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| 1 | +/* | |
| 2 | + * Copyright (c) 2007, 2011, 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 | + | |
| 26 | +package sun.java2d.pisces; | |
| 27 | + | |
| 28 | +import java.util.Arrays; | |
| 29 | +import static java.lang.Math.PI; | |
| 30 | +import static java.lang.Math.cos; | |
| 31 | +import static java.lang.Math.sqrt; | |
| 32 | +import static java.lang.Math.cbrt; | |
| 33 | +import static java.lang.Math.acos; | |
| 34 | + | |
| 35 | + | |
| 36 | +final class Helpers { | |
| 37 | + private Helpers() { | |
| 38 | + throw new Error("This is a non instantiable class"); | |
| 39 | + } | |
| 40 | + | |
| 41 | + static boolean within(final float x, final float y, final float err) { | |
| 42 | + final float d = y - x; | |
| 43 | + return (d <= err && d >= -err); | |
| 44 | + } | |
| 45 | + | |
| 46 | + static boolean within(final double x, final double y, final double err) { | |
| 47 | + final double d = y - x; | |
| 48 | + return (d <= err && d >= -err); | |
| 49 | + } | |
| 50 | + | |
| 51 | + static int quadraticRoots(final float a, final float b, | |
| 52 | + final float c, float[] zeroes, final int off) | |
| 53 | + { | |
| 54 | + int ret = off; | |
| 55 | + float t; | |
| 56 | + if (a != 0f) { | |
| 57 | + final float dis = b*b - 4*a*c; | |
| 58 | + if (dis > 0) { | |
| 59 | + final float sqrtDis = (float)Math.sqrt(dis); | |
| 60 | + // depending on the sign of b we use a slightly different | |
| 61 | + // algorithm than the traditional one to find one of the roots | |
| 62 | + // so we can avoid adding numbers of different signs (which | |
| 63 | + // might result in loss of precision). | |
| 64 | + if (b >= 0) { | |
| 65 | + zeroes[ret++] = (2 * c) / (-b - sqrtDis); | |
| 66 | + zeroes[ret++] = (-b - sqrtDis) / (2 * a); | |
| 67 | + } else { | |
| 68 | + zeroes[ret++] = (-b + sqrtDis) / (2 * a); | |
| 69 | + zeroes[ret++] = (2 * c) / (-b + sqrtDis); | |
| 70 | + } | |
| 71 | + } else if (dis == 0f) { | |
| 72 | + t = (-b) / (2 * a); | |
| 73 | + zeroes[ret++] = t; | |
| 74 | + } | |
| 75 | + } else { | |
| 76 | + if (b != 0f) { | |
| 77 | + t = (-c) / b; | |
| 78 | + zeroes[ret++] = t; | |
| 79 | + } | |
| 80 | + } | |
| 81 | + return ret - off; | |
| 82 | + } | |
| 83 | + | |
| 84 | + // find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B) | |
| 85 | + static int cubicRootsInAB(float d, float a, float b, float c, | |
| 86 | + float[] pts, final int off, | |
| 87 | + final float A, final float B) | |
| 88 | + { | |
| 89 | + if (d == 0) { | |
| 90 | + int num = quadraticRoots(a, b, c, pts, off); | |
| 91 | + return filterOutNotInAB(pts, off, num, A, B) - off; | |
| 92 | + } | |
| 93 | + // From Graphics Gems: | |
| 94 | + // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c | |
| 95 | + // (also from awt.geom.CubicCurve2D. But here we don't need as | |
| 96 | + // much accuracy and we don't want to create arrays so we use | |
| 97 | + // our own customized version). | |
| 98 | + | |
| 99 | + /* normal form: x^3 + ax^2 + bx + c = 0 */ | |
| 100 | + a /= d; | |
| 101 | + b /= d; | |
| 102 | + c /= d; | |
| 103 | + | |
| 104 | + // substitute x = y - A/3 to eliminate quadratic term: | |
| 105 | + // x^3 +Px + Q = 0 | |
| 106 | + // | |
| 107 | + // Since we actually need P/3 and Q/2 for all of the | |
| 108 | + // calculations that follow, we will calculate | |
| 109 | + // p = P/3 | |
| 110 | + // q = Q/2 | |
| 111 | + // instead and use those values for simplicity of the code. | |
| 112 | + double sq_A = a * a; | |
| 113 | + double p = 1.0/3 * (-1.0/3 * sq_A + b); | |
| 114 | + double q = 1.0/2 * (2.0/27 * a * sq_A - 1.0/3 * a * b + c); | |
| 115 | + | |
| 116 | + /* use Cardano's formula */ | |
| 117 | + | |
| 118 | + double cb_p = p * p * p; | |
| 119 | + double D = q * q + cb_p; | |
| 120 | + | |
| 121 | + int num; | |
| 122 | + if (D < 0) { | |
| 123 | + // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method | |
| 124 | + final double phi = 1.0/3 * acos(-q / sqrt(-cb_p)); | |
| 125 | + final double t = 2 * sqrt(-p); | |
| 126 | + | |
| 127 | + pts[ off+0 ] = (float)( t * cos(phi)); | |
| 128 | + pts[ off+1 ] = (float)(-t * cos(phi + PI / 3)); | |
| 129 | + pts[ off+2 ] = (float)(-t * cos(phi - PI / 3)); | |
| 130 | + num = 3; | |
| 131 | + } else { | |
| 132 | + final double sqrt_D = sqrt(D); | |
| 133 | + final double u = cbrt(sqrt_D - q); | |
| 134 | + final double v = - cbrt(sqrt_D + q); | |
| 135 | + | |
| 136 | + pts[ off ] = (float)(u + v); | |
| 137 | + num = 1; | |
| 138 | + | |
| 139 | + if (within(D, 0, 1e-8)) { | |
| 140 | + pts[off+1] = -(pts[off] / 2); | |
| 141 | + num = 2; | |
| 142 | + } | |
| 143 | + } | |
| 144 | + | |
| 145 | + final float sub = 1.0f/3 * a; | |
| 146 | + | |
| 147 | + for (int i = 0; i < num; ++i) { | |
| 148 | + pts[ off+i ] -= sub; | |
| 149 | + } | |
| 150 | + | |
| 151 | + return filterOutNotInAB(pts, off, num, A, B) - off; | |
| 152 | + } | |
| 153 | + | |
| 154 | + // These use a hardcoded factor of 2 for increasing sizes. Perhaps this | |
| 155 | + // should be provided as an argument. | |
| 156 | + static float[] widenArray(float[] in, final int cursize, final int numToAdd) { | |
| 157 | + if (in.length >= cursize + numToAdd) { | |
| 158 | + return in; | |
| 159 | + } | |
| 160 | + return Arrays.copyOf(in, 2 * (cursize + numToAdd)); | |
| 161 | + } | |
| 162 | + | |
| 163 | + static int[] widenArray(int[] in, final int cursize, final int numToAdd) { | |
| 164 | + if (in.length >= cursize + numToAdd) { | |
| 165 | + return in; | |
| 166 | + } | |
| 167 | + return Arrays.copyOf(in, 2 * (cursize + numToAdd)); | |
| 168 | + } | |
| 169 | + | |
| 170 | + static float evalCubic(final float a, final float b, | |
| 171 | + final float c, final float d, | |
| 172 | + final float t) | |
| 173 | + { | |
| 174 | + return t * (t * (t * a + b) + c) + d; | |
| 175 | + } | |
| 176 | + | |
| 177 | + static float evalQuad(final float a, final float b, | |
| 178 | + final float c, final float t) | |
| 179 | + { | |
| 180 | + return t * (t * a + b) + c; | |
| 181 | + } | |
| 182 | + | |
| 183 | + // returns the index 1 past the last valid element remaining after filtering | |
| 184 | + static int filterOutNotInAB(float[] nums, final int off, final int len, | |
| 185 | + final float a, final float b) | |
| 186 | + { | |
| 187 | + int ret = off; | |
| 188 | + for (int i = off; i < off + len; i++) { | |
| 189 | + if (nums[i] >= a && nums[i] < b) { | |
| 190 | + nums[ret++] = nums[i]; | |
| 191 | + } | |
| 192 | + } | |
| 193 | + return ret; | |
| 194 | + } | |
| 195 | + | |
| 196 | + static float polyLineLength(float[] poly, final int off, final int nCoords) { | |
| 197 | + assert nCoords % 2 == 0 && poly.length >= off + nCoords : ""; | |
| 198 | + float acc = 0; | |
| 199 | + for (int i = off + 2; i < off + nCoords; i += 2) { | |
| 200 | + acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]); | |
| 201 | + } | |
| 202 | + return acc; | |
| 203 | + } | |
| 204 | + | |
| 205 | + static float linelen(float x1, float y1, float x2, float y2) { | |
| 206 | + final float dx = x2 - x1; | |
| 207 | + final float dy = y2 - y1; | |
| 208 | + return (float)Math.sqrt(dx*dx + dy*dy); | |
| 209 | + } | |
| 210 | + | |
| 211 | + static void subdivide(float[] src, int srcoff, float[] left, int leftoff, | |
| 212 | + float[] right, int rightoff, int type) | |
| 213 | + { | |
| 214 | + switch(type) { | |
| 215 | + case 6: | |
| 216 | + Helpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff); | |
| 217 | + break; | |
| 218 | + case 8: | |
| 219 | + Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff); | |
| 220 | + break; | |
| 221 | + default: | |
| 222 | + throw new InternalError("Unsupported curve type"); | |
| 223 | + } | |
| 224 | + } | |
| 225 | + | |
| 226 | + static void isort(float[] a, int off, int len) { | |
| 227 | + for (int i = off + 1; i < off + len; i++) { | |
| 228 | + float ai = a[i]; | |
| 229 | + int j = i - 1; | |
| 230 | + for (; j >= off && a[j] > ai; j--) { | |
| 231 | + a[j+1] = a[j]; | |
| 232 | + } | |
| 233 | + a[j+1] = ai; | |
| 234 | + } | |
| 235 | + } | |
| 236 | + | |
| 237 | + // Most of these are copied from classes in java.awt.geom because we need | |
| 238 | + // float versions of these functions, and Line2D, CubicCurve2D, | |
| 239 | + // QuadCurve2D don't provide them. | |
| 240 | + /** | |
| 241 | + * Subdivides the cubic curve specified by the coordinates | |
| 242 | + * stored in the <code>src</code> array at indices <code>srcoff</code> | |
| 243 | + * through (<code>srcoff</code> + 7) and stores the | |
| 244 | + * resulting two subdivided curves into the two result arrays at the | |
| 245 | + * corresponding indices. | |
| 246 | + * Either or both of the <code>left</code> and <code>right</code> | |
| 247 | + * arrays may be <code>null</code> or a reference to the same array | |
| 248 | + * as the <code>src</code> array. | |
| 249 | + * Note that the last point in the first subdivided curve is the | |
| 250 | + * same as the first point in the second subdivided curve. Thus, | |
| 251 | + * it is possible to pass the same array for <code>left</code> | |
| 252 | + * and <code>right</code> and to use offsets, such as <code>rightoff</code> | |
| 253 | + * equals (<code>leftoff</code> + 6), in order | |
| 254 | + * to avoid allocating extra storage for this common point. | |
| 255 | + * @param src the array holding the coordinates for the source curve | |
| 256 | + * @param srcoff the offset into the array of the beginning of the | |
| 257 | + * the 6 source coordinates | |
| 258 | + * @param left the array for storing the coordinates for the first | |
| 259 | + * half of the subdivided curve | |
| 260 | + * @param leftoff the offset into the array of the beginning of the | |
| 261 | + * the 6 left coordinates | |
| 262 | + * @param right the array for storing the coordinates for the second | |
| 263 | + * half of the subdivided curve | |
| 264 | + * @param rightoff the offset into the array of the beginning of the | |
| 265 | + * the 6 right coordinates | |
| 266 | + * @since 1.7 | |
| 267 | + */ | |
| 268 | + static void subdivideCubic(float src[], int srcoff, | |
| 269 | + float left[], int leftoff, | |
| 270 | + float right[], int rightoff) | |
| 271 | + { | |
| 272 | + float x1 = src[srcoff + 0]; | |
| 273 | + float y1 = src[srcoff + 1]; | |
| 274 | + float ctrlx1 = src[srcoff + 2]; | |
| 275 | + float ctrly1 = src[srcoff + 3]; | |
| 276 | + float ctrlx2 = src[srcoff + 4]; | |
| 277 | + float ctrly2 = src[srcoff + 5]; | |
| 278 | + float x2 = src[srcoff + 6]; | |
| 279 | + float y2 = src[srcoff + 7]; | |
| 280 | + if (left != null) { | |
| 281 | + left[leftoff + 0] = x1; | |
| 282 | + left[leftoff + 1] = y1; | |
| 283 | + } | |
| 284 | + if (right != null) { | |
| 285 | + right[rightoff + 6] = x2; | |
| 286 | + right[rightoff + 7] = y2; | |
| 287 | + } | |
| 288 | + x1 = (x1 + ctrlx1) / 2.0f; | |
| 289 | + y1 = (y1 + ctrly1) / 2.0f; | |
| 290 | + x2 = (x2 + ctrlx2) / 2.0f; | |
| 291 | + y2 = (y2 + ctrly2) / 2.0f; | |
| 292 | + float centerx = (ctrlx1 + ctrlx2) / 2.0f; | |
| 293 | + float centery = (ctrly1 + ctrly2) / 2.0f; | |
| 294 | + ctrlx1 = (x1 + centerx) / 2.0f; | |
| 295 | + ctrly1 = (y1 + centery) / 2.0f; | |
| 296 | + ctrlx2 = (x2 + centerx) / 2.0f; | |
| 297 | + ctrly2 = (y2 + centery) / 2.0f; | |
| 298 | + centerx = (ctrlx1 + ctrlx2) / 2.0f; | |
| 299 | + centery = (ctrly1 + ctrly2) / 2.0f; | |
| 300 | + if (left != null) { | |
| 301 | + left[leftoff + 2] = x1; | |
| 302 | + left[leftoff + 3] = y1; | |
| 303 | + left[leftoff + 4] = ctrlx1; | |
| 304 | + left[leftoff + 5] = ctrly1; | |
| 305 | + left[leftoff + 6] = centerx; | |
| 306 | + left[leftoff + 7] = centery; | |
| 307 | + } | |
| 308 | + if (right != null) { | |
| 309 | + right[rightoff + 0] = centerx; | |
| 310 | + right[rightoff + 1] = centery; | |
| 311 | + right[rightoff + 2] = ctrlx2; | |
| 312 | + right[rightoff + 3] = ctrly2; | |
| 313 | + right[rightoff + 4] = x2; | |
| 314 | + right[rightoff + 5] = y2; | |
| 315 | + } | |
| 316 | + } | |
| 317 | + | |
| 318 | + | |
| 319 | + static void subdivideCubicAt(float t, float src[], int srcoff, | |
| 320 | + float left[], int leftoff, | |
| 321 | + float right[], int rightoff) | |
| 322 | + { | |
| 323 | + float x1 = src[srcoff + 0]; | |
| 324 | + float y1 = src[srcoff + 1]; | |
| 325 | + float ctrlx1 = src[srcoff + 2]; | |
| 326 | + float ctrly1 = src[srcoff + 3]; | |
| 327 | + float ctrlx2 = src[srcoff + 4]; | |
| 328 | + float ctrly2 = src[srcoff + 5]; | |
| 329 | + float x2 = src[srcoff + 6]; | |
| 330 | + float y2 = src[srcoff + 7]; | |
| 331 | + if (left != null) { | |
| 332 | + left[leftoff + 0] = x1; | |
| 333 | + left[leftoff + 1] = y1; | |
| 334 | + } | |
| 335 | + if (right != null) { | |
| 336 | + right[rightoff + 6] = x2; | |
| 337 | + right[rightoff + 7] = y2; | |
| 338 | + } | |
| 339 | + x1 = x1 + t * (ctrlx1 - x1); | |
| 340 | + y1 = y1 + t * (ctrly1 - y1); | |
| 341 | + x2 = ctrlx2 + t * (x2 - ctrlx2); | |
| 342 | + y2 = ctrly2 + t * (y2 - ctrly2); | |
| 343 | + float centerx = ctrlx1 + t * (ctrlx2 - ctrlx1); | |
| 344 | + float centery = ctrly1 + t * (ctrly2 - ctrly1); | |
| 345 | + ctrlx1 = x1 + t * (centerx - x1); | |
| 346 | + ctrly1 = y1 + t * (centery - y1); | |
| 347 | + ctrlx2 = centerx + t * (x2 - centerx); | |
| 348 | + ctrly2 = centery + t * (y2 - centery); | |
| 349 | + centerx = ctrlx1 + t * (ctrlx2 - ctrlx1); | |
| 350 | + centery = ctrly1 + t * (ctrly2 - ctrly1); | |
| 351 | + if (left != null) { | |
| 352 | + left[leftoff + 2] = x1; | |
| 353 | + left[leftoff + 3] = y1; | |
| 354 | + left[leftoff + 4] = ctrlx1; | |
| 355 | + left[leftoff + 5] = ctrly1; | |
| 356 | + left[leftoff + 6] = centerx; | |
| 357 | + left[leftoff + 7] = centery; | |
| 358 | + } | |
| 359 | + if (right != null) { | |
| 360 | + right[rightoff + 0] = centerx; | |
| 361 | + right[rightoff + 1] = centery; | |
| 362 | + right[rightoff + 2] = ctrlx2; | |
| 363 | + right[rightoff + 3] = ctrly2; | |
| 364 | + right[rightoff + 4] = x2; | |
| 365 | + right[rightoff + 5] = y2; | |
| 366 | + } | |
| 367 | + } | |
| 368 | + | |
| 369 | + static void subdivideQuad(float src[], int srcoff, | |
| 370 | + float left[], int leftoff, | |
| 371 | + float right[], int rightoff) | |
| 372 | + { | |
| 373 | + float x1 = src[srcoff + 0]; | |
| 374 | + float y1 = src[srcoff + 1]; | |
| 375 | + float ctrlx = src[srcoff + 2]; | |
| 376 | + float ctrly = src[srcoff + 3]; | |
| 377 | + float x2 = src[srcoff + 4]; | |
| 378 | + float y2 = src[srcoff + 5]; | |
| 379 | + if (left != null) { | |
| 380 | + left[leftoff + 0] = x1; | |
| 381 | + left[leftoff + 1] = y1; | |
| 382 | + } | |
| 383 | + if (right != null) { | |
| 384 | + right[rightoff + 4] = x2; | |
| 385 | + right[rightoff + 5] = y2; | |
| 386 | + } | |
| 387 | + x1 = (x1 + ctrlx) / 2.0f; | |
| 388 | + y1 = (y1 + ctrly) / 2.0f; | |
| 389 | + x2 = (x2 + ctrlx) / 2.0f; | |
| 390 | + y2 = (y2 + ctrly) / 2.0f; | |
| 391 | + ctrlx = (x1 + x2) / 2.0f; | |
| 392 | + ctrly = (y1 + y2) / 2.0f; | |
| 393 | + if (left != null) { | |
| 394 | + left[leftoff + 2] = x1; | |
| 395 | + left[leftoff + 3] = y1; | |
| 396 | + left[leftoff + 4] = ctrlx; | |
| 397 | + left[leftoff + 5] = ctrly; | |
| 398 | + } | |
| 399 | + if (right != null) { | |
| 400 | + right[rightoff + 0] = ctrlx; | |
| 401 | + right[rightoff + 1] = ctrly; | |
| 402 | + right[rightoff + 2] = x2; | |
| 403 | + right[rightoff + 3] = y2; | |
| 404 | + } | |
| 405 | + } | |
| 406 | + | |
| 407 | + static void subdivideQuadAt(float t, float src[], int srcoff, | |
| 408 | + float left[], int leftoff, | |
| 409 | + float right[], int rightoff) | |
| 410 | + { | |
| 411 | + float x1 = src[srcoff + 0]; | |
| 412 | + float y1 = src[srcoff + 1]; | |
| 413 | + float ctrlx = src[srcoff + 2]; | |
| 414 | + float ctrly = src[srcoff + 3]; | |
| 415 | + float x2 = src[srcoff + 4]; | |
| 416 | + float y2 = src[srcoff + 5]; | |
| 417 | + if (left != null) { | |
| 418 | + left[leftoff + 0] = x1; | |
| 419 | + left[leftoff + 1] = y1; | |
| 420 | + } | |
| 421 | + if (right != null) { | |
| 422 | + right[rightoff + 4] = x2; | |
| 423 | + right[rightoff + 5] = y2; | |
| 424 | + } | |
| 425 | + x1 = x1 + t * (ctrlx - x1); | |
| 426 | + y1 = y1 + t * (ctrly - y1); | |
| 427 | + x2 = ctrlx + t * (x2 - ctrlx); | |
| 428 | + y2 = ctrly + t * (y2 - ctrly); | |
| 429 | + ctrlx = x1 + t * (x2 - x1); | |
| 430 | + ctrly = y1 + t * (y2 - y1); | |
| 431 | + if (left != null) { | |
| 432 | + left[leftoff + 2] = x1; | |
| 433 | + left[leftoff + 3] = y1; | |
| 434 | + left[leftoff + 4] = ctrlx; | |
| 435 | + left[leftoff + 5] = ctrly; | |
| 436 | + } | |
| 437 | + if (right != null) { | |
| 438 | + right[rightoff + 0] = ctrlx; | |
| 439 | + right[rightoff + 1] = ctrly; | |
| 440 | + right[rightoff + 2] = x2; | |
| 441 | + right[rightoff + 3] = y2; | |
| 442 | + } | |
| 443 | + } | |
| 444 | + | |
| 445 | + static void subdivideAt(float t, float src[], int srcoff, | |
| 446 | + float left[], int leftoff, | |
| 447 | + float right[], int rightoff, int size) | |
| 448 | + { | |
| 449 | + switch(size) { | |
| 450 | + case 8: | |
| 451 | + subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff); | |
| 452 | + break; | |
| 453 | + case 6: | |
| 454 | + subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff); | |
| 455 | + break; | |
| 456 | + } | |
| 457 | + } | |
| 458 | +} | |