1 /*
   2  * Copyright (c) 2007, 2016, 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.marlin;
  27 
  28 import static java.lang.Math.PI;
  29 import static java.lang.Math.cos;
  30 import static java.lang.Math.sqrt;
  31 import static java.lang.Math.cbrt;
  32 import static java.lang.Math.acos;
  33 
  34 final class Helpers implements MarlinConst {
  35 
  36     private Helpers() {
  37         throw new Error("This is a non instantiable class");
  38     }
  39 
  40     static boolean within(final float x, final float y, final float err) {
  41         final float d = y - x;
  42         return (d <= err && d >= -err);
  43     }
  44 
  45     static boolean within(final double x, final double y, final double err) {
  46         final double d = y - x;
  47         return (d <= err && d >= -err);
  48     }
  49 
  50     static int quadraticRoots(final float a, final float b,
  51                               final float c, float[] zeroes, final int off)
  52     {
  53         int ret = off;
  54         float t;
  55         if (a != 0f) {
  56             final float dis = b*b - 4*a*c;
  57             if (dis > 0f) {
  58                 final float sqrtDis = (float)Math.sqrt(dis);
  59                 // depending on the sign of b we use a slightly different
  60                 // algorithm than the traditional one to find one of the roots
  61                 // so we can avoid adding numbers of different signs (which
  62                 // might result in loss of precision).
  63                 if (b >= 0f) {
  64                     zeroes[ret++] = (2f * c) / (-b - sqrtDis);
  65                     zeroes[ret++] = (-b - sqrtDis) / (2f * a);
  66                 } else {
  67                     zeroes[ret++] = (-b + sqrtDis) / (2f * a);
  68                     zeroes[ret++] = (2f * c) / (-b + sqrtDis);
  69                 }
  70             } else if (dis == 0f) {
  71                 t = (-b) / (2f * a);
  72                 zeroes[ret++] = t;
  73             }
  74         } else {
  75             if (b != 0f) {
  76                 t = (-c) / b;
  77                 zeroes[ret++] = t;
  78             }
  79         }
  80         return ret - off;
  81     }
  82 
  83     // find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
  84     static int cubicRootsInAB(float d, float a, float b, float c,
  85                               float[] pts, final int off,
  86                               final float A, final float B)
  87     {
  88         if (d == 0f) {
  89             int num = quadraticRoots(a, b, c, pts, off);
  90             return filterOutNotInAB(pts, off, num, A, B) - off;
  91         }
  92         // From Graphics Gems:
  93         // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
  94         // (also from awt.geom.CubicCurve2D. But here we don't need as
  95         // much accuracy and we don't want to create arrays so we use
  96         // our own customized version).
  97 
  98         // normal form: x^3 + ax^2 + bx + c = 0
  99         a /= d;
 100         b /= d;
 101         c /= d;
 102 
 103         //  substitute x = y - A/3 to eliminate quadratic term:
 104         //     x^3 +Px + Q = 0
 105         //
 106         // Since we actually need P/3 and Q/2 for all of the
 107         // calculations that follow, we will calculate
 108         // p = P/3
 109         // q = Q/2
 110         // instead and use those values for simplicity of the code.
 111         double sq_A = a * a;
 112         double p = (1.0/3.0) * ((-1.0/3.0) * sq_A + b);
 113         double q = (1.0/2.0) * ((2.0/27.0) * a * sq_A - (1.0/3.0) * a * b + c);
 114 
 115         // use Cardano's formula
 116 
 117         double cb_p = p * p * p;
 118         double D = q * q + cb_p;
 119 
 120         int num;
 121         if (D < 0.0) {
 122             // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
 123             final double phi = (1.0/3.0) * acos(-q / sqrt(-cb_p));
 124             final double t = 2.0 * sqrt(-p);
 125 
 126             pts[ off+0 ] =  (float)( t * cos(phi));
 127             pts[ off+1 ] =  (float)(-t * cos(phi + (PI / 3.0)));
 128             pts[ off+2 ] =  (float)(-t * cos(phi - (PI / 3.0)));
 129             num = 3;
 130         } else {
 131             final double sqrt_D = sqrt(D);
 132             final double u = cbrt(sqrt_D - q);
 133             final double v = - cbrt(sqrt_D + q);
 134 
 135             pts[ off ] = (float)(u + v);
 136             num = 1;
 137 
 138             if (within(D, 0.0, 1e-8)) {
 139                 pts[off+1] = -(pts[off] / 2f);
 140                 num = 2;
 141             }
 142         }
 143 
 144         final float sub = (1f/3f) * a;
 145 
 146         for (int i = 0; i < num; ++i) {
 147             pts[ off+i ] -= sub;
 148         }
 149 
 150         return filterOutNotInAB(pts, off, num, A, B) - off;
 151     }
 152 
 153     static float evalCubic(final float a, final float b,
 154                            final float c, final float d,
 155                            final float t)
 156     {
 157         return t * (t * (t * a + b) + c) + d;
 158     }
 159 
 160     static float evalQuad(final float a, final float b,
 161                           final float c, final float t)
 162     {
 163         return t * (t * a + b) + c;
 164     }
 165 
 166     // returns the index 1 past the last valid element remaining after filtering
 167     static int filterOutNotInAB(float[] nums, final int off, final int len,
 168                                 final float a, final float b)
 169     {
 170         int ret = off;
 171         for (int i = off, end = off + len; i < end; i++) {
 172             if (nums[i] >= a && nums[i] < b) {
 173                 nums[ret++] = nums[i];
 174             }
 175         }
 176         return ret;
 177     }
 178 
 179     static float polyLineLength(float[] poly, final int off, final int nCoords) {
 180         assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";
 181         float acc = 0;
 182         for (int i = off + 2; i < off + nCoords; i += 2) {
 183             acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]);
 184         }
 185         return acc;
 186     }
 187 
 188     static float linelen(float x1, float y1, float x2, float y2) {
 189         final float dx = x2 - x1;
 190         final float dy = y2 - y1;
 191         return (float)Math.sqrt(dx*dx + dy*dy);
 192     }
 193 
 194     static void subdivide(float[] src, int srcoff, float[] left, int leftoff,
 195                           float[] right, int rightoff, int type)
 196     {
 197         switch(type) {
 198         case 6:
 199             Helpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
 200             return;
 201         case 8:
 202             Helpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
 203             return;
 204         default:
 205             throw new InternalError("Unsupported curve type");
 206         }
 207     }
 208 
 209     static void isort(float[] a, int off, int len) {
 210         for (int i = off + 1, end = off + len; i < end; i++) {
 211             float ai = a[i];
 212             int j = i - 1;
 213             for (; j >= off && a[j] > ai; j--) {
 214                 a[j+1] = a[j];
 215             }
 216             a[j+1] = ai;
 217         }
 218     }
 219 
 220     // Most of these are copied from classes in java.awt.geom because we need
 221     // float versions of these functions, and Line2D, CubicCurve2D,
 222     // QuadCurve2D don't provide them.
 223     /**
 224      * Subdivides the cubic curve specified by the coordinates
 225      * stored in the <code>src</code> array at indices <code>srcoff</code>
 226      * through (<code>srcoff</code>&nbsp;+&nbsp;7) and stores the
 227      * resulting two subdivided curves into the two result arrays at the
 228      * corresponding indices.
 229      * Either or both of the <code>left</code> and <code>right</code>
 230      * arrays may be <code>null</code> or a reference to the same array
 231      * as the <code>src</code> array.
 232      * Note that the last point in the first subdivided curve is the
 233      * same as the first point in the second subdivided curve. Thus,
 234      * it is possible to pass the same array for <code>left</code>
 235      * and <code>right</code> and to use offsets, such as <code>rightoff</code>
 236      * equals (<code>leftoff</code> + 6), in order
 237      * to avoid allocating extra storage for this common point.
 238      * @param src the array holding the coordinates for the source curve
 239      * @param srcoff the offset into the array of the beginning of the
 240      * the 6 source coordinates
 241      * @param left the array for storing the coordinates for the first
 242      * half of the subdivided curve
 243      * @param leftoff the offset into the array of the beginning of the
 244      * the 6 left coordinates
 245      * @param right the array for storing the coordinates for the second
 246      * half of the subdivided curve
 247      * @param rightoff the offset into the array of the beginning of the
 248      * the 6 right coordinates
 249      * @since 1.7
 250      */
 251     static void subdivideCubic(float[] src, int srcoff,
 252                                float[] left, int leftoff,
 253                                float[] right, int rightoff)
 254     {
 255         float x1 = src[srcoff + 0];
 256         float y1 = src[srcoff + 1];
 257         float ctrlx1 = src[srcoff + 2];
 258         float ctrly1 = src[srcoff + 3];
 259         float ctrlx2 = src[srcoff + 4];
 260         float ctrly2 = src[srcoff + 5];
 261         float x2 = src[srcoff + 6];
 262         float y2 = src[srcoff + 7];
 263         if (left != null) {
 264             left[leftoff + 0] = x1;
 265             left[leftoff + 1] = y1;
 266         }
 267         if (right != null) {
 268             right[rightoff + 6] = x2;
 269             right[rightoff + 7] = y2;
 270         }
 271         x1 = (x1 + ctrlx1) / 2f;
 272         y1 = (y1 + ctrly1) / 2f;
 273         x2 = (x2 + ctrlx2) / 2f;
 274         y2 = (y2 + ctrly2) / 2f;
 275         float centerx = (ctrlx1 + ctrlx2) / 2f;
 276         float centery = (ctrly1 + ctrly2) / 2f;
 277         ctrlx1 = (x1 + centerx) / 2f;
 278         ctrly1 = (y1 + centery) / 2f;
 279         ctrlx2 = (x2 + centerx) / 2f;
 280         ctrly2 = (y2 + centery) / 2f;
 281         centerx = (ctrlx1 + ctrlx2) / 2f;
 282         centery = (ctrly1 + ctrly2) / 2f;
 283         if (left != null) {
 284             left[leftoff + 2] = x1;
 285             left[leftoff + 3] = y1;
 286             left[leftoff + 4] = ctrlx1;
 287             left[leftoff + 5] = ctrly1;
 288             left[leftoff + 6] = centerx;
 289             left[leftoff + 7] = centery;
 290         }
 291         if (right != null) {
 292             right[rightoff + 0] = centerx;
 293             right[rightoff + 1] = centery;
 294             right[rightoff + 2] = ctrlx2;
 295             right[rightoff + 3] = ctrly2;
 296             right[rightoff + 4] = x2;
 297             right[rightoff + 5] = y2;
 298         }
 299     }
 300 
 301 
 302     static void subdivideCubicAt(float t, float[] src, int srcoff,
 303                                  float[] left, int leftoff,
 304                                  float[] right, int rightoff)
 305     {
 306         float x1 = src[srcoff + 0];
 307         float y1 = src[srcoff + 1];
 308         float ctrlx1 = src[srcoff + 2];
 309         float ctrly1 = src[srcoff + 3];
 310         float ctrlx2 = src[srcoff + 4];
 311         float ctrly2 = src[srcoff + 5];
 312         float x2 = src[srcoff + 6];
 313         float y2 = src[srcoff + 7];
 314         if (left != null) {
 315             left[leftoff + 0] = x1;
 316             left[leftoff + 1] = y1;
 317         }
 318         if (right != null) {
 319             right[rightoff + 6] = x2;
 320             right[rightoff + 7] = y2;
 321         }
 322         x1 = x1 + t * (ctrlx1 - x1);
 323         y1 = y1 + t * (ctrly1 - y1);
 324         x2 = ctrlx2 + t * (x2 - ctrlx2);
 325         y2 = ctrly2 + t * (y2 - ctrly2);
 326         float centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
 327         float centery = ctrly1 + t * (ctrly2 - ctrly1);
 328         ctrlx1 = x1 + t * (centerx - x1);
 329         ctrly1 = y1 + t * (centery - y1);
 330         ctrlx2 = centerx + t * (x2 - centerx);
 331         ctrly2 = centery + t * (y2 - centery);
 332         centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
 333         centery = ctrly1 + t * (ctrly2 - ctrly1);
 334         if (left != null) {
 335             left[leftoff + 2] = x1;
 336             left[leftoff + 3] = y1;
 337             left[leftoff + 4] = ctrlx1;
 338             left[leftoff + 5] = ctrly1;
 339             left[leftoff + 6] = centerx;
 340             left[leftoff + 7] = centery;
 341         }
 342         if (right != null) {
 343             right[rightoff + 0] = centerx;
 344             right[rightoff + 1] = centery;
 345             right[rightoff + 2] = ctrlx2;
 346             right[rightoff + 3] = ctrly2;
 347             right[rightoff + 4] = x2;
 348             right[rightoff + 5] = y2;
 349         }
 350     }
 351 
 352     static void subdivideQuad(float[] src, int srcoff,
 353                               float[] left, int leftoff,
 354                               float[] right, int rightoff)
 355     {
 356         float x1 = src[srcoff + 0];
 357         float y1 = src[srcoff + 1];
 358         float ctrlx = src[srcoff + 2];
 359         float ctrly = src[srcoff + 3];
 360         float x2 = src[srcoff + 4];
 361         float y2 = src[srcoff + 5];
 362         if (left != null) {
 363             left[leftoff + 0] = x1;
 364             left[leftoff + 1] = y1;
 365         }
 366         if (right != null) {
 367             right[rightoff + 4] = x2;
 368             right[rightoff + 5] = y2;
 369         }
 370         x1 = (x1 + ctrlx) / 2f;
 371         y1 = (y1 + ctrly) / 2f;
 372         x2 = (x2 + ctrlx) / 2f;
 373         y2 = (y2 + ctrly) / 2f;
 374         ctrlx = (x1 + x2) / 2f;
 375         ctrly = (y1 + y2) / 2f;
 376         if (left != null) {
 377             left[leftoff + 2] = x1;
 378             left[leftoff + 3] = y1;
 379             left[leftoff + 4] = ctrlx;
 380             left[leftoff + 5] = ctrly;
 381         }
 382         if (right != null) {
 383             right[rightoff + 0] = ctrlx;
 384             right[rightoff + 1] = ctrly;
 385             right[rightoff + 2] = x2;
 386             right[rightoff + 3] = y2;
 387         }
 388     }
 389 
 390     static void subdivideQuadAt(float t, float[] src, int srcoff,
 391                                 float[] left, int leftoff,
 392                                 float[] right, int rightoff)
 393     {
 394         float x1 = src[srcoff + 0];
 395         float y1 = src[srcoff + 1];
 396         float ctrlx = src[srcoff + 2];
 397         float ctrly = src[srcoff + 3];
 398         float x2 = src[srcoff + 4];
 399         float y2 = src[srcoff + 5];
 400         if (left != null) {
 401             left[leftoff + 0] = x1;
 402             left[leftoff + 1] = y1;
 403         }
 404         if (right != null) {
 405             right[rightoff + 4] = x2;
 406             right[rightoff + 5] = y2;
 407         }
 408         x1 = x1 + t * (ctrlx - x1);
 409         y1 = y1 + t * (ctrly - y1);
 410         x2 = ctrlx + t * (x2 - ctrlx);
 411         y2 = ctrly + t * (y2 - ctrly);
 412         ctrlx = x1 + t * (x2 - x1);
 413         ctrly = y1 + t * (y2 - y1);
 414         if (left != null) {
 415             left[leftoff + 2] = x1;
 416             left[leftoff + 3] = y1;
 417             left[leftoff + 4] = ctrlx;
 418             left[leftoff + 5] = ctrly;
 419         }
 420         if (right != null) {
 421             right[rightoff + 0] = ctrlx;
 422             right[rightoff + 1] = ctrly;
 423             right[rightoff + 2] = x2;
 424             right[rightoff + 3] = y2;
 425         }
 426     }
 427 
 428     static void subdivideAt(float t, float[] src, int srcoff,
 429                             float[] left, int leftoff,
 430                             float[] right, int rightoff, int size)
 431     {
 432         switch(size) {
 433         case 8:
 434             subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
 435             return;
 436         case 6:
 437             subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
 438             return;
 439         }
 440     }
 441 }
--- EOF ---