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

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