1 /*
2 * Copyright (c) 2007, 2017, 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 DHelpers implements MarlinConst {
35
36 private DHelpers() {
37 throw new Error("This is a non instantiable class");
38 }
39
40 static boolean within(final double x, final double y, final double err) {
41 final double d = y - x;
42 return (d <= err && d >= -err);
43 }
44
45 static int quadraticRoots(final double a, final double b,
46 final double c, double[] zeroes, final int off)
47 {
48 int ret = off;
49 double t;
50 if (a != 0.0d) {
51 final double dis = b*b - 4*a*c;
52 if (dis > 0.0d) {
53 final double sqrtDis = Math.sqrt(dis);
54 // depending on the sign of b we use a slightly different
55 // algorithm than the traditional one to find one of the roots
56 // so we can avoid adding numbers of different signs (which
57 // might result in loss of precision).
58 if (b >= 0.0d) {
59 zeroes[ret++] = (2.0d * c) / (-b - sqrtDis);
60 zeroes[ret++] = (-b - sqrtDis) / (2.0d * a);
61 } else {
62 zeroes[ret++] = (-b + sqrtDis) / (2.0d * a);
63 zeroes[ret++] = (2.0d * c) / (-b + sqrtDis);
64 }
65 } else if (dis == 0.0d) {
66 t = (-b) / (2.0d * a);
67 zeroes[ret++] = t;
68 }
69 } else {
70 if (b != 0.0d) {
71 t = (-c) / b;
72 zeroes[ret++] = t;
73 }
74 }
75 return ret - off;
76 }
77
78 // find the roots of g(t) = d*t^3 + a*t^2 + b*t + c in [A,B)
79 static int cubicRootsInAB(double d, double a, double b, double c,
80 double[] pts, final int off,
81 final double A, final double B)
82 {
83 if (d == 0.0d) {
84 int num = quadraticRoots(a, b, c, pts, off);
85 return filterOutNotInAB(pts, off, num, A, B) - off;
86 }
87 // From Graphics Gems:
88 // http://tog.acm.org/resources/GraphicsGems/gems/Roots3And4.c
89 // (also from awt.geom.CubicCurve2D. But here we don't need as
90 // much accuracy and we don't want to create arrays so we use
91 // our own customized version).
92
93 // normal form: x^3 + ax^2 + bx + c = 0
94 a /= d;
95 b /= d;
96 c /= d;
97
98 // substitute x = y - A/3 to eliminate quadratic term:
99 // x^3 +Px + Q = 0
100 //
101 // Since we actually need P/3 and Q/2 for all of the
102 // calculations that follow, we will calculate
103 // p = P/3
104 // q = Q/2
105 // instead and use those values for simplicity of the code.
106 double sq_A = a * a;
107 double p = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
108 double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * a * b + c);
109
110 // use Cardano's formula
111
112 double cb_p = p * p * p;
113 double D = q * q + cb_p;
114
115 int num;
116 if (D < 0.0d) {
117 // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
118 final double phi = (1.0d/3.0d) * acos(-q / sqrt(-cb_p));
119 final double t = 2.0d * sqrt(-p);
120
121 pts[ off+0 ] = ( t * cos(phi));
122 pts[ off+1 ] = (-t * cos(phi + (PI / 3.0d)));
123 pts[ off+2 ] = (-t * cos(phi - (PI / 3.0d)));
124 num = 3;
125 } else {
126 final double sqrt_D = sqrt(D);
127 final double u = cbrt(sqrt_D - q);
128 final double v = - cbrt(sqrt_D + q);
129
130 pts[ off ] = (u + v);
131 num = 1;
132
133 if (within(D, 0.0d, 1e-8d)) {
134 pts[off+1] = -(pts[off] / 2.0d);
135 num = 2;
136 }
137 }
138
139 final double sub = (1.0d/3.0d) * a;
140
141 for (int i = 0; i < num; ++i) {
142 pts[ off+i ] -= sub;
143 }
144
145 return filterOutNotInAB(pts, off, num, A, B) - off;
146 }
147
148 static double evalCubic(final double a, final double b,
149 final double c, final double d,
150 final double t)
151 {
152 return t * (t * (t * a + b) + c) + d;
153 }
154
155 static double evalQuad(final double a, final double b,
156 final double c, final double t)
157 {
158 return t * (t * a + b) + c;
159 }
160
161 // returns the index 1 past the last valid element remaining after filtering
162 static int filterOutNotInAB(double[] nums, final int off, final int len,
163 final double a, final double b)
164 {
165 int ret = off;
166 for (int i = off, end = off + len; i < end; i++) {
167 if (nums[i] >= a && nums[i] < b) {
168 nums[ret++] = nums[i];
169 }
170 }
171 return ret;
172 }
173
174 static double polyLineLength(double[] poly, final int off, final int nCoords) {
175 assert nCoords % 2 == 0 && poly.length >= off + nCoords : "";
176 double acc = 0.0d;
177 for (int i = off + 2; i < off + nCoords; i += 2) {
178 acc += linelen(poly[i], poly[i+1], poly[i-2], poly[i-1]);
179 }
180 return acc;
181 }
182
183 static double linelen(double x1, double y1, double x2, double y2) {
184 final double dx = x2 - x1;
185 final double dy = y2 - y1;
186 return Math.sqrt(dx*dx + dy*dy);
187 }
188
189 static void subdivide(double[] src, int srcoff, double[] left, int leftoff,
190 double[] right, int rightoff, int type)
191 {
192 switch(type) {
193 case 6:
194 DHelpers.subdivideQuad(src, srcoff, left, leftoff, right, rightoff);
195 return;
196 case 8:
197 DHelpers.subdivideCubic(src, srcoff, left, leftoff, right, rightoff);
198 return;
199 default:
200 throw new InternalError("Unsupported curve type");
201 }
202 }
203
204 static void isort(double[] a, int off, int len) {
205 for (int i = off + 1, end = off + len; i < end; i++) {
206 double ai = a[i];
207 int j = i - 1;
208 for (; j >= off && a[j] > ai; j--) {
209 a[j+1] = a[j];
210 }
211 a[j+1] = ai;
212 }
213 }
214
215 // Most of these are copied from classes in java.awt.geom because we need
216 // both single and double precision variants of these functions, and Line2D,
217 // CubicCurve2D, QuadCurve2D don't provide them.
218 /**
219 * Subdivides the cubic curve specified by the coordinates
220 * stored in the <code>src</code> array at indices <code>srcoff</code>
221 * through (<code>srcoff</code> + 7) and stores the
222 * resulting two subdivided curves into the two result arrays at the
223 * corresponding indices.
224 * Either or both of the <code>left</code> and <code>right</code>
225 * arrays may be <code>null</code> or a reference to the same array
226 * as the <code>src</code> array.
227 * Note that the last point in the first subdivided curve is the
228 * same as the first point in the second subdivided curve. Thus,
229 * it is possible to pass the same array for <code>left</code>
230 * and <code>right</code> and to use offsets, such as <code>rightoff</code>
231 * equals (<code>leftoff</code> + 6), in order
232 * to avoid allocating extra storage for this common point.
233 * @param src the array holding the coordinates for the source curve
234 * @param srcoff the offset into the array of the beginning of the
235 * the 6 source coordinates
236 * @param left the array for storing the coordinates for the first
237 * half of the subdivided curve
238 * @param leftoff the offset into the array of the beginning of the
239 * the 6 left coordinates
240 * @param right the array for storing the coordinates for the second
241 * half of the subdivided curve
242 * @param rightoff the offset into the array of the beginning of the
243 * the 6 right coordinates
244 * @since 1.7
245 */
246 static void subdivideCubic(double[] src, int srcoff,
247 double[] left, int leftoff,
248 double[] right, int rightoff)
249 {
250 double x1 = src[srcoff + 0];
251 double y1 = src[srcoff + 1];
252 double ctrlx1 = src[srcoff + 2];
253 double ctrly1 = src[srcoff + 3];
254 double ctrlx2 = src[srcoff + 4];
255 double ctrly2 = src[srcoff + 5];
256 double x2 = src[srcoff + 6];
257 double y2 = src[srcoff + 7];
258 if (left != null) {
259 left[leftoff + 0] = x1;
260 left[leftoff + 1] = y1;
261 }
262 if (right != null) {
263 right[rightoff + 6] = x2;
264 right[rightoff + 7] = y2;
265 }
266 x1 = (x1 + ctrlx1) / 2.0d;
267 y1 = (y1 + ctrly1) / 2.0d;
268 x2 = (x2 + ctrlx2) / 2.0d;
269 y2 = (y2 + ctrly2) / 2.0d;
270 double centerx = (ctrlx1 + ctrlx2) / 2.0d;
271 double centery = (ctrly1 + ctrly2) / 2.0d;
272 ctrlx1 = (x1 + centerx) / 2.0d;
273 ctrly1 = (y1 + centery) / 2.0d;
274 ctrlx2 = (x2 + centerx) / 2.0d;
275 ctrly2 = (y2 + centery) / 2.0d;
276 centerx = (ctrlx1 + ctrlx2) / 2.0d;
277 centery = (ctrly1 + ctrly2) / 2.0d;
278 if (left != null) {
279 left[leftoff + 2] = x1;
280 left[leftoff + 3] = y1;
281 left[leftoff + 4] = ctrlx1;
282 left[leftoff + 5] = ctrly1;
283 left[leftoff + 6] = centerx;
284 left[leftoff + 7] = centery;
285 }
286 if (right != null) {
287 right[rightoff + 0] = centerx;
288 right[rightoff + 1] = centery;
289 right[rightoff + 2] = ctrlx2;
290 right[rightoff + 3] = ctrly2;
291 right[rightoff + 4] = x2;
292 right[rightoff + 5] = y2;
293 }
294 }
295
296
297 static void subdivideCubicAt(double t, double[] src, int srcoff,
298 double[] left, int leftoff,
299 double[] right, int rightoff)
300 {
301 double x1 = src[srcoff + 0];
302 double y1 = src[srcoff + 1];
303 double ctrlx1 = src[srcoff + 2];
304 double ctrly1 = src[srcoff + 3];
305 double ctrlx2 = src[srcoff + 4];
306 double ctrly2 = src[srcoff + 5];
307 double x2 = src[srcoff + 6];
308 double y2 = src[srcoff + 7];
309 if (left != null) {
310 left[leftoff + 0] = x1;
311 left[leftoff + 1] = y1;
312 }
313 if (right != null) {
314 right[rightoff + 6] = x2;
315 right[rightoff + 7] = y2;
316 }
317 x1 = x1 + t * (ctrlx1 - x1);
318 y1 = y1 + t * (ctrly1 - y1);
319 x2 = ctrlx2 + t * (x2 - ctrlx2);
320 y2 = ctrly2 + t * (y2 - ctrly2);
321 double centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
322 double centery = ctrly1 + t * (ctrly2 - ctrly1);
323 ctrlx1 = x1 + t * (centerx - x1);
324 ctrly1 = y1 + t * (centery - y1);
325 ctrlx2 = centerx + t * (x2 - centerx);
326 ctrly2 = centery + t * (y2 - centery);
327 centerx = ctrlx1 + t * (ctrlx2 - ctrlx1);
328 centery = ctrly1 + t * (ctrly2 - ctrly1);
329 if (left != null) {
330 left[leftoff + 2] = x1;
331 left[leftoff + 3] = y1;
332 left[leftoff + 4] = ctrlx1;
333 left[leftoff + 5] = ctrly1;
334 left[leftoff + 6] = centerx;
335 left[leftoff + 7] = centery;
336 }
337 if (right != null) {
338 right[rightoff + 0] = centerx;
339 right[rightoff + 1] = centery;
340 right[rightoff + 2] = ctrlx2;
341 right[rightoff + 3] = ctrly2;
342 right[rightoff + 4] = x2;
343 right[rightoff + 5] = y2;
344 }
345 }
346
347 static void subdivideQuad(double[] src, int srcoff,
348 double[] left, int leftoff,
349 double[] right, int rightoff)
350 {
351 double x1 = src[srcoff + 0];
352 double y1 = src[srcoff + 1];
353 double ctrlx = src[srcoff + 2];
354 double ctrly = src[srcoff + 3];
355 double x2 = src[srcoff + 4];
356 double y2 = src[srcoff + 5];
357 if (left != null) {
358 left[leftoff + 0] = x1;
359 left[leftoff + 1] = y1;
360 }
361 if (right != null) {
362 right[rightoff + 4] = x2;
363 right[rightoff + 5] = y2;
364 }
365 x1 = (x1 + ctrlx) / 2.0d;
366 y1 = (y1 + ctrly) / 2.0d;
367 x2 = (x2 + ctrlx) / 2.0d;
368 y2 = (y2 + ctrly) / 2.0d;
369 ctrlx = (x1 + x2) / 2.0d;
370 ctrly = (y1 + y2) / 2.0d;
371 if (left != null) {
372 left[leftoff + 2] = x1;
373 left[leftoff + 3] = y1;
374 left[leftoff + 4] = ctrlx;
375 left[leftoff + 5] = ctrly;
376 }
377 if (right != null) {
378 right[rightoff + 0] = ctrlx;
379 right[rightoff + 1] = ctrly;
380 right[rightoff + 2] = x2;
381 right[rightoff + 3] = y2;
382 }
383 }
384
385 static void subdivideQuadAt(double t, double[] src, int srcoff,
386 double[] left, int leftoff,
387 double[] right, int rightoff)
388 {
389 double x1 = src[srcoff + 0];
390 double y1 = src[srcoff + 1];
391 double ctrlx = src[srcoff + 2];
392 double ctrly = src[srcoff + 3];
393 double x2 = src[srcoff + 4];
394 double y2 = src[srcoff + 5];
395 if (left != null) {
396 left[leftoff + 0] = x1;
397 left[leftoff + 1] = y1;
398 }
399 if (right != null) {
400 right[rightoff + 4] = x2;
401 right[rightoff + 5] = y2;
402 }
403 x1 = x1 + t * (ctrlx - x1);
404 y1 = y1 + t * (ctrly - y1);
405 x2 = ctrlx + t * (x2 - ctrlx);
406 y2 = ctrly + t * (y2 - ctrly);
407 ctrlx = x1 + t * (x2 - x1);
408 ctrly = y1 + t * (y2 - y1);
409 if (left != null) {
410 left[leftoff + 2] = x1;
411 left[leftoff + 3] = y1;
412 left[leftoff + 4] = ctrlx;
413 left[leftoff + 5] = ctrly;
414 }
415 if (right != null) {
416 right[rightoff + 0] = ctrlx;
417 right[rightoff + 1] = ctrly;
418 right[rightoff + 2] = x2;
419 right[rightoff + 3] = y2;
420 }
421 }
422
423 static void subdivideAt(double t, double[] src, int srcoff,
424 double[] left, int leftoff,
425 double[] right, int rightoff, int size)
426 {
427 switch(size) {
428 case 8:
429 subdivideCubicAt(t, src, srcoff, left, leftoff, right, rightoff);
430 return;
431 case 6:
432 subdivideQuadAt(t, src, srcoff, left, leftoff, right, rightoff);
433 return;
434 }
435 }
436 }
--- EOF ---