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} array at indices {@code srcoff} 243 * through ({@code srcoff} + 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} and {@code right} 247 * arrays may be {@code null} or a reference to the same array 248 * as the {@code src} 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} 252 * and {@code right} and to use offsets, such as {@code rightoff} 253 * equals ({@code leftoff} + 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 } --- EOF ---