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>&nbsp;+&nbsp;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 }
--- EOF ---