1/*
2 * Copyright (c) 1997, 2003, Oracle and/or its affiliates. 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.  Oracle designates this
8 * particular file as subject to the "Classpath" exception as provided
9 * by Oracle 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 Oracle, 500 Oracle Parkway, Redwood Shores, CA 94065 USA
22 * or visit www.oracle.com if you need additional information or have any
23 * questions.
24 */
25
26package java.awt.geom;
27
28import 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 */
36class 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}
313