1 /*
2 * Copyright 1997-2003 Sun Microsystems, Inc. All Rights Reserved.
3 * DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS FILE HEADER.
4 *
5 * This code is free software; you can redistribute it and/or modify it
6 * under the terms of the GNU General Public License version 2 only, as
7 * published by the Free Software Foundation. Sun designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Sun in the LICENSE file that accompanied this code.
10 *
11 * This code is distributed in the hope that it will be useful, but WITHOUT
12 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
13 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
14 * version 2 for more details (a copy is included in the LICENSE file that
15 * accompanied this code).
16 *
17 * You should have received a copy of the GNU General Public License version
18 * 2 along with this work; if not, write to the Free Software Foundation,
19 * Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA.
20 *
21 * Please contact Sun Microsystems, Inc., 4150 Network Circle, Santa Clara,
22 * CA 95054 USA or visit www.sun.com if you need additional information or
23 * have any questions.
24 */
25
26 package java.awt.geom;
27
28 import java.util;
29
30 /**
31 * A utility class to iterate over the path segments of an arc
32 * through the PathIterator interface.
33 *
34 * @author Jim Graham
35 */
36 class ArcIterator implements PathIterator {
37 double x, y, w, h, angStRad, increment, cv;
38 AffineTransform affine;
39 int index;
40 int arcSegs;
41 int lineSegs;
42
43 ArcIterator(Arc2D a, AffineTransform at) {
44 this.w = a.getWidth() / 2;
45 this.h = a.getHeight() / 2;
46 this.x = a.getX() + w;
47 this.y = a.getY() + h;
48 this.angStRad = -Math.toRadians(a.getAngleStart());
49 this.affine = at;
50 double ext = -a.getAngleExtent();
51 if (ext >= 360.0 || ext <= -360) {
52 arcSegs = 4;
53 this.increment = Math.PI / 2;
54 // btan(Math.PI / 2);
55 this.cv = 0.5522847498307933;
56 if (ext < 0) {
57 increment = -increment;
58 cv = -cv;
59 }
60 } else {
61 arcSegs = (int) Math.ceil(Math.abs(ext) / 90.0);
62 this.increment = Math.toRadians(ext / arcSegs);
63 this.cv = btan(increment);
64 if (cv == 0) {
65 arcSegs = 0;
66 }
67 }
68 switch (a.getArcType()) {
69 case Arc2D.OPEN:
70 lineSegs = 0;
71 break;
72 case Arc2D.CHORD:
73 lineSegs = 1;
74 break;
75 case Arc2D.PIE:
76 lineSegs = 2;
77 break;
78 }
79 if (w < 0 || h < 0) {
80 arcSegs = lineSegs = -1;
81 }
82 }
83
84 /**
85 * Return the winding rule for determining the insideness of the
86 * path.
87 * @see #WIND_EVEN_ODD
88 * @see #WIND_NON_ZERO
89 */
90 public int getWindingRule() {
91 return WIND_NON_ZERO;
92 }
93
94 /**
95 * Tests if there are more points to read.
96 * @return true if there are more points to read
97 */
98 public boolean isDone() {
99 return index > arcSegs + lineSegs;
100 }
101
102 /**
103 * Moves the iterator to the next segment of the path forwards
104 * along the primary direction of traversal as long as there are
105 * more points in that direction.
106 */
107 public void next() {
108 index++;
109 }
110
111 /*
112 * btan computes the length (k) of the control segments at
113 * the beginning and end of a cubic bezier that approximates
114 * a segment of an arc with extent less than or equal to
115 * 90 degrees. This length (k) will be used to generate the
116 * 2 bezier control points for such a segment.
117 *
118 * Assumptions:
119 * a) arc is centered on 0,0 with radius of 1.0
120 * b) arc extent is less than 90 degrees
121 * c) control points should preserve tangent
122 * d) control segments should have equal length
123 *
124 * Initial data:
125 * start angle: ang1
126 * end angle: ang2 = ang1 + extent
127 * start point: P1 = (x1, y1) = (cos(ang1), sin(ang1))
128 * end point: P4 = (x4, y4) = (cos(ang2), sin(ang2))
129 *
130 * Control points:
131 * P2 = (x2, y2)
132 * | x2 = x1 - k * sin(ang1) = cos(ang1) - k * sin(ang1)
133 * | y2 = y1 + k * cos(ang1) = sin(ang1) + k * cos(ang1)
134 *
135 * P3 = (x3, y3)
136 * | x3 = x4 + k * sin(ang2) = cos(ang2) + k * sin(ang2)
137 * | y3 = y4 - k * cos(ang2) = sin(ang2) - k * cos(ang2)
138 *
139 * The formula for this length (k) can be found using the
140 * following derivations:
141 *
142 * Midpoints:
143 * a) bezier (t = 1/2)
144 * bPm = P1 * (1-t)^3 +
145 * 3 * P2 * t * (1-t)^2 +
146 * 3 * P3 * t^2 * (1-t) +
147 * P4 * t^3 =
148 * = (P1 + 3P2 + 3P3 + P4)/8
149 *
150 * b) arc
151 * aPm = (cos((ang1 + ang2)/2), sin((ang1 + ang2)/2))
152 *
153 * Let angb = (ang2 - ang1)/2; angb is half of the angle
154 * between ang1 and ang2.
155 *
156 * Solve the equation bPm == aPm
157 *
158 * a) For xm coord:
159 * x1 + 3*x2 + 3*x3 + x4 = 8*cos((ang1 + ang2)/2)
160 *
161 * cos(ang1) + 3*cos(ang1) - 3*k*sin(ang1) +
162 * 3*cos(ang2) + 3*k*sin(ang2) + cos(ang2) =
163 * = 8*cos((ang1 + ang2)/2)
164 *
165 * 4*cos(ang1) + 4*cos(ang2) + 3*k*(sin(ang2) - sin(ang1)) =
166 * = 8*cos((ang1 + ang2)/2)
167 *
168 * 8*cos((ang1 + ang2)/2)*cos((ang2 - ang1)/2) +
169 * 6*k*sin((ang2 - ang1)/2)*cos((ang1 + ang2)/2) =
170 * = 8*cos((ang1 + ang2)/2)
171 *
172 * 4*cos(angb) + 3*k*sin(angb) = 4
173 *
174 * k = 4 / 3 * (1 - cos(angb)) / sin(angb)
175 *
176 * b) For ym coord we derive the same formula.
177 *
178 * Since this formula can generate "NaN" values for small
179 * angles, we will derive a safer form that does not involve
180 * dividing by very small values:
181 * (1 - cos(angb)) / sin(angb) =
182 * = (1 - cos(angb))*(1 + cos(angb)) / sin(angb)*(1 + cos(angb)) =
183 * = (1 - cos(angb)^2) / sin(angb)*(1 + cos(angb)) =
184 * = sin(angb)^2 / sin(angb)*(1 + cos(angb)) =
185 * = sin(angb) / (1 + cos(angb))
186 *
187 */
188 private static double btan(double increment) {
189 increment /= 2.0;
190 return 4.0 / 3.0 * Math.sin(increment) / (1.0 + Math.cos(increment));
191 }
192
193 /**
194 * Returns the coordinates and type of the current path segment in
195 * the iteration.
196 * The return value is the path segment type:
197 * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.
198 * A float array of length 6 must be passed in and may be used to
199 * store the coordinates of the point(s).
200 * Each point is stored as a pair of float x,y coordinates.
201 * SEG_MOVETO and SEG_LINETO types will return one point,
202 * SEG_QUADTO will return two points,
203 * SEG_CUBICTO will return 3 points
204 * and SEG_CLOSE will not return any points.
205 * @see #SEG_MOVETO
206 * @see #SEG_LINETO
207 * @see #SEG_QUADTO
208 * @see #SEG_CUBICTO
209 * @see #SEG_CLOSE
210 */
211 public int currentSegment(float[] coords) {
212 if (isDone()) {
213 throw new NoSuchElementException("arc iterator out of bounds");
214 }
215 double angle = angStRad;
216 if (index == 0) {
217 coords[0] = (float) (x + Math.cos(angle) * w);
218 coords[1] = (float) (y + Math.sin(angle) * h);
219 if (affine != null) {
220 affine.transform(coords, 0, coords, 0, 1);
221 }
222 return SEG_MOVETO;
223 }
224 if (index > arcSegs) {
225 if (index == arcSegs + lineSegs) {
226 return SEG_CLOSE;
227 }
228 coords[0] = (float) x;
229 coords[1] = (float) y;
230 if (affine != null) {
231 affine.transform(coords, 0, coords, 0, 1);
232 }
233 return SEG_LINETO;
234 }
235 angle += increment * (index - 1);
236 double relx = Math.cos(angle);
237 double rely = Math.sin(angle);
238 coords[0] = (float) (x + (relx - cv * rely) * w);
239 coords[1] = (float) (y + (rely + cv * relx) * h);
240 angle += increment;
241 relx = Math.cos(angle);
242 rely = Math.sin(angle);
243 coords[2] = (float) (x + (relx + cv * rely) * w);
244 coords[3] = (float) (y + (rely - cv * relx) * h);
245 coords[4] = (float) (x + relx * w);
246 coords[5] = (float) (y + rely * h);
247 if (affine != null) {
248 affine.transform(coords, 0, coords, 0, 3);
249 }
250 return SEG_CUBICTO;
251 }
252
253 /**
254 * Returns the coordinates and type of the current path segment in
255 * the iteration.
256 * The return value is the path segment type:
257 * SEG_MOVETO, SEG_LINETO, SEG_QUADTO, SEG_CUBICTO, or SEG_CLOSE.
258 * A double array of length 6 must be passed in and may be used to
259 * store the coordinates of the point(s).
260 * Each point is stored as a pair of double x,y coordinates.
261 * SEG_MOVETO and SEG_LINETO types will return one point,
262 * SEG_QUADTO will return two points,
263 * SEG_CUBICTO will return 3 points
264 * and SEG_CLOSE will not return any points.
265 * @see #SEG_MOVETO
266 * @see #SEG_LINETO
267 * @see #SEG_QUADTO
268 * @see #SEG_CUBICTO
269 * @see #SEG_CLOSE
270 */
271 public int currentSegment(double[] coords) {
272 if (isDone()) {
273 throw new NoSuchElementException("arc iterator out of bounds");
274 }
275 double angle = angStRad;
276 if (index == 0) {
277 coords[0] = x + Math.cos(angle) * w;
278 coords[1] = y + Math.sin(angle) * h;
279 if (affine != null) {
280 affine.transform(coords, 0, coords, 0, 1);
281 }
282 return SEG_MOVETO;
283 }
284 if (index > arcSegs) {
285 if (index == arcSegs + lineSegs) {
286 return SEG_CLOSE;
287 }
288 coords[0] = x;
289 coords[1] = y;
290 if (affine != null) {
291 affine.transform(coords, 0, coords, 0, 1);
292 }
293 return SEG_LINETO;
294 }
295 angle += increment * (index - 1);
296 double relx = Math.cos(angle);
297 double rely = Math.sin(angle);
298 coords[0] = x + (relx - cv * rely) * w;
299 coords[1] = y + (rely + cv * relx) * h;
300 angle += increment;
301 relx = Math.cos(angle);
302 rely = Math.sin(angle);
303 coords[2] = x + (relx + cv * rely) * w;
304 coords[3] = y + (rely - cv * relx) * h;
305 coords[4] = x + relx * w;
306 coords[5] = y + rely * h;
307 if (affine != null) {
308 affine.transform(coords, 0, coords, 0, 3);
309 }
310 return SEG_CUBICTO;
311 }
312 }
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