1 |
14 |
jlechner |
/* 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’s start
|
75 |
|
|
* point.
|
76 |
|
|
*/
|
77 |
|
|
public abstract double getX1();
|
78 |
|
|
|
79 |
|
|
/**
|
80 |
|
|
* Returns the <i>y</i> coordinate of the curve’s start
|
81 |
|
|
* point.
|
82 |
|
|
*/
|
83 |
|
|
public abstract double getY1();
|
84 |
|
|
|
85 |
|
|
/**
|
86 |
|
|
* Returns the curve’s start point.
|
87 |
|
|
*/
|
88 |
|
|
public abstract Point2D getP1();
|
89 |
|
|
|
90 |
|
|
/**
|
91 |
|
|
* Returns the <i>x</i> coordinate of the curve’s first
|
92 |
|
|
* control point.
|
93 |
|
|
*/
|
94 |
|
|
public abstract double getCtrlX1();
|
95 |
|
|
|
96 |
|
|
/**
|
97 |
|
|
* Returns the <i>y</i> coordinate of the curve’s first
|
98 |
|
|
* control point.
|
99 |
|
|
*/
|
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 = (float) Math.min(Math.min(x1, ctrlx1), Math.min(ctrlx2, x2));
|
1718 |
|
|
float ny1 = (float) Math.min(Math.min(y1, ctrly1), Math.min(ctrly2, y2));
|
1719 |
|
|
float nx2 = (float) Math.max(Math.max(x1, ctrlx1), Math.max(ctrlx2, x2));
|
1720 |
|
|
float ny2 = (float) Math.max(Math.max(y1, ctrly1), Math.max(ctrly2, y2));
|
1721 |
|
|
return new Rectangle2D.Float(nx1, ny1, nx2 - nx1, ny2 - ny1);
|
1722 |
|
|
}
|
1723 |
|
|
}
|
1724 |
|
|
}
|