34417
|
1 |
/*
|
|
2 |
* Copyright (c) 2007, 2015, 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> + 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 |
}
|