @param p2 the new end point.
218 */
219 public void setCurve(Point2D p1, Point2D c1, Point2D c2, Point2D p2)
220 {
221 setCurve(p1.getX(), p1.getY(), c1.getX(), c1.getY(), c2.getX(), c2.getY(),
222 p2.getX(), p2.getY());
223 }
224
225 /**
226 * Changes the curve geometry, specifying coordinate values in an
227 * array of Point objects.
228 *
229 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
230 * alt="A drawing of a CubicCurve2D" />
231 *
232 * <p>The curve does not keep references to the passed point
233 * objects. Therefore, a later change to the <code>pts</code> array
234 * or any of its elements will not affect the curve geometry.
235 *
236 * @param pts an array containing the points. The new start point
237 * is located at <code>pts[offset]</code>, the new first control
238 * point at <code>pts[offset + 1]</code>, the new second control
239 * point at <code>pts[offset + 2]</code>, and the new end point
240 * at <code>pts[offset + 3]</code>.
241 *
242 * @param offset the offset of the start point in <code>pts</code>.
243 */
244 public void setCurve(Point2D[] pts, int offset)
245 {
246 setCurve(pts[offset].getX(), pts[offset++].getY(), pts[offset].getX(),
247 pts[offset++].getY(), pts[offset].getX(), pts[offset++].getY(),
248 pts[offset].getX(), pts[offset++].getY());
249 }
250
251 /**
252 * Changes the curve geometry to that of another curve.
253 *
254 * @param c the curve whose coordinates will be copied.
255 */
256 public void setCurve(CubicCurve2D c)
257 {
258 setCurve(c.getX1(), c.getY1(), c.getCtrlX1(), c.getCtrlY1(),
259 c.getCtrlX2(), c.getCtrlY2(), c.getX2(), c.getY2());
260 }
261
262 /**
263 * Calculates the squared flatness of a cubic curve, directly
264 * specifying each coordinate value. The flatness is the maximal
265 * distance of a control point to the line between start and end
266 * point.
267 *
268 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
269 * alt="A drawing that illustrates the flatness" />
270 *
271 * <p>In the above drawing, the straight line connecting start point
272 * P1 and end point P2 is depicted in gray. In comparison to C1,
273 * control point C2 is father away from the gray line. Therefore,
274 * the result will be the square of the distance between C2 and the
275 * gray line, i.e. the squared length of the red line.
276 *
277 * @param x1 the <i>x</i> coordinate of the start point P1.
278 * @param y1 the <i>y</i> coordinate of the start point P1.
279 * @param cx1 the <i>x</i> coordinate of the first control point C1.
280 * @param cy1 the <i>y</i> coordinate of the first control point C1.
281 * @param cx2 the <i>x</i> coordinate of the second control point C2.
282 * @param cy2 the <i>y</i> coordinate of the second control point C2.
283 * @param x2 the <i>x</i> coordinate of the end point P2.
284 * @param y2 the <i>y</i> coordinate of the end point P2.
285 */
286 public static double getFlatnessSq(double x1, double y1, double cx1,
287 double cy1, double cx2, double cy2,
288 double x2, double y2)
289 {
290 return Math.max(Line2D.ptSegDistSq(x1, y1, x2, y2, cx1, cy1),
291 Line2D.ptSegDistSq(x1, y1, x2, y2, cx2, cy2));
292 }
293
294 /**
295 * Calculates the flatness of a cubic curve, directly specifying
296 * each coordinate value. The flatness is the maximal distance of a
297 * control point to the line between start and end point.
298 *
299 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
300 * alt="A drawing that illustrates the flatness" />
301 *
302 * <p>In the above drawing, the straight line connecting start point
303 * P1 and end point P2 is depicted in gray. In comparison to C1,
304 * control point C2 is father away from the gray line. Therefore,
305 * the result will be the distance between C2 and the gray line,
306 * i.e. the length of the red line.
307 *
308 * @param x1 the <i>x</i> coordinate of the start point P1.
309 * @param y1 the <i>y</i> coordinate of the start point P1.
310 * @param cx1 the <i>x</i> coordinate of the first control point C1.
311 * @param cy1 the <i>y</i> coordinate of the first control point C1.
312 * @param cx2 the <i>x</i> coordinate of the second control point C2.
313 * @param cy2 the <i>y</i> coordinate of the second control point C2.
314 * @param x2 the <i>x</i> coordinate of the end point P2.
315 * @param y2 the <i>y</i> coordinate of the end point P2.
316 */
317 public static double getFlatness(double x1, double y1, double cx1,
318 double cy1, double cx2, double cy2,
319 double x2, double y2)
320 {
321 return Math.sqrt(getFlatnessSq(x1, y1, cx1, cy1, cx2, cy2, x2, y2));
322 }
323
324 /**
325 * Calculates the squared flatness of a cubic curve, specifying the
326 * coordinate values in an array. The flatness is the maximal
327 * distance of a control point to the line between start and end
328 * point.
329 *
330 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
331 * alt="A drawing that illustrates the flatness" />
332 *
333 * <p>In the above drawing, the straight line connecting start point
334 * P1 and end point P2 is depicted in gray. In comparison to C1,
335 * control point C2 is father away from the gray line. Therefore,
336 * the result will be the square of the distance between C2 and the
337 * gray line, i.e. the squared length of the red line.
338 *
339 * @param coords an array containing the coordinate values. The
340 * <i>x</i> coordinate of the start point P1 is located at
341 * <code>coords[offset]</code>, its <i>y</i> coordinate at
342 * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
343 * first control point C1 is located at <code>coords[offset +
344 * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
345 * 3]</code>. The <i>x</i> coordinate of the second control point C2
346 * is located at <code>coords[offset + 4]</code>, its <i>y</i>
347 * coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
348 * coordinate of the end point P2 is located at <code>coords[offset
349 * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
350 * 7]</code>.
351 *
352 * @param offset the offset of the first coordinate value in
353 * <code>coords</code>.
354 */
355 public static double getFlatnessSq(double[] coords, int offset)
356 {
357 return getFlatnessSq(coords[offset++], coords[offset++], coords[offset++],
358 coords[offset++], coords[offset++], coords[offset++],
359 coords[offset++], coords[offset++]);
360 }
361
362 /**
363 * Calculates the flatness of a cubic curve, specifying the
364 * coordinate values in an array. The flatness is the maximal
365 * distance of a control point to the line between start and end
366 * point.
367 *
368 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
369 * alt="A drawing that illustrates the flatness" />
370 *
371 * <p>In the above drawing, the straight line connecting start point
372 * P1 and end point P2 is depicted in gray. In comparison to C1,
373 * control point C2 is father away from the gray line. Therefore,
374 * the result will be the distance between C2 and the gray line,
375 * i.e. the length of the red line.
376 *
377 * @param coords an array containing the coordinate values. The
378 * <i>x</i> coordinate of the start point P1 is located at
379 * <code>coords[offset]</code>, its <i>y</i> coordinate at
380 * <code>coords[offset + 1]</code>. The <i>x</i> coordinate of the
381 * first control point C1 is located at <code>coords[offset +
382 * 2]</code>, its <i>y</i> coordinate at <code>coords[offset +
383 * 3]</code>. The <i>x</i> coordinate of the second control point C2
384 * is located at <code>coords[offset + 4]</code>, its <i>y</i>
385 * coordinate at <code>coords[offset + 5]</code>. The <i>x</i>
386 * coordinate of the end point P2 is located at <code>coords[offset
387 * + 6]</code>, its <i>y</i> coordinate at <code>coords[offset +
388 * 7]</code>.
389 *
390 * @param offset the offset of the first coordinate value in
391 * <code>coords</code>.
392 */
393 public static double getFlatness(double[] coords, int offset)
394 {
395 return Math.sqrt(getFlatnessSq(coords[offset++], coords[offset++],
396 coords[offset++], coords[offset++],
397 coords[offset++], coords[offset++],
398 coords[offset++], coords[offset++]));
399 }
400
401 /**
402 * Calculates the squared flatness of this curve. The flatness is
403 * the maximal distance of a control point to the line between start
404 * and end point.
405 *
406 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
407 * alt="A drawing that illustrates the flatness" />
408 *
409 * <p>In the above drawing, the straight line connecting start point
410 * P1 and end point P2 is depicted in gray. In comparison to C1,
411 * control point C2 is father away from the gray line. Therefore,
412 * the result will be the square of the distance between C2 and the
413 * gray line, i.e. the squared length of the red line.
414 */
415 public double getFlatnessSq()
416 {
417 return getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
418 getCtrlX2(), getCtrlY2(), getX2(), getY2());
419 }
420
421 /**
422 * Calculates the flatness of this curve. The flatness is the
423 * maximal distance of a control point to the line between start and
424 * end point.
425 *
426 * <p><img src="doc-files/CubicCurve2D-4.png" width="350" height="180"
427 * alt="A drawing that illustrates the flatness" />
428 *
429 * <p>In the above drawing, the straight line connecting start point
430 * P1 and end point P2 is depicted in gray. In comparison to C1,
431 * control point C2 is father away from the gray line. Therefore,
432 * the result will be the distance between C2 and the gray line,
433 * i.e. the length of the red line.
434 */
435 public double getFlatness()
436 {
437 return Math.sqrt(getFlatnessSq(getX1(), getY1(), getCtrlX1(), getCtrlY1(),
438 getCtrlX2(), getCtrlY2(), getX2(), getY2()));
439 }
440
441 /**
442 * Subdivides this curve into two halves.
443 *
444 * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
445 * height="180" alt="A drawing that illustrates the effects of
446 * subdividing a CubicCurve2D" />
447 *
448 * @param left a curve whose geometry will be set to the left half
449 * of this curve, or <code>null</code> if the caller is not
450 * interested in the left half.
451 *
452 * @param right a curve whose geometry will be set to the right half
453 * of this curve, or <code>null</code> if the caller is not
454 * interested in the right half.
455 */
456 public void subdivide(CubicCurve2D left, CubicCurve2D right)
457 {
458 // Use empty slots at end to share single array.
459 double[] d = new double[]
460 {
461 getX1(), getY1(), getCtrlX1(), getCtrlY1(), getCtrlX2(),
462 getCtrlY2(), getX2(), getY2(), 0, 0, 0, 0, 0, 0
463 };
464 subdivide(d, 0, d, 0, d, 6);
465 if (left != null)
466 left.setCurve(d, 0);
467 if (right != null)
468 right.setCurve(d, 6);
469 }
470
471 /**
472 * Subdivides a cubic curve into two halves.
473 *
474 * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
475 * height="180" alt="A drawing that illustrates the effects of
476 * subdividing a CubicCurve2D" />
477 *
478 * @param src the curve to be subdivided.
479 *
480 * @param left a curve whose geometry will be set to the left half
481 * of <code>src</code>, or <code>null</code> if the caller is not
482 * interested in the left half.
483 *
484 * @param right a curve whose geometry will be set to the right half
485 * of <code>src</code>, or <code>null</code> if the caller is not
486 * interested in the right half.
487 */
488 public static void subdivide(CubicCurve2D src, CubicCurve2D left,
489 CubicCurve2D right)
490 {
491 src.subdivide(left, right);
492 }
493
494 /**
495 * Subdivides a cubic curve into two halves, passing all coordinates
496 * in an array.
497 *
498 * <p><img src="doc-files/CubicCurve2D-3.png" width="700"
499 * height="180" alt="A drawing that illustrates the effects of
500 * subdividing a CubicCurve2D" />
501 *
502 * <p>The left end point and the right start point will always be
503 * identical. Memory-concious programmers thus may want to pass the
504 * same array for both <code>left</code> and <code>right</code>, and
505 * set <code>rightOff</code> to <code>leftOff + 6</code>.
506 *
507 * @param src an array containing the coordinates of the curve to be
508 * subdivided. The <i>x</i> coordinate of the start point P1 is
509 * located at <code>src[srcOff]</code>, its <i>y</i> at
510 * <code>src[srcOff + 1]</code>. The <i>x</i> coordinate of the
511 * first control point C1 is located at <code>src[srcOff +
512 * 2]</code>, its <i>y</i> at <code>src[srcOff + 3]</code>. The
513 * <i>x</i> coordinate of the second control point C2 is located at
514 * <code>src[srcOff + 4]</code>, its <i>y</i> at <code>src[srcOff +
515 * 5]</code>. The <i>x</i> coordinate of the end point is located at
516 * <code>src[srcOff + 6]</code>, its <i>y</i> at <code>src[srcOff +
517 * 7]</code>.
518 *
519 * @param srcOff an offset into <code>src</code>, specifying
520 * the index of the start point’s <i>x</i> coordinate.
521 *
522 * @param left an array that will receive the coordinates of the
523 * left half of <code>src</code>. It is acceptable to pass
524 * <code>src</code>. A caller who is not interested in the left half
525 * can pass <code>null</code>.
526 *
527 * @param leftOff an offset into <code>left</code>, specifying the
528 * index where the start point’s <i>x</i> coordinate will be
529 * stored.
530 *
531 * @param right an array that will receive the coordinates of the
532 * right half of <code>src</code>. It is acceptable to pass
533 * <code>src</code> or <code>left</code>. A caller who is not
534 * interested in the right half can pass <code>null</code>.
535 *
536 * @param rightOff an offset into <code>right</code>, specifying the
537 * index where the start point’s <i>x</i> coordinate will be
538 * stored.
539 */
540 public static void subdivide(double[] src, int srcOff, double[] left,
541 int leftOff, double[] right, int rightOff)
542 {
543 // To understand this code, please have a look at the image
544 // "CubicCurve2D-3.png" in the sub-directory "doc-files".
545 double src_C1_x;
546 double src_C1_y;
547 double src_C2_x;
548 double src_C2_y;
549 double left_P1_x;
550 double left_P1_y;
551 double left_C1_x;
552 double left_C1_y;
553 double left_C2_x;
554 double left_C2_y;
555 double right_C1_x;
556 double right_C1_y;
557 double right_C2_x;
558 double right_C2_y;
559 double right_P2_x;
560 double right_P2_y;
561 double Mid_x; // Mid = left.P2 = right.P1
562 double Mid_y; // Mid = left.P2 = right.P1
563
564 left_P1_x = src[srcOff];
565 left_P1_y = src[srcOff + 1];
566 src_C1_x = src[srcOff + 2];
567 src_C1_y = src[srcOff + 3];
568 src_C2_x = src[srcOff + 4];
569 src_C2_y = src[srcOff + 5];
570 right_P2_x = src[srcOff + 6];
571 right_P2_y = src[srcOff + 7];
572
573 left_C1_x = (left_P1_x + src_C1_x) / 2;
574 left_C1_y = (left_P1_y + src_C1_y) / 2;
575 right_C2_x = (right_P2_x + src_C2_x) / 2;
576 right_C2_y = (right_P2_y + src_C2_y) / 2;
577 Mid_x = (src_C1_x + src_C2_x) / 2;
578 Mid_y = (src_C1_y + src_C2_y) / 2;
579 left_C2_x = (left_C1_x + Mid_x) / 2;
580 left_C2_y = (left_C1_y + Mid_y) / 2;
581 right_C1_x = (Mid_x + right_C2_x) / 2;
582 right_C1_y = (Mid_y + right_C2_y) / 2;
583 Mid_x = (left_C2_x + right_C1_x) / 2;
584 Mid_y = (left_C2_y + right_C1_y) / 2;
585
586 if (left != null)
587 {
588 left[leftOff] = left_P1_x;
589 left[leftOff + 1] = left_P1_y;
590 left[leftOff + 2] = left_C1_x;
591 left[leftOff + 3] = left_C1_y;
592 left[leftOff + 4] = left_C2_x;
593 left[leftOff + 5] = left_C2_y;
594 left[leftOff + 6] = Mid_x;
595 left[leftOff + 7] = Mid_y;
596 }
597
598 if (right != null)
599 {
600 right[rightOff] = Mid_x;
601 right[rightOff + 1] = Mid_y;
602 right[rightOff + 2] = right_C1_x;
603 right[rightOff + 3] = right_C1_y;
604 right[rightOff + 4] = right_C2_x;
605 right[rightOff + 5] = right_C2_y;
606 right[rightOff + 6] = right_P2_x;
607 right[rightOff + 7] = right_P2_y;
608 }
609 }
610
611 /**
612 * Finds the non-complex roots of a cubic equation, placing the
613 * results into the same array as the equation coefficients. The
614 * following equation is being solved:
615 *
616 * <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup>
617 * + <code>eqn[2]</code> · <i>x</i><sup>2</sup>
618 * + <code>eqn[1]</code> · <i>x</i>
619 * + <code>eqn[0]</code>
620 * = 0
621 * </blockquote>
622 *
623 * <p>For some background about solving cubic equations, see the
624 * article <a
625 * href="http://planetmath.org/encyclopedia/CubicFormula.html"
626 * >“Cubic Formula”</a> in <a
627 * href="http://planetmath.org/" >PlanetMath</a>. For an extensive
628 * library of numerical algorithms written in the C programming
629 * language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
630 * Scientific Library</a>, from which this implementation was
631 * adapted.
632 *
633 * @param eqn an array with the coefficients of the equation. When
634 * this procedure has returned, <code>eqn</code> will contain the
635 * non-complex solutions of the equation, in no particular order.
636 *
637 * @return the number of non-complex solutions. A result of 0
638 * indicates that the equation has no non-complex solutions. A
639 * result of -1 indicates that the equation is constant (i.e.,
640 * always or never zero).
641 *
642 * @see #solveCubic(double[], double[])
643 * @see QuadCurve2D#solveQuadratic(double[],double[])
644 *
645 * @author Brian Gough (bjg@network-theory.com)
646 * (original C implementation in the <a href=
647 * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
648 *
649 * @author Sascha Brawer (brawer@dandelis.ch)
650 * (adaptation to Java)
651 */
652 public static int solveCubic(double[] eqn)
653 {
654 return solveCubic(eqn, eqn);
655 }
656
657 /**
658 * Finds the non-complex roots of a cubic equation. The following
659 * equation is being solved:
660 *
661 * <blockquote><code>eqn[3]</code> · <i>x</i><sup>3</sup>
662 * + <code>eqn[2]</code> · <i>x</i><sup>2</sup>
663 * + <code>eqn[1]</code> · <i>x</i>
664 * + <code>eqn[0]</code>
665 * = 0
666 * </blockquote>
667 *
668 * <p>For some background about solving cubic equations, see the
669 * article <a
670 * href="http://planetmath.org/encyclopedia/CubicFormula.html"
671 * >“Cubic Formula”</a> in <a
672 * href="http://planetmath.org/" >PlanetMath</a>. For an extensive
673 * library of numerical algorithms written in the C programming
674 * language, see the <a href= "http://www.gnu.org/software/gsl/">GNU
675 * Scientific Library</a>, from which this implementation was
676 * adapted.
677 *
678 * @see QuadCurve2D#solveQuadratic(double[],double[])
679 *
680 * @param eqn an array with the coefficients of the equation.
681 *
682 * @param res an array into which the non-complex roots will be
683 * stored. The results may be in an arbitrary order. It is safe to
684 * pass the same array object reference for both <code>eqn</code>
685 * and <code>res</code>.
686 *
687 * @return the number of non-complex solutions. A result of 0
688 * indicates that the equation has no non-complex solutions. A
689 * result of -1 indicates that the equation is constant (i.e.,
690 * always or never zero).
691 *
692 * @author Brian Gough (bjg@network-theory.com)
693 * (original C implementation in the <a href=
694 * "http://www.gnu.org/software/gsl/">GNU Scientific Library</a>)
695 *
696 * @author Sascha Brawer (brawer@dandelis.ch)
697 * (adaptation to Java)
698 */
699 public static int solveCubic(double[] eqn, double[] res)
700 {
701 // Adapted from poly/solve_cubic.c in the GNU Scientific Library
702 // (GSL), revision 1.7 of 2003-07-26. For the original source, see
703 // http://www.gnu.org/software/gsl/
704 //
705 // Brian Gough, the author of that code, has granted the
706 // permission to use it in GNU Classpath under the GNU Classpath
707 // license, and has assigned the copyright to the Free Software
708 // Foundation.
709 //
710 // The Java implementation is very similar to the GSL code, but
711 // not a strict one-to-one copy. For example, GSL would sort the
712 // result.
713
714 double a;
715 double b;
716 double c;
717 double q;
718 double r;
719 double Q;
720 double R;
721 double c3;
722 double Q3;
723 double R2;
724 double CR2;
725 double CQ3;
726
727 // If the cubic coefficient is zero, we have a quadratic equation.
728 c3 = eqn[3];
729 if (c3 == 0)
730 return QuadCurve2D.solveQuadratic(eqn, res);
731
732 // Divide the equation by the cubic coefficient.
733 c = eqn[0] / c3;
734 b = eqn[1] / c3;
735 a = eqn[2] / c3;
736
737 // We now need to solve x^3 + ax^2 + bx + c = 0.
738 q = a * a - 3 * b;
739 r = 2 * a * a * a - 9 * a * b + 27 * c;
740
741 Q = q / 9;
742 R = r / 54;
743
744 Q3 = Q * Q * Q;
745 R2 = R * R;
746
747 CR2 = 729 * r * r;
748 CQ3 = 2916 * q * q * q;
749
750 if (R == 0 && Q == 0)
751 {
752 // The GNU Scientific Library would return three identical
753 // solutions in this case.
754 res[0] = -a / 3;
755 return 1;
756 }
757
758 if (CR2 == CQ3)
759 {
760 /* this test is actually R2 == Q3, written in a form suitable
761 for exact computation with integers */
762 /* Due to finite precision some double roots may be missed, and
763 considered to be a pair of complex roots z = x +/- epsilon i
764 close to the real axis. */
765 double sqrtQ = Math.sqrt(Q);
766
767 if (R > 0)
768 {
769 res[0] = -2 * sqrtQ - a / 3;
770 res[1] = sqrtQ - a / 3;
771 }
772 else
773 {
774 res[0] = -sqrtQ - a / 3;
775 res[1] = 2 * sqrtQ - a / 3;
776 }
777 return 2;
778 }
779
780 if (CR2 < CQ3) /* equivalent to R2 < Q3 */
781 {
782 double sqrtQ = Math.sqrt(Q);
783 double sqrtQ3 = sqrtQ * sqrtQ * sqrtQ;
784 double theta = Math.acos(R / sqrtQ3);
785 double norm = -2 * sqrtQ;
786 res[0] = norm * Math.cos(theta / 3) - a / 3;
787 res[1] = norm * Math.cos((theta + 2.0 * Math.PI) / 3) - a / 3;
788 res[2] = norm * Math.cos((theta - 2.0 * Math.PI) / 3) - a / 3;
789
790 // The GNU Scientific Library sorts the results. We don't.
791 return 3;
792 }
793
794 double sgnR = (R >= 0 ? 1 : -1);
795 double A = -sgnR * Math.pow(Math.abs(R) + Math.sqrt(R2 - Q3), 1.0 / 3.0);
796 double B = Q / A;
797 res[0] = A + B - a / 3;
798 return 1;
799 }
800
801 /**
802 * Determines whether a position lies inside the area bounded
803 * by the curve and the straight line connecting its end points.
804 *
805 * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
806 * alt="A drawing of the area spanned by the curve" />
807 *
808 * <p>The above drawing illustrates in which area points are
809 * considered “inside” a CubicCurve2D.
810 */
811 public boolean contains(double x, double y)
812 {
813 if (! getBounds2D().contains(x, y))
814 return false;
815
816 return ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0);
817 }
818
819 /**
820 * Determines whether a point lies inside the area bounded
821 * by the curve and the straight line connecting its end points.
822 *
823 * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
824 * alt="A drawing of the area spanned by the curve" />
825 *
826 * <p>The above drawing illustrates in which area points are
827 * considered “inside” a CubicCurve2D.
828 */
829 public boolean contains(Point2D p)
830 {
831 return contains(p.getX(), p.getY());
832 }
833
834 /**
835 * Determines whether any part of a rectangle is inside the area bounded
836 * by the curve and the straight line connecting its end points.
837 *
838 * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
839 * alt="A drawing of the area spanned by the curve" />
840 *
841 * <p>The above drawing illustrates in which area points are
842 * considered “inside” in a CubicCurve2D.
843 * @see #contains(double, double)
844 */
845 public boolean intersects(double x, double y, double w, double h)
846 {
847 if (! getBounds2D().contains(x, y, w, h))
848 return false;
849
850 /* Does any edge intersect? */
851 if (getAxisIntersections(x, y, true, w) != 0 /* top */
852 || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
853 || getAxisIntersections(x + w, y, false, h) != 0 /* right */
854 || getAxisIntersections(x, y, false, h) != 0) /* left */
855 return true;
856
857 /* No intersections, is any point inside? */
858 if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
859 return true;
860
861 return false;
862 }
863
864 /**
865 * Determines whether any part of a Rectangle2D is inside the area bounded
866 * by the curve and the straight line connecting its end points.
867 * @see #intersects(double, double, double, double)
868 */
869 public boolean intersects(Rectangle2D r)
870 {
871 return intersects(r.getX(), r.getY(), r.getWidth(), r.getHeight());
872 }
873
874 /**
875 * Determine whether a rectangle is entirely inside the area that is bounded
876 * by the curve and the straight line connecting its end points.
877 *
878 * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
879 * alt="A drawing of the area spanned by the curve" />
880 *
881 * <p>The above drawing illustrates in which area points are
882 * considered “inside” a CubicCurve2D.
883 * @see #contains(double, double)
884 */
885 public boolean contains(double x, double y, double w, double h)
886 {
887 if (! getBounds2D().intersects(x, y, w, h))
888 return false;
889
890 /* Does any edge intersect? */
891 if (getAxisIntersections(x, y, true, w) != 0 /* top */
892 || getAxisIntersections(x, y + h, true, w) != 0 /* bottom */
893 || getAxisIntersections(x + w, y, false, h) != 0 /* right */
894 || getAxisIntersections(x, y, false, h) != 0) /* left */
895 return false;
896
897 /* No intersections, is any point inside? */
898 if ((getAxisIntersections(x, y, true, BIG_VALUE) & 1) != 0)
899 return true;
900
901 return false;
902 }
903
904 /**
905 * Determine whether a Rectangle2D is entirely inside the area that is
906 * bounded by the curve and the straight line connecting its end points.
907 *
908 * <p><img src="doc-files/CubicCurve2D-5.png" width="350" height="180"
909 * alt="A drawing of the area spanned by the curve" />
910 *
911 * <p>The above drawing illustrates in which area points are
912 * considered “inside” a CubicCurve2D.
913 * @see #contains(double, double)
914 */
915 public boolean contains(Rectangle2D r)
916 {
917 return contains(r.getX(), r.getY(), r.getWidth(), r.getHeight());
918 }
919
920 /**
921 * Determines the smallest rectangle that encloses the
922 * curve’s start, end and control points.
923 */
924 public Rectangle getBounds()
925 {
926 return getBounds2D().getBounds();
927 }
928
929 public PathIterator getPathIterator(final AffineTransform at)
930 {
931 return new PathIterator()
932 {
933 /** Current coordinate. */
934 private int current = 0;
935
936 public int getWindingRule()
937 {
938 return WIND_NON_ZERO;
939 }
940
941 public boolean isDone()
942 {
943 return current >= 2;
944 }
945
946 public void next()
947 {
948 current++;
949 }
950
951 public int currentSegment(float[] coords)
952 {
953 int result;
954 switch (current)
955 {
956 case 0:
957 coords[0] = (float) getX1();
958 coords[1] = (float) getY1();
959 result = SEG_MOVETO;
960 break;
961 case 1:
962 coords[0] = (float) getCtrlX1();
963 coords[1] = (float) getCtrlY1();
964 coords[2] = (float) getCtrlX2();
965 coords[3] = (float) getCtrlY2();
966 coords[4] = (float) getX2();
967 coords[5] = (float) getY2();
968 result = SEG_CUBICTO;
969 break;
970 default:
971 throw new NoSuchElementException("cubic iterator out of bounds");
972 }
973 if (at != null)
974 at.transform(coords, 0, coords, 0, 3);
975 return result;
976 }
977
978 public int currentSegment(double[] coords)
979 {
980 int result;
981 switch (current)
982 {
983 case 0:
984 coords[0] = getX1();
985 coords[1] = getY1();
986 result = SEG_MOVETO;
987 break;
988 case 1:
989 coords[0] = getCtrlX1();
990 coords[1] = getCtrlY1();
991 coords[2] = getCtrlX2();
992 coords[3] = getCtrlY2();
993 coords[4] = getX2();
994 coords[5] = getY2();
995 result = SEG_CUBICTO;
996 break;
997 default:
998 throw new NoSuchElementException("cubic iterator out of bounds");
999 }
1000 if (at != null)
1001 at.transform(coords, 0, coords, 0, 3);
1002 return result;
1003 }
1004 };
1005 }
1006
1007 public PathIterator getPathIterator(AffineTransform at, double flatness)
1008 {
1009 return new FlatteningPathIterator(getPathIterator(at), flatness);
1010 }
1011
1012 /**
1013 * Create a new curve with the same contents as this one.
1014 *
1015 * @return the clone.
1016 */
1017 public Object clone()
1018 {
1019 try
1020 {
1021 return super.clone();
1022 }
1023 catch (CloneNotSupportedException e)
1024 {
1025 throw (Error) new InternalError().initCause(e); // Impossible
1026 }
1027 }
1028
1029 /**
1030 * Helper method used by contains() and intersects() methods, that
1031 * returns the number of curve/line intersections on a given axis
1032 * extending from a certain point.
1033 *
1034 * @param x x coordinate of the origin point
1035 * @param y y coordinate of the origin point
1036 * @param useYaxis axis used, if true the positive Y axis is used,
1037 * false uses the positive X axis.
1038 *
1039 * This is an implementation of the line-crossings algorithm,
1040 * Detailed in an article on Eric Haines' page:
1041 * http://www.acm.org/tog/editors/erich/ptinpoly/
1042 *
1043 * A special-case not adressed in this code is self-intersections
1044 * of the curve, e.g. if the axis intersects the self-itersection,
1045 * the degenerate roots of the polynomial will erroneously count as
1046 * a single intersection of the curve, and not two.
1047 */
1048 private int getAxisIntersections(double x, double y, boolean useYaxis,
1049 double distance)
1050 {
1051 int nCrossings = 0;
1052 double a0;
1053 double a1;
1054 double a2;
1055 double a3;
1056 double b0;
1057 double b1;
1058 double b2;
1059 double b3;
1060 double[] r = new double[4];
1061 int nRoots;
1062
1063 a0 = a3 = 0.0;
1064
1065 if (useYaxis)
1066 {
1067 a0 = getY1() - y;
1068 a1 = getCtrlY1() - y;
1069 a2 = getCtrlY2() - y;
1070 a3 = getY2() - y;
1071 b0 = getX1() - x;
1072 b1 = getCtrlX1() - x;
1073 b2 = getCtrlX2() - x;
1074 b3 = getX2() - x;
1075 }
1076 else
1077 {
1078 a0 = getX1() - x;
1079 a1 = getCtrlX1() - x;
1080 a2 = getCtrlX2() - x;
1081 a3 = getX2() - x;
1082 b0 = getY1() - y;
1083 b1 = getCtrlY1() - y;
1084 b2 = getCtrlY2() - y;
1085 b3 = getY2() - y;
1086 }
1087
1088 /* If the axis intersects a start/endpoint, shift it up by some small
1089 amount to guarantee the line is 'inside'
1090 If this is not done, bad behaviour may result for points on that axis.*/
1091 if (a0 == 0.0 || a3 == 0.0)
1092 {
1093 double small = getFlatness() * EPSILON;
1094 if (a0 == 0.0)
1095 a0 -= small;
1096 if (a3 == 0.0)
1097 a3 -= small;
1098 }
1099
1100 if (useYaxis)
1101 {
1102 if (Line2D.linesIntersect(b0, a0, b3, a3, EPSILON, 0.0, distance, 0.0))
1103 nCrossings++;
1104 }
1105 else
1106 {
1107 if (Line2D.linesIntersect(a0, b0, a3, b3, 0.0, EPSILON, 0.0, distance))
1108 nCrossings++;
1109 }
1110
1111 r[0] = a0;
1112 r[1] = 3 * (a1 - a0);
1113 r[2] = 3 * (a2 + a0 - 2 * a1);
1114 r[3] = a3 - 3 * a2 + 3 * a1 - a0;
1115
1116 if ((nRoots = solveCubic(r)) != 0)
1117 for (int i = 0; i < nRoots; i++)
1118 {
1119 double t = r[i];
1120 if (t >= 0.0 && t <= 1.0)
1121 {
1122 double crossing = -(t * t * t) * (b0 - 3 * b1 + 3 * b2 - b3)
1123 + 3 * t * t * (b0 - 2 * b1 + b2)
1124 + 3 * t * (b1 - b0) + b0;
1125 if (crossing > 0.0 && crossing <= distance)
1126 nCrossings++;
1127 }
1128 }
1129
1130 return (nCrossings);
1131 }
1132
1133 /**
1134 * A two-dimensional curve that is parameterized with a cubic
1135 * function and stores coordinate values in double-precision
1136 * floating-point format.
1137 *
1138 * @see CubicCurve2D.Float
1139 *
1140 * @author Eric Blake (ebb9@email.byu.edu)
1141 * @author Sascha Brawer (brawer@dandelis.ch)
1142 */
1143 public static class Double extends CubicCurve2D
1144 {
1145 /**
1146 * The <i>x</i> coordinate of the curve’s start point.
1147 */
1148 public double x1;
1149
1150 /**
1151 * The <i>y</i> coordinate of the curve’s start point.
1152 */
1153 public double y1;
1154
1155 /**
1156 * The <i>x</i> coordinate of the curve’s first control point.
1157 */
1158 public double ctrlx1;
1159
1160 /**
1161 * The <i>y</i> coordinate of the curve’s first control point.
1162 */
1163 public double ctrly1;
1164
1165 /**
1166 * The <i>x</i> coordinate of the curve’s second control point.
1167 */
1168 public double ctrlx2;
1169
1170 /**
1171 * The <i>y</i> coordinate of the curve’s second control point.
1172 */
1173 public double ctrly2;
1174
1175 /**
1176 * The <i>x</i> coordinate of the curve’s end point.
1177 */
1178 public double x2;
1179
1180 /**
1181 * The <i>y</i> coordinate of the curve’s end point.
1182 */
1183 public double y2;
1184
1185 /**
1186 * Constructs a new CubicCurve2D that stores its coordinate values
1187 * in double-precision floating-point format. All points are
1188 * initially at position (0, 0).
1189 */
1190 public Double()
1191 {
1192 }
1193
1194 /**
1195 * Constructs a new CubicCurve2D that stores its coordinate values
1196 * in double-precision floating-point format, specifying the
1197 * initial position of each point.
1198 *
1199 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1200 * alt="A drawing of a CubicCurve2D" />
1201 *
1202 * @param x1 the <i>x</i> coordinate of the curve’s start
1203 * point.
1204 *
1205 * @param y1 the <i>y</i> coordinate of the curve’s start
1206 * point.
1207 *
1208 * @param cx1 the <i>x</i> coordinate of the curve’s first
1209 * control point.
1210 *
1211 * @param cy1 the <i>y</i> coordinate of the curve’s first
1212 * control point.
1213 *
1214 * @param cx2 the <i>x</i> coordinate of the curve’s second
1215 * control point.
1216 *
1217 * @param cy2 the <i>y</i> coordinate of the curve’s second
1218 * control point.
1219 *
1220 * @param x2 the <i>x</i> coordinate of the curve’s end
1221 * point.
1222 *
1223 * @param y2 the <i>y</i> coordinate of the curve’s end
1224 * point.
1225 */
1226 public Double(double x1, double y1, double cx1, double cy1, double cx2,
1227 double cy2, double x2, double y2)
1228 {
1229 this.x1 = x1;
1230 this.y1 = y1;
1231 ctrlx1 = cx1;
1232 ctrly1 = cy1;
1233 ctrlx2 = cx2;
1234 ctrly2 = cy2;
1235 this.x2 = x2;
1236 this.y2 = y2;
1237 }
1238
1239 /**
1240 * Returns the <i>x</i> coordinate of the curve’s start
1241 * point.
1242 */
1243 public double getX1()
1244 {
1245 return x1;
1246 }
1247
1248 /**
1249 * Returns the <i>y</i> coordinate of the curve’s start
1250 * point.
1251 */
1252 public double getY1()
1253 {
1254 return y1;
1255 }
1256
1257 /**
1258 * Returns the curve’s start point.
1259 */
1260 public Point2D getP1()
1261 {
1262 return new Point2D.Double(x1, y1);
1263 }
1264
1265 /**
1266 * Returns the <i>x</i> coordinate of the curve’s first
1267 * control point.
1268 */
1269 public double getCtrlX1()
1270 {
1271 return ctrlx1;
1272 }
1273
1274 /**
1275 * Returns the <i>y</i> coordinate of the curve’s first
1276 * control point.
1277 */
1278 public double getCtrlY1()
1279 {
1280 return ctrly1;
1281 }
1282
1283 /**
1284 * Returns the curve’s first control point.
1285 */
1286 public Point2D getCtrlP1()
1287 {
1288 return new Point2D.Double(ctrlx1, ctrly1);
1289 }
1290
1291 /**
1292 * Returns the <i>x</i> coordinate of the curve’s second
1293 * control point.
1294 */
1295 public double getCtrlX2()
1296 {
1297 return ctrlx2;
1298 }
1299
1300 /**
1301 * Returns the <i>y</i> coordinate of the curve’s second
1302 * control point.
1303 */
1304 public double getCtrlY2()
1305 {
1306 return ctrly2;
1307 }
1308
1309 /**
1310 * Returns the curve’s second control point.
1311 */
1312 public Point2D getCtrlP2()
1313 {
1314 return new Point2D.Double(ctrlx2, ctrly2);
1315 }
1316
1317 /**
1318 * Returns the <i>x</i> coordinate of the curve’s end
1319 * point.
1320 */
1321 public double getX2()
1322 {
1323 return x2;
1324 }
1325
1326 /**
1327 * Returns the <i>y</i> coordinate of the curve’s end
1328 * point.
1329 */
1330 public double getY2()
1331 {
1332 return y2;
1333 }
1334
1335 /**
1336 * Returns the curve’s end point.
1337 */
1338 public Point2D getP2()
1339 {
1340 return new Point2D.Double(x2, y2);
1341 }
1342
1343 /**
1344 * Changes the curve geometry, separately specifying each coordinate
1345 * value.
1346 *
1347 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1348 * alt="A drawing of a CubicCurve2D" />
1349 *
1350 * @param x1 the <i>x</i> coordinate of the curve’s new start
1351 * point.
1352 *
1353 * @param y1 the <i>y</i> coordinate of the curve’s new start
1354 * point.
1355 *
1356 * @param cx1 the <i>x</i> coordinate of the curve’s new
1357 * first control point.
1358 *
1359 * @param cy1 the <i>y</i> coordinate of the curve’s new
1360 * first control point.
1361 *
1362 * @param cx2 the <i>x</i> coordinate of the curve’s new
1363 * second control point.
1364 *
1365 * @param cy2 the <i>y</i> coordinate of the curve’s new
1366 * second control point.
1367 *
1368 * @param x2 the <i>x</i> coordinate of the curve’s new end
1369 * point.
1370 *
1371 * @param y2 the <i>y</i> coordinate of the curve’s new end
1372 * point.
1373 */
1374 public void setCurve(double x1, double y1, double cx1, double cy1,
1375 double cx2, double cy2, double x2, double y2)
1376 {
1377 this.x1 = x1;
1378 this.y1 = y1;
1379 ctrlx1 = cx1;
1380 ctrly1 = cy1;
1381 ctrlx2 = cx2;
1382 ctrly2 = cy2;
1383 this.x2 = x2;
1384 this.y2 = y2;
1385 }
1386
1387 /**
1388 * Determines the smallest rectangle that encloses the
1389 * curve’s start, end and control points. As the
1390 * illustration below shows, the invisible control points may cause
1391 * the bounds to be much larger than the area that is actually
1392 * covered by the curve.
1393 *
1394 * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
1395 * alt="An illustration of the bounds of a CubicCurve2D" />
1396 */
1397 public Rectangle2D getBounds2D()
1398 {
1399 double nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
1400 double ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
1401 double nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
1402 double ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
1403 return new Rectangle2D.Double(nx1, ny1, nx2 - nx1, ny2 - ny1);
1404 }
1405 }
1406
1407 /**
1408 * A two-dimensional curve that is parameterized with a cubic
1409 * function and stores coordinate values in single-precision
1410 * floating-point format.
1411 *
1412 * @see CubicCurve2D.Float
1413 *
1414 * @author Eric Blake (ebb9@email.byu.edu)
1415 * @author Sascha Brawer (brawer@dandelis.ch)
1416 */
1417 public static class Float extends CubicCurve2D
1418 {
1419 /**
1420 * The <i>x</i> coordinate of the curve’s start point.
1421 */
1422 public float x1;
1423
1424 /**
1425 * The <i>y</i> coordinate of the curve’s start point.
1426 */
1427 public float y1;
1428
1429 /**
1430 * The <i>x</i> coordinate of the curve’s first control point.
1431 */
1432 public float ctrlx1;
1433
1434 /**
1435 * The <i>y</i> coordinate of the curve’s first control point.
1436 */
1437 public float ctrly1;
1438
1439 /**
1440 * The <i>x</i> coordinate of the curve’s second control point.
1441 */
1442 public float ctrlx2;
1443
1444 /**
1445 * The <i>y</i> coordinate of the curve’s second control point.
1446 */
1447 public float ctrly2;
1448
1449 /**
1450 * The <i>x</i> coordinate of the curve’s end point.
1451 */
1452 public float x2;
1453
1454 /**
1455 * The <i>y</i> coordinate of the curve’s end point.
1456 */
1457 public float y2;
1458
1459 /**
1460 * Constructs a new CubicCurve2D that stores its coordinate values
1461 * in single-precision floating-point format. All points are
1462 * initially at position (0, 0).
1463 */
1464 public Float()
1465 {
1466 }
1467
1468 /**
1469 * Constructs a new CubicCurve2D that stores its coordinate values
1470 * in single-precision floating-point format, specifying the
1471 * initial position of each point.
1472 *
1473 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1474 * alt="A drawing of a CubicCurve2D" />
1475 *
1476 * @param x1 the <i>x</i> coordinate of the curve’s start
1477 * point.
1478 *
1479 * @param y1 the <i>y</i> coordinate of the curve’s start
1480 * point.
1481 *
1482 * @param cx1 the <i>x</i> coordinate of the curve’s first
1483 * control point.
1484 *
1485 * @param cy1 the <i>y</i> coordinate of the curve’s first
1486 * control point.
1487 *
1488 * @param cx2 the <i>x</i> coordinate of the curve’s second
1489 * control point.
1490 *
1491 * @param cy2 the <i>y</i> coordinate of the curve’s second
1492 * control point.
1493 *
1494 * @param x2 the <i>x</i> coordinate of the curve’s end
1495 * point.
1496 *
1497 * @param y2 the <i>y</i> coordinate of the curve’s end
1498 * point.
1499 */
1500 public Float(float x1, float y1, float cx1, float cy1, float cx2,
1501 float cy2, float x2, float y2)
1502 {
1503 this.x1 = x1;
1504 this.y1 = y1;
1505 ctrlx1 = cx1;
1506 ctrly1 = cy1;
1507 ctrlx2 = cx2;
1508 ctrly2 = cy2;
1509 this.x2 = x2;
1510 this.y2 = y2;
1511 }
1512
1513 /**
1514 * Returns the <i>x</i> coordinate of the curve’s start
1515 * point.
1516 */
1517 public double getX1()
1518 {
1519 return x1;
1520 }
1521
1522 /**
1523 * Returns the <i>y</i> coordinate of the curve’s start
1524 * point.
1525 */
1526 public double getY1()
1527 {
1528 return y1;
1529 }
1530
1531 /**
1532 * Returns the curve’s start point.
1533 */
1534 public Point2D getP1()
1535 {
1536 return new Point2D.Float(x1, y1);
1537 }
1538
1539 /**
1540 * Returns the <i>x</i> coordinate of the curve’s first
1541 * control point.
1542 */
1543 public double getCtrlX1()
1544 {
1545 return ctrlx1;
1546 }
1547
1548 /**
1549 * Returns the <i>y</i> coordinate of the curve’s first
1550 * control point.
1551 */
1552 public double getCtrlY1()
1553 {
1554 return ctrly1;
1555 }
1556
1557 /**
1558 * Returns the curve’s first control point.
1559 */
1560 public Point2D getCtrlP1()
1561 {
1562 return new Point2D.Float(ctrlx1, ctrly1);
1563 }
1564
1565 /**
1566 * Returns the <i>s</i> coordinate of the curve’s second
1567 * control point.
1568 */
1569 public double getCtrlX2()
1570 {
1571 return ctrlx2;
1572 }
1573
1574 /**
1575 * Returns the <i>y</i> coordinate of the curve’s second
1576 * control point.
1577 */
1578 public double getCtrlY2()
1579 {
1580 return ctrly2;
1581 }
1582
1583 /**
1584 * Returns the curve’s second control point.
1585 */
1586 public Point2D getCtrlP2()
1587 {
1588 return new Point2D.Float(ctrlx2, ctrly2);
1589 }
1590
1591 /**
1592 * Returns the <i>x</i> coordinate of the curve’s end
1593 * point.
1594 */
1595 public double getX2()
1596 {
1597 return x2;
1598 }
1599
1600 /**
1601 * Returns the <i>y</i> coordinate of the curve’s end
1602 * point.
1603 */
1604 public double getY2()
1605 {
1606 return y2;
1607 }
1608
1609 /**
1610 * Returns the curve’s end point.
1611 */
1612 public Point2D getP2()
1613 {
1614 return new Point2D.Float(x2, y2);
1615 }
1616
1617 /**
1618 * Changes the curve geometry, separately specifying each coordinate
1619 * value as a double-precision floating-point number.
1620 *
1621 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1622 * alt="A drawing of a CubicCurve2D" />
1623 *
1624 * @param x1 the <i>x</i> coordinate of the curve’s new start
1625 * point.
1626 *
1627 * @param y1 the <i>y</i> coordinate of the curve’s new start
1628 * point.
1629 *
1630 * @param cx1 the <i>x</i> coordinate of the curve’s new
1631 * first control point.
1632 *
1633 * @param cy1 the <i>y</i> coordinate of the curve’s new
1634 * first control point.
1635 *
1636 * @param cx2 the <i>x</i> coordinate of the curve’s new
1637 * second control point.
1638 *
1639 * @param cy2 the <i>y</i> coordinate of the curve’s new
1640 * second control point.
1641 *
1642 * @param x2 the <i>x</i> coordinate of the curve’s new end
1643 * point.
1644 *
1645 * @param y2 the <i>y</i> coordinate of the curve’s new end
1646 * point.
1647 */
1648 public void setCurve(double x1, double y1, double cx1, double cy1,
1649 double cx2, double cy2, double x2, double y2)
1650 {
1651 this.x1 = (float) x1;
1652 this.y1 = (float) y1;
1653 ctrlx1 = (float) cx1;
1654 ctrly1 = (float) cy1;
1655 ctrlx2 = (float) cx2;
1656 ctrly2 = (float) cy2;
1657 this.x2 = (float) x2;
1658 this.y2 = (float) y2;
1659 }
1660
1661 /**
1662 * Changes the curve geometry, separately specifying each coordinate
1663 * value as a single-precision floating-point number.
1664 *
1665 * <p><img src="doc-files/CubicCurve2D-1.png" width="350" height="180"
1666 * alt="A drawing of a CubicCurve2D" />
1667 *
1668 * @param x1 the <i>x</i> coordinate of the curve’s new start
1669 * point.
1670 *
1671 * @param y1 the <i>y</i> coordinate of the curve’s new start
1672 * point.
1673 *
1674 * @param cx1 the <i>x</i> coordinate of the curve’s new
1675 * first control point.
1676 *
1677 * @param cy1 the <i>y</i> coordinate of the curve’s new
1678 * first control point.
1679 *
1680 * @param cx2 the <i>x</i> coordinate of the curve’s new
1681 * second control point.
1682 *
1683 * @param cy2 the <i>y</i> coordinate of the curve’s new
1684 * second control point.
1685 *
1686 * @param x2 the <i>x</i> coordinate of the curve’s new end
1687 * point.
1688 *
1689 * @param y2 the <i>y</i> coordinate of the curve’s new end
1690 * point.
1691 */
1692 public void setCurve(float x1, float y1, float cx1, float cy1, float cx2,
1693 float cy2, float x2, float y2)
1694 {
1695 this.x1 = x1;
1696 this.y1 = y1;
1697 ctrlx1 = cx1;
1698 ctrly1 = cy1;
1699 ctrlx2 = cx2;
1700 ctrly2 = cy2;
1701 this.x2 = x2;
1702 this.y2 = y2;
1703 }
1704
1705 /**
1706 * Determines the smallest rectangle that encloses the
1707 * curve’s start, end and control points. As the
1708 * illustration below shows, the invisible control points may cause
1709 * the bounds to be much larger than the area that is actually
1710 * covered by the curve.
1711 *
1712 * <p><img src="doc-files/CubicCurve2D-2.png" width="350" height="180"
1713 * alt="An illustration of the bounds of a CubicCurve2D" />
1714 */
1715 public Rectangle2D getBounds2D()
1716 {
1717 float nx1 = Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
1718 float ny1 = Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
1719 float nx2 = Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
1720 float ny2 = Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
1721 return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
1722 }
1723 }
1724 }