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 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 != 0.0f) {
56 final float dis = b*b - 4*a*c;
57 if (dis > 0.0f) {
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 >= 0.0f) {
64 zeroes[ret++] = (2.0f * c) / (-b - sqrtDis);
65 zeroes[ret++] = (-b - sqrtDis) / (2.0f * a);
66 } else {
67 zeroes[ret++] = (-b + sqrtDis) / (2.0f * a);
68 zeroes[ret++] = (2.0f * c) / (-b + sqrtDis);
69 }
70 } else if (dis == 0.0f) {
71 t = (-b) / (2.0f * a);
72 zeroes[ret++] = t;
73 }
74 } else {
75 if (b != 0.0f) {
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 == 0.0f) {
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 = (1.0d/3.0d) * ((-1.0d/3.0d) * sq_A + b);
113 double q = (1.0d/2.0d) * ((2.0d/27.0d) * a * sq_A - (1.0d/3.0d) * 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 < 0.0d) {
122 // see: http://en.wikipedia.org/wiki/Cubic_function#Trigonometric_.28and_hyperbolic.29_method
123 final double phi = (1.0d/3.0d) * acos(-q / sqrt(-cb_p));
124 final double t = 2.0d * sqrt(-p);
125
126 pts[ off+0 ] = (float) ( t * cos(phi));
127 pts[ off+1 ] = (float) (-t * cos(phi + (PI / 3.0d)));
128 pts[ off+2 ] = (float) (-t * cos(phi - (PI / 3.0d)));
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, 0.0d, 1e-8d)) {
139 pts[off+1] = -(pts[off] / 2.0f);
140 num = 2;
141 }
142 }
143
144 final float sub = (1.0f/3.0f) * 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 = 0.0f;
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 // both single and double precision variants of these functions, and Line2D,
222 // CubicCurve2D, 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> + 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) / 2.0f;
272 y1 = (y1 + ctrly1) / 2.0f;
273 x2 = (x2 + ctrlx2) / 2.0f;
274 y2 = (y2 + ctrly2) / 2.0f;
275 float centerx = (ctrlx1 + ctrlx2) / 2.0f;
276 float centery = (ctrly1 + ctrly2) / 2.0f;
277 ctrlx1 = (x1 + centerx) / 2.0f;
278 ctrly1 = (y1 + centery) / 2.0f;
279 ctrlx2 = (x2 + centerx) / 2.0f;
280 ctrly2 = (y2 + centery) / 2.0f;
281 centerx = (ctrlx1 + ctrlx2) / 2.0f;
282 centery = (ctrly1 + ctrly2) / 2.0f;
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) / 2.0f;
371 y1 = (y1 + ctrly) / 2.0f;
372 x2 = (x2 + ctrlx) / 2.0f;
373 y2 = (y2 + ctrly) / 2.0f;
374 ctrlx = (x1 + x2) / 2.0f;
375 ctrly = (y1 + y2) / 2.0f;
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 }