1 /***************************************************************************/ 2 /* */ 3 /* ftbbox.c */ 4 /* */ 5 /* FreeType bbox computation (body). */ 6 /* */ 7 /* Copyright 1996-2018 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 <ft2build.h> 28 #include FT_INTERNAL_DEBUG_H 29 30 #include FT_BBOX_H 31 #include FT_IMAGE_H 32 #include FT_OUTLINE_H 33 #include FT_INTERNAL_CALC_H 34 #include FT_INTERNAL_OBJECTS_H 35 36 37 typedef struct TBBox_Rec_ 38 { 39 FT_Vector last; 40 FT_BBox bbox; 41 42 } TBBox_Rec; 43 44 45 #define FT_UPDATE_BBOX( p, bbox ) \ 46 FT_BEGIN_STMNT \ 47 if ( p->x < bbox.xMin ) \ 48 bbox.xMin = p->x; \ 49 if ( p->x > bbox.xMax ) \ 50 bbox.xMax = p->x; \ 51 if ( p->y < bbox.yMin ) \ 52 bbox.yMin = p->y; \ 53 if ( p->y > bbox.yMax ) \ 54 bbox.yMax = p->y; \ 55 FT_END_STMNT 56 57 #define CHECK_X( p, bbox ) \ 58 ( p->x < bbox.xMin || p->x > bbox.xMax ) 59 60 #define CHECK_Y( p, bbox ) \ 61 ( p->y < bbox.yMin || p->y > bbox.yMax ) 62 63 64 /*************************************************************************/ 65 /* */ 66 /* <Function> */ 67 /* BBox_Move_To */ 68 /* */ 69 /* <Description> */ 70 /* This function is used as a `move_to' emitter during */ 71 /* FT_Outline_Decompose(). It simply records the destination point */ 72 /* in `user->last'. We also update bbox in case contour starts with */ 73 /* an implicit `on' point. */ 74 /* */ 75 /* <Input> */ 76 /* to :: A pointer to the destination vector. */ 77 /* */ 78 /* <InOut> */ 79 /* user :: A pointer to the current walk context. */ 80 /* */ 81 /* <Return> */ 82 /* Always 0. Needed for the interface only. */ 83 /* */ 84 static int 85 BBox_Move_To( FT_Vector* to, 86 TBBox_Rec* user ) 87 { 88 FT_UPDATE_BBOX( to, user->bbox ); 89 90 user->last = *to; 91 92 return 0; 93 } 94 95 96 /*************************************************************************/ 97 /* */ 98 /* <Function> */ 99 /* BBox_Line_To */ 100 /* */ 101 /* <Description> */ 102 /* This function is used as a `line_to' emitter during */ 103 /* FT_Outline_Decompose(). It simply records the destination point */ 104 /* in `user->last'; no further computations are necessary because */ 105 /* bbox already contains both explicit ends of the line segment. */ 106 /* */ 107 /* <Input> */ 108 /* to :: A pointer to the destination vector. */ 109 /* */ 110 /* <InOut> */ 111 /* user :: A pointer to the current walk context. */ 112 /* */ 113 /* <Return> */ 114 /* Always 0. Needed for the interface only. */ 115 /* */ 116 static int 117 BBox_Line_To( FT_Vector* to, 118 TBBox_Rec* user ) 119 { 120 user->last = *to; 121 122 return 0; 123 } 124 125 126 /*************************************************************************/ 127 /* */ 128 /* <Function> */ 129 /* BBox_Conic_Check */ 130 /* */ 131 /* <Description> */ 132 /* Find the extrema of a 1-dimensional conic Bezier curve and update */ 133 /* a bounding range. This version uses direct computation, as it */ 134 /* doesn't need square roots. */ 135 /* */ 136 /* <Input> */ 137 /* y1 :: The start coordinate. */ 138 /* */ 139 /* y2 :: The coordinate of the control point. */ 140 /* */ 141 /* y3 :: The end coordinate. */ 142 /* */ 143 /* <InOut> */ 144 /* min :: The address of the current minimum. */ 145 /* */ 146 /* max :: The address of the current maximum. */ 147 /* */ 148 static void 149 BBox_Conic_Check( FT_Pos y1, 150 FT_Pos y2, 151 FT_Pos y3, 152 FT_Pos* min, 153 FT_Pos* max ) 154 { 155 /* This function is only called when a control off-point is outside */ 156 /* the bbox that contains all on-points. It finds a local extremum */ 157 /* within the segment, equal to (y1*y3 - y2*y2)/(y1 - 2*y2 + y3). */ 158 /* Or, offsetting from y2, we get */ 159 160 y1 -= y2; 161 y3 -= y2; 162 y2 += FT_MulDiv( y1, y3, y1 + y3 ); 163 164 if ( y2 < *min ) 165 *min = y2; 166 if ( y2 > *max ) 167 *max = y2; 168 } 169 170 171 /*************************************************************************/ 172 /* */ 173 /* <Function> */ 174 /* BBox_Conic_To */ 175 /* */ 176 /* <Description> */ 177 /* This function is used as a `conic_to' emitter during */ 178 /* FT_Outline_Decompose(). It checks a conic Bezier curve with the */ 179 /* current bounding box, and computes its extrema if necessary to */ 180 /* update it. */ 181 /* */ 182 /* <Input> */ 183 /* control :: A pointer to a control point. */ 184 /* */ 185 /* to :: A pointer to the destination vector. */ 186 /* */ 187 /* <InOut> */ 188 /* user :: The address of the current walk context. */ 189 /* */ 190 /* <Return> */ 191 /* Always 0. Needed for the interface only. */ 192 /* */ 193 /* <Note> */ 194 /* In the case of a non-monotonous arc, we compute directly the */ 195 /* extremum coordinates, as it is sufficiently fast. */ 196 /* */ 197 static int 198 BBox_Conic_To( FT_Vector* control, 199 FT_Vector* to, 200 TBBox_Rec* user ) 201 { 202 /* in case `to' is implicit and not included in bbox yet */ 203 FT_UPDATE_BBOX( to, user->bbox ); 204 205 if ( CHECK_X( control, user->bbox ) ) 206 BBox_Conic_Check( user->last.x, 207 control->x, 208 to->x, 209 &user->bbox.xMin, 210 &user->bbox.xMax ); 211 212 if ( CHECK_Y( control, user->bbox ) ) 213 BBox_Conic_Check( user->last.y, 214 control->y, 215 to->y, 216 &user->bbox.yMin, 217 &user->bbox.yMax ); 218 219 user->last = *to; 220 221 return 0; 222 } 223 224 225 /*************************************************************************/ 226 /* */ 227 /* <Function> */ 228 /* BBox_Cubic_Check */ 229 /* */ 230 /* <Description> */ 231 /* Find the extrema of a 1-dimensional cubic Bezier curve and */ 232 /* update a bounding range. This version uses iterative splitting */ 233 /* because it is faster than the exact solution with square roots. */ 234 /* */ 235 /* <Input> */ 236 /* p1 :: The start coordinate. */ 237 /* */ 238 /* p2 :: The coordinate of the first control point. */ 239 /* */ 240 /* p3 :: The coordinate of the second control point. */ 241 /* */ 242 /* p4 :: The end coordinate. */ 243 /* */ 244 /* <InOut> */ 245 /* min :: The address of the current minimum. */ 246 /* */ 247 /* max :: The address of the current maximum. */ 248 /* */ 249 static FT_Pos 250 cubic_peak( FT_Pos q1, 251 FT_Pos q2, 252 FT_Pos q3, 253 FT_Pos q4 ) 254 { 255 FT_Pos peak = 0; 256 FT_Int shift; 257 258 259 /* This function finds a peak of a cubic segment if it is above 0 */ 260 /* using iterative bisection of the segment, or returns 0. */ 261 /* The fixed-point arithmetic of bisection is inherently stable */ 262 /* but may loose accuracy in the two lowest bits. To compensate, */ 263 /* we upscale the segment if there is room. Large values may need */ 264 /* to be downscaled to avoid overflows during bisection. */ 265 /* It is called with either q2 or q3 positive, which is necessary */ 266 /* for the peak to exist and avoids undefined FT_MSB. */ 267 268 shift = 27 - FT_MSB( (FT_UInt32)( FT_ABS( q1 ) | 269 FT_ABS( q2 ) | 270 FT_ABS( q3 ) | 271 FT_ABS( q4 ) ) ); 272 273 if ( shift > 0 ) 274 { 275 /* upscaling too much just wastes time */ 276 if ( shift > 2 ) 277 shift = 2; 278 279 q1 <<= shift; 280 q2 <<= shift; 281 q3 <<= shift; 282 q4 <<= shift; 283 } 284 else 285 { 286 q1 >>= -shift; 287 q2 >>= -shift; 288 q3 >>= -shift; 289 q4 >>= -shift; 290 } 291 292 /* for a peak to exist above 0, the cubic segment must have */ 293 /* at least one of its control off-points above 0. */ 294 while ( q2 > 0 || q3 > 0 ) 295 { 296 /* determine which half contains the maximum and split */ 297 if ( q1 + q2 > q3 + q4 ) /* first half */ 298 { 299 q4 = q4 + q3; 300 q3 = q3 + q2; 301 q2 = q2 + q1; 302 q4 = q4 + q3; 303 q3 = q3 + q2; 304 q4 = ( q4 + q3 ) / 8; 305 q3 = q3 / 4; 306 q2 = q2 / 2; 307 } 308 else /* second half */ 309 { 310 q1 = q1 + q2; 311 q2 = q2 + q3; 312 q3 = q3 + q4; 313 q1 = q1 + q2; 314 q2 = q2 + q3; 315 q1 = ( q1 + q2 ) / 8; 316 q2 = q2 / 4; 317 q3 = q3 / 2; 318 } 319 320 /* check whether either end reached the maximum */ 321 if ( q1 == q2 && q1 >= q3 ) 322 { 323 peak = q1; 324 break; 325 } 326 if ( q3 == q4 && q2 <= q4 ) 327 { 328 peak = q4; 329 break; 330 } 331 } 332 333 if ( shift > 0 ) 334 peak >>= shift; 335 else 336 peak <<= -shift; 337 338 return peak; 339 } 340 341 342 static void 343 BBox_Cubic_Check( FT_Pos p1, 344 FT_Pos p2, 345 FT_Pos p3, 346 FT_Pos p4, 347 FT_Pos* min, 348 FT_Pos* max ) 349 { 350 /* This function is only called when a control off-point is outside */ 351 /* the bbox that contains all on-points. So at least one of the */ 352 /* conditions below holds and cubic_peak is called with at least one */ 353 /* non-zero argument. */ 354 355 if ( p2 > *max || p3 > *max ) 356 *max += cubic_peak( p1 - *max, p2 - *max, p3 - *max, p4 - *max ); 357 358 /* now flip the signs to update the minimum */ 359 if ( p2 < *min || p3 < *min ) 360 *min -= cubic_peak( *min - p1, *min - p2, *min - p3, *min - p4 ); 361 } 362 363 364 /*************************************************************************/ 365 /* */ 366 /* <Function> */ 367 /* BBox_Cubic_To */ 368 /* */ 369 /* <Description> */ 370 /* This function is used as a `cubic_to' emitter during */ 371 /* FT_Outline_Decompose(). It checks a cubic Bezier curve with the */ 372 /* current bounding box, and computes its extrema if necessary to */ 373 /* update it. */ 374 /* */ 375 /* <Input> */ 376 /* control1 :: A pointer to the first control point. */ 377 /* */ 378 /* control2 :: A pointer to the second control point. */ 379 /* */ 380 /* to :: A pointer to the destination vector. */ 381 /* */ 382 /* <InOut> */ 383 /* user :: The address of the current walk context. */ 384 /* */ 385 /* <Return> */ 386 /* Always 0. Needed for the interface only. */ 387 /* */ 388 /* <Note> */ 389 /* In the case of a non-monotonous arc, we don't compute directly */ 390 /* extremum coordinates, we subdivide instead. */ 391 /* */ 392 static int 393 BBox_Cubic_To( FT_Vector* control1, 394 FT_Vector* control2, 395 FT_Vector* to, 396 TBBox_Rec* user ) 397 { 398 /* We don't need to check `to' since it is always an on-point, */ 399 /* thus within the bbox. Only segments with an off-point outside */ 400 /* the bbox can possibly reach new extreme values. */ 401 402 if ( CHECK_X( control1, user->bbox ) || 403 CHECK_X( control2, user->bbox ) ) 404 BBox_Cubic_Check( user->last.x, 405 control1->x, 406 control2->x, 407 to->x, 408 &user->bbox.xMin, 409 &user->bbox.xMax ); 410 411 if ( CHECK_Y( control1, user->bbox ) || 412 CHECK_Y( control2, user->bbox ) ) 413 BBox_Cubic_Check( user->last.y, 414 control1->y, 415 control2->y, 416 to->y, 417 &user->bbox.yMin, 418 &user->bbox.yMax ); 419 420 user->last = *to; 421 422 return 0; 423 } 424 425 426 FT_DEFINE_OUTLINE_FUNCS( 427 bbox_interface, 428 429 (FT_Outline_MoveTo_Func) BBox_Move_To, /* move_to */ 430 (FT_Outline_LineTo_Func) BBox_Line_To, /* line_to */ 431 (FT_Outline_ConicTo_Func)BBox_Conic_To, /* conic_to */ 432 (FT_Outline_CubicTo_Func)BBox_Cubic_To, /* cubic_to */ 433 0, /* shift */ 434 0 /* delta */ 435 ) 436 437 438 /* documentation is in ftbbox.h */ 439 440 FT_EXPORT_DEF( FT_Error ) 441 FT_Outline_Get_BBox( FT_Outline* outline, 442 FT_BBox *abbox ) 443 { 444 FT_BBox cbox = { 0x7FFFFFFFL, 0x7FFFFFFFL, 445 -0x7FFFFFFFL, -0x7FFFFFFFL }; 446 FT_BBox bbox = { 0x7FFFFFFFL, 0x7FFFFFFFL, 447 -0x7FFFFFFFL, -0x7FFFFFFFL }; 448 FT_Vector* vec; 449 FT_UShort n; 450 451 452 if ( !abbox ) 453 return FT_THROW( Invalid_Argument ); 454 455 if ( !outline ) 456 return FT_THROW( Invalid_Outline ); 457 458 /* if outline is empty, return (0,0,0,0) */ 459 if ( outline->n_points == 0 || outline->n_contours <= 0 ) 460 { 461 abbox->xMin = abbox->xMax = 0; 462 abbox->yMin = abbox->yMax = 0; 463 464 return 0; 465 } 466 467 /* We compute the control box as well as the bounding box of */ 468 /* all `on' points in the outline. Then, if the two boxes */ 469 /* coincide, we exit immediately. */ 470 471 vec = outline->points; 472 473 for ( n = 0; n < outline->n_points; n++ ) 474 { 475 FT_UPDATE_BBOX( vec, cbox ); 476 477 if ( FT_CURVE_TAG( outline->tags[n] ) == FT_CURVE_TAG_ON ) 478 FT_UPDATE_BBOX( vec, bbox ); 479 480 vec++; 481 } 482 483 /* test two boxes for equality */ 484 if ( cbox.xMin < bbox.xMin || cbox.xMax > bbox.xMax || 485 cbox.yMin < bbox.yMin || cbox.yMax > bbox.yMax ) 486 { 487 /* the two boxes are different, now walk over the outline to */ 488 /* get the Bezier arc extrema. */ 489 490 FT_Error error; 491 TBBox_Rec user; 492 493 #ifdef FT_CONFIG_OPTION_PIC 494 FT_Outline_Funcs bbox_interface; 495 496 497 Init_Class_bbox_interface( &bbox_interface ); 498 #endif 499 500 user.bbox = bbox; 501 502 error = FT_Outline_Decompose( outline, &bbox_interface, &user ); 503 if ( error ) 504 return error; 505 506 *abbox = user.bbox; 507 } 508 else 509 *abbox = bbox; 510 511 return FT_Err_Ok; 512 } 513 514 515 /* END */ 516
