J. Duke | 319a3b9 | 2007-12-01 00:00:00 +0000 | [diff] [blame^] | 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 | } |