OLD | NEW |
| (Empty) |
1 /***************************************************************************/ | |
2 /* */ | |
3 /* ftbbox.c */ | |
4 /* */ | |
5 /* FreeType bbox computation (body). */ | |
6 /* */ | |
7 /* Copyright 1996-2002, 2004, 2006, 2010, 2013 by */ | |
8 /* David Turner, Robert Wilhelm, and Werner Lemberg. */ | |
9 /* */ | |
10 /* This file is part of the FreeType project, and may only be used */ | |
11 /* modified and distributed under the terms of the FreeType project */ | |
12 /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ | |
13 /* this file you indicate that you have read the license and */ | |
14 /* understand and accept it fully. */ | |
15 /* */ | |
16 /***************************************************************************/ | |
17 | |
18 | |
19 /*************************************************************************/ | |
20 /* */ | |
21 /* This component has a _single_ role: to compute exact outline bounding */ | |
22 /* boxes. */ | |
23 /* */ | |
24 /*************************************************************************/ | |
25 | |
26 | |
27 #include "../../include/ft2build.h" | |
28 #include "../../include/freetype/internal/ftdebug.h" | |
29 | |
30 #include "../../include/freetype/ftbbox.h" | |
31 #include "../../include/freetype/ftimage.h" | |
32 #include "../../include/freetype/ftoutln.h" | |
33 #include "../../include/freetype/internal/ftcalc.h" | |
34 #include "../../include/freetype/internal/ftobjs.h" | |
35 | |
36 | |
37 typedef struct TBBox_Rec_ | |
38 { | |
39 FT_Vector last; | |
40 FT_BBox bbox; | |
41 | |
42 } TBBox_Rec; | |
43 | |
44 | |
45 /*************************************************************************/ | |
46 /* */ | |
47 /* <Function> */ | |
48 /* BBox_Move_To */ | |
49 /* */ | |
50 /* <Description> */ | |
51 /* This function is used as a `move_to' and `line_to' emitter during */ | |
52 /* FT_Outline_Decompose(). It simply records the destination point */ | |
53 /* in `user->last'; no further computations are necessary since we */ | |
54 /* use the cbox as the starting bbox which must be refined. */ | |
55 /* */ | |
56 /* <Input> */ | |
57 /* to :: A pointer to the destination vector. */ | |
58 /* */ | |
59 /* <InOut> */ | |
60 /* user :: A pointer to the current walk context. */ | |
61 /* */ | |
62 /* <Return> */ | |
63 /* Always 0. Needed for the interface only. */ | |
64 /* */ | |
65 static int | |
66 BBox_Move_To( FT_Vector* to, | |
67 TBBox_Rec* user ) | |
68 { | |
69 user->last = *to; | |
70 | |
71 return 0; | |
72 } | |
73 | |
74 | |
75 #define CHECK_X( p, bbox ) \ | |
76 ( p->x < bbox.xMin || p->x > bbox.xMax ) | |
77 | |
78 #define CHECK_Y( p, bbox ) \ | |
79 ( p->y < bbox.yMin || p->y > bbox.yMax ) | |
80 | |
81 | |
82 /*************************************************************************/ | |
83 /* */ | |
84 /* <Function> */ | |
85 /* BBox_Conic_Check */ | |
86 /* */ | |
87 /* <Description> */ | |
88 /* Finds the extrema of a 1-dimensional conic Bezier curve and update */ | |
89 /* a bounding range. This version uses direct computation, as it */ | |
90 /* doesn't need square roots. */ | |
91 /* */ | |
92 /* <Input> */ | |
93 /* y1 :: The start coordinate. */ | |
94 /* */ | |
95 /* y2 :: The coordinate of the control point. */ | |
96 /* */ | |
97 /* y3 :: The end coordinate. */ | |
98 /* */ | |
99 /* <InOut> */ | |
100 /* min :: The address of the current minimum. */ | |
101 /* */ | |
102 /* max :: The address of the current maximum. */ | |
103 /* */ | |
104 static void | |
105 BBox_Conic_Check( FT_Pos y1, | |
106 FT_Pos y2, | |
107 FT_Pos y3, | |
108 FT_Pos* min, | |
109 FT_Pos* max ) | |
110 { | |
111 if ( y1 <= y3 && y2 == y1 ) /* flat arc */ | |
112 goto Suite; | |
113 | |
114 if ( y1 < y3 ) | |
115 { | |
116 if ( y2 >= y1 && y2 <= y3 ) /* ascending arc */ | |
117 goto Suite; | |
118 } | |
119 else | |
120 { | |
121 if ( y2 >= y3 && y2 <= y1 ) /* descending arc */ | |
122 { | |
123 y2 = y1; | |
124 y1 = y3; | |
125 y3 = y2; | |
126 goto Suite; | |
127 } | |
128 } | |
129 | |
130 y1 = y3 = y1 - FT_MulDiv( y2 - y1, y2 - y1, y1 - 2*y2 + y3 ); | |
131 | |
132 Suite: | |
133 if ( y1 < *min ) *min = y1; | |
134 if ( y3 > *max ) *max = y3; | |
135 } | |
136 | |
137 | |
138 /*************************************************************************/ | |
139 /* */ | |
140 /* <Function> */ | |
141 /* BBox_Conic_To */ | |
142 /* */ | |
143 /* <Description> */ | |
144 /* This function is used as a `conic_to' emitter during */ | |
145 /* FT_Outline_Decompose(). It checks a conic Bezier curve with the */ | |
146 /* current bounding box, and computes its extrema if necessary to */ | |
147 /* update it. */ | |
148 /* */ | |
149 /* <Input> */ | |
150 /* control :: A pointer to a control point. */ | |
151 /* */ | |
152 /* to :: A pointer to the destination vector. */ | |
153 /* */ | |
154 /* <InOut> */ | |
155 /* user :: The address of the current walk context. */ | |
156 /* */ | |
157 /* <Return> */ | |
158 /* Always 0. Needed for the interface only. */ | |
159 /* */ | |
160 /* <Note> */ | |
161 /* In the case of a non-monotonous arc, we compute directly the */ | |
162 /* extremum coordinates, as it is sufficiently fast. */ | |
163 /* */ | |
164 static int | |
165 BBox_Conic_To( FT_Vector* control, | |
166 FT_Vector* to, | |
167 TBBox_Rec* user ) | |
168 { | |
169 /* we don't need to check `to' since it is always an `on' point, thus */ | |
170 /* within the bbox */ | |
171 | |
172 if ( CHECK_X( control, user->bbox ) ) | |
173 BBox_Conic_Check( user->last.x, | |
174 control->x, | |
175 to->x, | |
176 &user->bbox.xMin, | |
177 &user->bbox.xMax ); | |
178 | |
179 if ( CHECK_Y( control, user->bbox ) ) | |
180 BBox_Conic_Check( user->last.y, | |
181 control->y, | |
182 to->y, | |
183 &user->bbox.yMin, | |
184 &user->bbox.yMax ); | |
185 | |
186 user->last = *to; | |
187 | |
188 return 0; | |
189 } | |
190 | |
191 | |
192 /*************************************************************************/ | |
193 /* */ | |
194 /* <Function> */ | |
195 /* BBox_Cubic_Check */ | |
196 /* */ | |
197 /* <Description> */ | |
198 /* Finds the extrema of a 1-dimensional cubic Bezier curve and */ | |
199 /* updates a bounding range. This version uses splitting because we */ | |
200 /* don't want to use square roots and extra accuracy. */ | |
201 /* */ | |
202 /* <Input> */ | |
203 /* p1 :: The start coordinate. */ | |
204 /* */ | |
205 /* p2 :: The coordinate of the first control point. */ | |
206 /* */ | |
207 /* p3 :: The coordinate of the second control point. */ | |
208 /* */ | |
209 /* p4 :: The end coordinate. */ | |
210 /* */ | |
211 /* <InOut> */ | |
212 /* min :: The address of the current minimum. */ | |
213 /* */ | |
214 /* max :: The address of the current maximum. */ | |
215 /* */ | |
216 | |
217 #if 0 | |
218 | |
219 static void | |
220 BBox_Cubic_Check( FT_Pos p1, | |
221 FT_Pos p2, | |
222 FT_Pos p3, | |
223 FT_Pos p4, | |
224 FT_Pos* min, | |
225 FT_Pos* max ) | |
226 { | |
227 FT_Pos q1, q2, q3, q4; | |
228 | |
229 | |
230 q1 = p1; | |
231 q2 = p2; | |
232 q3 = p3; | |
233 q4 = p4; | |
234 | |
235 /* for a conic segment to possibly reach new maximum */ | |
236 /* one of its off-points must be above the current value */ | |
237 while ( q2 > *max || q3 > *max ) | |
238 { | |
239 /* determine which half contains the maximum and split */ | |
240 if ( q1 + q2 > q3 + q4 ) /* first half */ | |
241 { | |
242 q4 = q4 + q3; | |
243 q3 = q3 + q2; | |
244 q2 = q2 + q1; | |
245 q4 = q4 + q3; | |
246 q3 = q3 + q2; | |
247 q4 = ( q4 + q3 ) / 8; | |
248 q3 = q3 / 4; | |
249 q2 = q2 / 2; | |
250 } | |
251 else /* second half */ | |
252 { | |
253 q1 = q1 + q2; | |
254 q2 = q2 + q3; | |
255 q3 = q3 + q4; | |
256 q1 = q1 + q2; | |
257 q2 = q2 + q3; | |
258 q1 = ( q1 + q2 ) / 8; | |
259 q2 = q2 / 4; | |
260 q3 = q3 / 2; | |
261 } | |
262 | |
263 /* check if either end reached the maximum */ | |
264 if ( q1 == q2 && q1 >= q3 ) | |
265 { | |
266 *max = q1; | |
267 break; | |
268 } | |
269 if ( q3 == q4 && q2 <= q4 ) | |
270 { | |
271 *max = q4; | |
272 break; | |
273 } | |
274 } | |
275 | |
276 q1 = p1; | |
277 q2 = p2; | |
278 q3 = p3; | |
279 q4 = p4; | |
280 | |
281 /* for a conic segment to possibly reach new minimum */ | |
282 /* one of its off-points must be below the current value */ | |
283 while ( q2 < *min || q3 < *min ) | |
284 { | |
285 /* determine which half contains the minimum and split */ | |
286 if ( q1 + q2 < q3 + q4 ) /* first half */ | |
287 { | |
288 q4 = q4 + q3; | |
289 q3 = q3 + q2; | |
290 q2 = q2 + q1; | |
291 q4 = q4 + q3; | |
292 q3 = q3 + q2; | |
293 q4 = ( q4 + q3 ) / 8; | |
294 q3 = q3 / 4; | |
295 q2 = q2 / 2; | |
296 } | |
297 else /* second half */ | |
298 { | |
299 q1 = q1 + q2; | |
300 q2 = q2 + q3; | |
301 q3 = q3 + q4; | |
302 q1 = q1 + q2; | |
303 q2 = q2 + q3; | |
304 q1 = ( q1 + q2 ) / 8; | |
305 q2 = q2 / 4; | |
306 q3 = q3 / 2; | |
307 } | |
308 | |
309 /* check if either end reached the minimum */ | |
310 if ( q1 == q2 && q1 <= q3 ) | |
311 { | |
312 *min = q1; | |
313 break; | |
314 } | |
315 if ( q3 == q4 && q2 >= q4 ) | |
316 { | |
317 *min = q4; | |
318 break; | |
319 } | |
320 } | |
321 } | |
322 | |
323 #else | |
324 | |
325 static void | |
326 test_cubic_extrema( FT_Pos y1, | |
327 FT_Pos y2, | |
328 FT_Pos y3, | |
329 FT_Pos y4, | |
330 FT_Fixed u, | |
331 FT_Pos* min, | |
332 FT_Pos* max ) | |
333 { | |
334 /* FT_Pos a = y4 - 3*y3 + 3*y2 - y1; */ | |
335 FT_Pos b = y3 - 2*y2 + y1; | |
336 FT_Pos c = y2 - y1; | |
337 FT_Pos d = y1; | |
338 FT_Pos y; | |
339 FT_Fixed uu; | |
340 | |
341 FT_UNUSED ( y4 ); | |
342 | |
343 | |
344 /* The polynomial is */ | |
345 /* */ | |
346 /* P(x) = a*x^3 + 3b*x^2 + 3c*x + d , */ | |
347 /* */ | |
348 /* dP/dx = 3a*x^2 + 6b*x + 3c . */ | |
349 /* */ | |
350 /* However, we also have */ | |
351 /* */ | |
352 /* dP/dx(u) = 0 , */ | |
353 /* */ | |
354 /* which implies by subtraction that */ | |
355 /* */ | |
356 /* P(u) = b*u^2 + 2c*u + d . */ | |
357 | |
358 if ( u > 0 && u < 0x10000L ) | |
359 { | |
360 uu = FT_MulFix( u, u ); | |
361 y = d + FT_MulFix( c, 2*u ) + FT_MulFix( b, uu ); | |
362 | |
363 if ( y < *min ) *min = y; | |
364 if ( y > *max ) *max = y; | |
365 } | |
366 } | |
367 | |
368 | |
369 static void | |
370 BBox_Cubic_Check( FT_Pos y1, | |
371 FT_Pos y2, | |
372 FT_Pos y3, | |
373 FT_Pos y4, | |
374 FT_Pos* min, | |
375 FT_Pos* max ) | |
376 { | |
377 /* always compare first and last points */ | |
378 if ( y1 < *min ) *min = y1; | |
379 else if ( y1 > *max ) *max = y1; | |
380 | |
381 if ( y4 < *min ) *min = y4; | |
382 else if ( y4 > *max ) *max = y4; | |
383 | |
384 /* now, try to see if there are split points here */ | |
385 if ( y1 <= y4 ) | |
386 { | |
387 /* flat or ascending arc test */ | |
388 if ( y1 <= y2 && y2 <= y4 && y1 <= y3 && y3 <= y4 ) | |
389 return; | |
390 } | |
391 else /* y1 > y4 */ | |
392 { | |
393 /* descending arc test */ | |
394 if ( y1 >= y2 && y2 >= y4 && y1 >= y3 && y3 >= y4 ) | |
395 return; | |
396 } | |
397 | |
398 /* There are some split points. Find them. */ | |
399 /* We already made sure that a, b, and c below cannot be all zero. */ | |
400 { | |
401 FT_Pos a = y4 - 3*y3 + 3*y2 - y1; | |
402 FT_Pos b = y3 - 2*y2 + y1; | |
403 FT_Pos c = y2 - y1; | |
404 FT_Pos d; | |
405 FT_Fixed t; | |
406 FT_Int shift; | |
407 | |
408 | |
409 /* We need to solve `ax^2+2bx+c' here, without floating points! */ | |
410 /* The trick is to normalize to a different representation in order */ | |
411 /* to use our 16.16 fixed-point routines. */ | |
412 /* */ | |
413 /* We compute FT_MulFix(b,b) and FT_MulFix(a,c) after normalization. */ | |
414 /* These values must fit into a single 16.16 value. */ | |
415 /* */ | |
416 /* We normalize a, b, and c to `8.16' fixed-point values to ensure */ | |
417 /* that their product is held in a `16.16' value including the sign. */ | |
418 /* Necessarily, we need to shift `a', `b', and `c' so that the most */ | |
419 /* significant bit of their absolute values is at position 22. */ | |
420 /* */ | |
421 /* This also means that we are using 23 bits of precision to compute */ | |
422 /* the zeros, independently of the range of the original polynomial */ | |
423 /* coefficients. */ | |
424 /* */ | |
425 /* This algorithm should ensure reasonably accurate values for the */ | |
426 /* zeros. Note that they are only expressed with 16 bits when */ | |
427 /* computing the extrema (the zeros need to be in 0..1 exclusive */ | |
428 /* to be considered part of the arc). */ | |
429 | |
430 shift = FT_MSB( FT_ABS( a ) | FT_ABS( b ) | FT_ABS( c ) ); | |
431 | |
432 if ( shift > 22 ) | |
433 { | |
434 shift -= 22; | |
435 | |
436 /* this loses some bits of precision, but we use 23 of them */ | |
437 /* for the computation anyway */ | |
438 a >>= shift; | |
439 b >>= shift; | |
440 c >>= shift; | |
441 } | |
442 else | |
443 { | |
444 shift = 22 - shift; | |
445 | |
446 a <<= shift; | |
447 b <<= shift; | |
448 c <<= shift; | |
449 } | |
450 | |
451 /* handle a == 0 */ | |
452 if ( a == 0 ) | |
453 { | |
454 if ( b != 0 ) | |
455 { | |
456 t = - FT_DivFix( c, b ) / 2; | |
457 test_cubic_extrema( y1, y2, y3, y4, t, min, max ); | |
458 } | |
459 } | |
460 else | |
461 { | |
462 /* solve the equation now */ | |
463 d = FT_MulFix( b, b ) - FT_MulFix( a, c ); | |
464 if ( d < 0 ) | |
465 return; | |
466 | |
467 if ( d == 0 ) | |
468 { | |
469 /* there is a single split point at -b/a */ | |
470 t = - FT_DivFix( b, a ); | |
471 test_cubic_extrema( y1, y2, y3, y4, t, min, max ); | |
472 } | |
473 else | |
474 { | |
475 /* there are two solutions; we need to filter them */ | |
476 d = FT_SqrtFixed( (FT_Int32)d ); | |
477 t = - FT_DivFix( b - d, a ); | |
478 test_cubic_extrema( y1, y2, y3, y4, t, min, max ); | |
479 | |
480 t = - FT_DivFix( b + d, a ); | |
481 test_cubic_extrema( y1, y2, y3, y4, t, min, max ); | |
482 } | |
483 } | |
484 } | |
485 } | |
486 | |
487 #endif | |
488 | |
489 | |
490 /*************************************************************************/ | |
491 /* */ | |
492 /* <Function> */ | |
493 /* BBox_Cubic_To */ | |
494 /* */ | |
495 /* <Description> */ | |
496 /* This function is used as a `cubic_to' emitter during */ | |
497 /* FT_Outline_Decompose(). It checks a cubic Bezier curve with the */ | |
498 /* current bounding box, and computes its extrema if necessary to */ | |
499 /* update it. */ | |
500 /* */ | |
501 /* <Input> */ | |
502 /* control1 :: A pointer to the first control point. */ | |
503 /* */ | |
504 /* control2 :: A pointer to the second control point. */ | |
505 /* */ | |
506 /* to :: A pointer to the destination vector. */ | |
507 /* */ | |
508 /* <InOut> */ | |
509 /* user :: The address of the current walk context. */ | |
510 /* */ | |
511 /* <Return> */ | |
512 /* Always 0. Needed for the interface only. */ | |
513 /* */ | |
514 /* <Note> */ | |
515 /* In the case of a non-monotonous arc, we don't compute directly */ | |
516 /* extremum coordinates, we subdivide instead. */ | |
517 /* */ | |
518 static int | |
519 BBox_Cubic_To( FT_Vector* control1, | |
520 FT_Vector* control2, | |
521 FT_Vector* to, | |
522 TBBox_Rec* user ) | |
523 { | |
524 /* we don't need to check `to' since it is always an `on' point, thus */ | |
525 /* within the bbox */ | |
526 | |
527 if ( CHECK_X( control1, user->bbox ) || | |
528 CHECK_X( control2, user->bbox ) ) | |
529 BBox_Cubic_Check( user->last.x, | |
530 control1->x, | |
531 control2->x, | |
532 to->x, | |
533 &user->bbox.xMin, | |
534 &user->bbox.xMax ); | |
535 | |
536 if ( CHECK_Y( control1, user->bbox ) || | |
537 CHECK_Y( control2, user->bbox ) ) | |
538 BBox_Cubic_Check( user->last.y, | |
539 control1->y, | |
540 control2->y, | |
541 to->y, | |
542 &user->bbox.yMin, | |
543 &user->bbox.yMax ); | |
544 | |
545 user->last = *to; | |
546 | |
547 return 0; | |
548 } | |
549 | |
550 FT_DEFINE_OUTLINE_FUNCS(bbox_interface, | |
551 (FT_Outline_MoveTo_Func) BBox_Move_To, | |
552 (FT_Outline_LineTo_Func) BBox_Move_To, | |
553 (FT_Outline_ConicTo_Func)BBox_Conic_To, | |
554 (FT_Outline_CubicTo_Func)BBox_Cubic_To, | |
555 0, 0 | |
556 ) | |
557 | |
558 /* documentation is in ftbbox.h */ | |
559 | |
560 FT_EXPORT_DEF( FT_Error ) | |
561 FT_Outline_Get_BBox( FT_Outline* outline, | |
562 FT_BBox *abbox ) | |
563 { | |
564 FT_BBox cbox; | |
565 FT_BBox bbox; | |
566 FT_Vector* vec; | |
567 FT_UShort n; | |
568 | |
569 | |
570 if ( !abbox ) | |
571 return FT_THROW( Invalid_Argument ); | |
572 | |
573 if ( !outline ) | |
574 return FT_THROW( Invalid_Outline ); | |
575 | |
576 /* if outline is empty, return (0,0,0,0) */ | |
577 if ( outline->n_points == 0 || outline->n_contours <= 0 ) | |
578 { | |
579 abbox->xMin = abbox->xMax = 0; | |
580 abbox->yMin = abbox->yMax = 0; | |
581 return 0; | |
582 } | |
583 | |
584 /* We compute the control box as well as the bounding box of */ | |
585 /* all `on' points in the outline. Then, if the two boxes */ | |
586 /* coincide, we exit immediately. */ | |
587 | |
588 vec = outline->points; | |
589 bbox.xMin = bbox.xMax = cbox.xMin = cbox.xMax = vec->x; | |
590 bbox.yMin = bbox.yMax = cbox.yMin = cbox.yMax = vec->y; | |
591 vec++; | |
592 | |
593 for ( n = 1; n < outline->n_points; n++ ) | |
594 { | |
595 FT_Pos x = vec->x; | |
596 FT_Pos y = vec->y; | |
597 | |
598 | |
599 /* update control box */ | |
600 if ( x < cbox.xMin ) cbox.xMin = x; | |
601 if ( x > cbox.xMax ) cbox.xMax = x; | |
602 | |
603 if ( y < cbox.yMin ) cbox.yMin = y; | |
604 if ( y > cbox.yMax ) cbox.yMax = y; | |
605 | |
606 if ( FT_CURVE_TAG( outline->tags[n] ) == FT_CURVE_TAG_ON ) | |
607 { | |
608 /* update bbox for `on' points only */ | |
609 if ( x < bbox.xMin ) bbox.xMin = x; | |
610 if ( x > bbox.xMax ) bbox.xMax = x; | |
611 | |
612 if ( y < bbox.yMin ) bbox.yMin = y; | |
613 if ( y > bbox.yMax ) bbox.yMax = y; | |
614 } | |
615 | |
616 vec++; | |
617 } | |
618 | |
619 /* test two boxes for equality */ | |
620 if ( cbox.xMin < bbox.xMin || cbox.xMax > bbox.xMax || | |
621 cbox.yMin < bbox.yMin || cbox.yMax > bbox.yMax ) | |
622 { | |
623 /* the two boxes are different, now walk over the outline to */ | |
624 /* get the Bezier arc extrema. */ | |
625 | |
626 FT_Error error; | |
627 TBBox_Rec user; | |
628 | |
629 #ifdef FT_CONFIG_OPTION_PIC | |
630 FT_Outline_Funcs bbox_interface; | |
631 Init_Class_bbox_interface(&bbox_interface); | |
632 #endif | |
633 | |
634 user.bbox = bbox; | |
635 | |
636 error = FT_Outline_Decompose( outline, &bbox_interface, &user ); | |
637 if ( error ) | |
638 return error; | |
639 | |
640 *abbox = user.bbox; | |
641 } | |
642 else | |
643 *abbox = bbox; | |
644 | |
645 return FT_Err_Ok; | |
646 } | |
647 | |
648 | |
649 /* END */ | |
OLD | NEW |