Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 1 | /***************************************************************************/ |
| 2 | /* */ |
| 3 | /* afangles.c */ |
| 4 | /* */ |
| 5 | /* Routines used to compute vector angles with limited accuracy */ |
| 6 | /* and very high speed. It also contains sorting routines (body). */ |
| 7 | /* */ |
| 8 | /* Copyright 2003, 2004, 2005 by */ |
| 9 | /* David Turner, Robert Wilhelm, and Werner Lemberg. */ |
| 10 | /* */ |
| 11 | /* This file is part of the FreeType project, and may only be used, */ |
| 12 | /* modified, and distributed under the terms of the FreeType project */ |
| 13 | /* license, LICENSE.TXT. By continuing to use, modify, or distribute */ |
| 14 | /* this file you indicate that you have read the license and */ |
| 15 | /* understand and accept it fully. */ |
| 16 | /* */ |
| 17 | /***************************************************************************/ |
| 18 | |
| 19 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 20 | #include "aftypes.h" |
| 21 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 22 | |
David Turner | 03ee7c8 | 2005-09-23 14:14:15 +0000 | [diff] [blame] | 23 | #if 1 |
| 24 | |
| 25 | /* the following table has been automatically generated with */ |
| 26 | /* the `mather.py' Python script */ |
| 27 | |
Werner Lemberg | 7c25946 | 2005-09-28 07:34:45 +0000 | [diff] [blame] | 28 | #define AF_ATAN_BITS 8 |
David Turner | 03ee7c8 | 2005-09-23 14:14:15 +0000 | [diff] [blame] | 29 | |
| 30 | static const FT_Byte af_arctan[1L << AF_ATAN_BITS] = |
| 31 | { |
| 32 | 0, 0, 1, 1, 1, 2, 2, 2, |
| 33 | 3, 3, 3, 3, 4, 4, 4, 5, |
| 34 | 5, 5, 6, 6, 6, 7, 7, 7, |
| 35 | 8, 8, 8, 9, 9, 9, 10, 10, |
| 36 | 10, 10, 11, 11, 11, 12, 12, 12, |
| 37 | 13, 13, 13, 14, 14, 14, 14, 15, |
| 38 | 15, 15, 16, 16, 16, 17, 17, 17, |
| 39 | 18, 18, 18, 18, 19, 19, 19, 20, |
| 40 | 20, 20, 21, 21, 21, 21, 22, 22, |
| 41 | 22, 23, 23, 23, 24, 24, 24, 24, |
| 42 | 25, 25, 25, 26, 26, 26, 26, 27, |
| 43 | 27, 27, 28, 28, 28, 28, 29, 29, |
| 44 | 29, 30, 30, 30, 30, 31, 31, 31, |
| 45 | 31, 32, 32, 32, 33, 33, 33, 33, |
| 46 | 34, 34, 34, 34, 35, 35, 35, 35, |
| 47 | 36, 36, 36, 36, 37, 37, 37, 38, |
| 48 | 38, 38, 38, 39, 39, 39, 39, 40, |
| 49 | 40, 40, 40, 41, 41, 41, 41, 42, |
| 50 | 42, 42, 42, 42, 43, 43, 43, 43, |
| 51 | 44, 44, 44, 44, 45, 45, 45, 45, |
| 52 | 46, 46, 46, 46, 46, 47, 47, 47, |
| 53 | 47, 48, 48, 48, 48, 48, 49, 49, |
| 54 | 49, 49, 50, 50, 50, 50, 50, 51, |
| 55 | 51, 51, 51, 51, 52, 52, 52, 52, |
| 56 | 52, 53, 53, 53, 53, 53, 54, 54, |
| 57 | 54, 54, 54, 55, 55, 55, 55, 55, |
| 58 | 56, 56, 56, 56, 56, 57, 57, 57, |
| 59 | 57, 57, 57, 58, 58, 58, 58, 58, |
| 60 | 59, 59, 59, 59, 59, 59, 60, 60, |
| 61 | 60, 60, 60, 61, 61, 61, 61, 61, |
| 62 | 61, 62, 62, 62, 62, 62, 62, 63, |
| 63 | 63, 63, 63, 63, 63, 64, 64, 64 |
| 64 | }; |
| 65 | |
| 66 | |
| 67 | FT_LOCAL_DEF( AF_Angle ) |
| 68 | af_angle_atan( FT_Fixed dx, |
| 69 | FT_Fixed dy ) |
| 70 | { |
| 71 | AF_Angle angle; |
| 72 | |
| 73 | |
| 74 | /* check trivial cases */ |
| 75 | if ( dy == 0 ) |
| 76 | { |
| 77 | angle = 0; |
| 78 | if ( dx < 0 ) |
| 79 | angle = AF_ANGLE_PI; |
| 80 | return angle; |
| 81 | } |
| 82 | else if ( dx == 0 ) |
| 83 | { |
| 84 | angle = AF_ANGLE_PI2; |
| 85 | if ( dy < 0 ) |
| 86 | angle = -AF_ANGLE_PI2; |
| 87 | return angle; |
| 88 | } |
| 89 | |
| 90 | angle = 0; |
| 91 | if ( dx < 0 ) |
| 92 | { |
| 93 | dx = -dx; |
| 94 | dy = -dy; |
| 95 | angle = AF_ANGLE_PI; |
| 96 | } |
| 97 | |
| 98 | if ( dy < 0 ) |
| 99 | { |
| 100 | FT_Pos tmp; |
| 101 | |
| 102 | |
| 103 | tmp = dx; |
| 104 | dx = -dy; |
| 105 | dy = tmp; |
| 106 | angle -= AF_ANGLE_PI2; |
| 107 | } |
| 108 | |
| 109 | if ( dx == 0 && dy == 0 ) |
| 110 | return 0; |
| 111 | |
| 112 | if ( dx == dy ) |
| 113 | angle += AF_ANGLE_PI4; |
| 114 | else if ( dx > dy ) |
| 115 | angle += af_arctan[FT_DivFix( dy, dx ) >> ( 16 - AF_ATAN_BITS )]; |
| 116 | else |
| 117 | angle += AF_ANGLE_PI2 - |
| 118 | af_arctan[FT_DivFix( dx, dy ) >> ( 16 - AF_ATAN_BITS )]; |
| 119 | |
| 120 | if ( angle > AF_ANGLE_PI ) |
| 121 | angle -= AF_ANGLE_2PI; |
| 122 | |
| 123 | return angle; |
| 124 | } |
| 125 | |
| 126 | |
| 127 | #else /* 0 */ |
Werner Lemberg | 7c25946 | 2005-09-28 07:34:45 +0000 | [diff] [blame] | 128 | |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 129 | /* |
| 130 | * a python script used to generate the following table |
| 131 | * |
| 132 | |
| 133 | import sys, math |
| 134 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 135 | units = 256 |
| 136 | scale = units/math.pi |
| 137 | comma = "" |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 138 | |
| 139 | print "" |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 140 | print "table of arctan( 1/2^n ) for PI = " + repr( units / 65536.0 ) + " units" |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 141 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 142 | r = [-1] + range( 32 ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 143 | |
| 144 | for n in r: |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 145 | if n >= 0: |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 146 | x = 1.0 / ( 2.0 ** n ) # tangent value |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 147 | else: |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 148 | x = 2.0 ** ( -n ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 149 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 150 | angle = math.atan( x ) # arctangent |
| 151 | angle2 = angle * scale # arctangent in FT_Angle units |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 152 | |
| 153 | # determine which integer value for angle gives the best tangent |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 154 | lo = int( angle2 ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 155 | hi = lo + 1 |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 156 | tlo = math.tan( lo / scale ) |
| 157 | thi = math.tan( hi / scale ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 158 | |
| 159 | errlo = abs( tlo - x ) |
| 160 | errhi = abs( thi - x ) |
| 161 | |
| 162 | angle2 = hi |
| 163 | if errlo < errhi: |
| 164 | angle2 = lo |
| 165 | |
| 166 | if angle2 <= 0: |
| 167 | break |
| 168 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 169 | sys.stdout.write( comma + repr( int( angle2 ) ) ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 170 | comma = ", " |
| 171 | |
| 172 | * |
| 173 | * end of python script |
| 174 | */ |
| 175 | |
| 176 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 177 | /* this table was generated for AF_ANGLE_PI = 256 */ |
| 178 | #define AF_ANGLE_MAX_ITERS 8 |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 179 | #define AF_TRIG_MAX_ITERS 8 |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 180 | |
| 181 | static const FT_Fixed |
| 182 | af_angle_arctan_table[9] = |
| 183 | { |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 184 | 90, 64, 38, 20, 10, 5, 3, 1, 1 |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 185 | }; |
| 186 | |
David Turner | ff9d241 | 2003-11-23 21:39:51 +0000 | [diff] [blame] | 187 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 188 | static FT_Int |
| 189 | af_angle_prenorm( FT_Vector* vec ) |
| 190 | { |
| 191 | FT_Fixed x, y, z; |
| 192 | FT_Int shift; |
| 193 | |
| 194 | |
| 195 | x = vec->x; |
| 196 | y = vec->y; |
| 197 | |
| 198 | z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y ); |
| 199 | shift = 0; |
| 200 | |
| 201 | if ( z < ( 1L << 27 ) ) |
| 202 | { |
| 203 | do |
| 204 | { |
| 205 | shift++; |
| 206 | z <<= 1; |
| 207 | } while ( z < ( 1L << 27 ) ); |
| 208 | |
| 209 | vec->x = x << shift; |
| 210 | vec->y = y << shift; |
| 211 | } |
| 212 | else if ( z > ( 1L << 28 ) ) |
| 213 | { |
| 214 | do |
| 215 | { |
| 216 | shift++; |
| 217 | z >>= 1; |
| 218 | } while ( z > ( 1L << 28 ) ); |
| 219 | |
| 220 | vec->x = x >> shift; |
| 221 | vec->y = y >> shift; |
| 222 | shift = -shift; |
| 223 | } |
| 224 | return shift; |
| 225 | } |
| 226 | |
| 227 | |
| 228 | static void |
| 229 | af_angle_pseudo_polarize( FT_Vector* vec ) |
| 230 | { |
| 231 | FT_Fixed theta; |
| 232 | FT_Fixed yi, i; |
| 233 | FT_Fixed x, y; |
| 234 | const FT_Fixed *arctanptr; |
| 235 | |
| 236 | |
| 237 | x = vec->x; |
| 238 | y = vec->y; |
| 239 | |
| 240 | /* Get the vector into the right half plane */ |
| 241 | theta = 0; |
| 242 | if ( x < 0 ) |
| 243 | { |
| 244 | x = -x; |
| 245 | y = -y; |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 246 | theta = AF_ANGLE_PI; |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 247 | } |
| 248 | |
| 249 | if ( y > 0 ) |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 250 | theta = -theta; |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 251 | |
| 252 | arctanptr = af_angle_arctan_table; |
| 253 | |
| 254 | if ( y < 0 ) |
| 255 | { |
| 256 | /* Rotate positive */ |
| 257 | yi = y + ( x << 1 ); |
| 258 | x = x - ( y << 1 ); |
| 259 | y = yi; |
| 260 | theta -= *arctanptr++; /* Subtract angle */ |
| 261 | } |
| 262 | else |
| 263 | { |
| 264 | /* Rotate negative */ |
| 265 | yi = y - ( x << 1 ); |
| 266 | x = x + ( y << 1 ); |
| 267 | y = yi; |
| 268 | theta += *arctanptr++; /* Add angle */ |
| 269 | } |
| 270 | |
| 271 | i = 0; |
| 272 | do |
| 273 | { |
| 274 | if ( y < 0 ) |
| 275 | { |
| 276 | /* Rotate positive */ |
| 277 | yi = y + ( x >> i ); |
| 278 | x = x - ( y >> i ); |
| 279 | y = yi; |
| 280 | theta -= *arctanptr++; |
| 281 | } |
| 282 | else |
| 283 | { |
| 284 | /* Rotate negative */ |
| 285 | yi = y - ( x >> i ); |
| 286 | x = x + ( y >> i ); |
| 287 | y = yi; |
| 288 | theta += *arctanptr++; |
| 289 | } |
| 290 | } while ( ++i < AF_TRIG_MAX_ITERS ); |
| 291 | |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 292 | #if 0 |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 293 | /* round theta */ |
| 294 | if ( theta >= 0 ) |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 295 | theta = FT_PAD_ROUND( theta, 2 ); |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 296 | else |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 297 | theta = -FT_PAD_ROUND( -theta, 2 ); |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 298 | #endif |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 299 | |
| 300 | vec->x = x; |
| 301 | vec->y = theta; |
| 302 | } |
| 303 | |
| 304 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 305 | /* cf. documentation in fttrigon.h */ |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 306 | |
| 307 | FT_LOCAL_DEF( AF_Angle ) |
| 308 | af_angle_atan( FT_Fixed dx, |
| 309 | FT_Fixed dy ) |
| 310 | { |
| 311 | FT_Vector v; |
| 312 | |
| 313 | |
| 314 | if ( dx == 0 && dy == 0 ) |
| 315 | return 0; |
| 316 | |
| 317 | v.x = dx; |
| 318 | v.y = dy; |
| 319 | af_angle_prenorm( &v ); |
| 320 | af_angle_pseudo_polarize( &v ); |
| 321 | |
| 322 | return v.y; |
| 323 | } |
| 324 | |
Werner Lemberg | 7c25946 | 2005-09-28 07:34:45 +0000 | [diff] [blame] | 325 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 326 | FT_LOCAL_DEF( AF_Angle ) |
| 327 | af_angle_diff( AF_Angle angle1, |
| 328 | AF_Angle angle2 ) |
| 329 | { |
| 330 | AF_Angle delta = angle2 - angle1; |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 331 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 332 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 333 | delta %= AF_ANGLE_2PI; |
| 334 | if ( delta < 0 ) |
| 335 | delta += AF_ANGLE_2PI; |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 336 | |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 337 | if ( delta > AF_ANGLE_PI ) |
| 338 | delta -= AF_ANGLE_2PI; |
David Turner | d25ad56 | 2003-10-02 21:07:10 +0000 | [diff] [blame] | 339 | |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 340 | return delta; |
| 341 | } |
| 342 | |
Werner Lemberg | 4309edc | 2005-11-11 15:49:14 +0000 | [diff] [blame^] | 343 | #endif /* 0 */ |
| 344 | |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 345 | |
David Turner | ff9d241 | 2003-11-23 21:39:51 +0000 | [diff] [blame] | 346 | FT_LOCAL_DEF( void ) |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 347 | af_sort_pos( FT_UInt count, |
| 348 | FT_Pos* table ) |
David Turner | ff9d241 | 2003-11-23 21:39:51 +0000 | [diff] [blame] | 349 | { |
David Turner | cf2c49c | 2003-12-24 18:42:04 +0000 | [diff] [blame] | 350 | FT_UInt i, j; |
| 351 | FT_Pos swap; |
David Turner | ff9d241 | 2003-11-23 21:39:51 +0000 | [diff] [blame] | 352 | |
| 353 | |
| 354 | for ( i = 1; i < count; i++ ) |
| 355 | { |
| 356 | for ( j = i; j > 0; j-- ) |
| 357 | { |
| 358 | if ( table[j] > table[j - 1] ) |
| 359 | break; |
| 360 | |
| 361 | swap = table[j]; |
| 362 | table[j] = table[j - 1]; |
| 363 | table[j - 1] = swap; |
| 364 | } |
| 365 | } |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 366 | } |
David Turner | cf2c49c | 2003-12-24 18:42:04 +0000 | [diff] [blame] | 367 | |
| 368 | |
| 369 | FT_LOCAL_DEF( void ) |
| 370 | af_sort_widths( FT_UInt count, |
| 371 | AF_Width table ) |
| 372 | { |
| 373 | FT_UInt i, j; |
| 374 | AF_WidthRec swap; |
| 375 | |
| 376 | |
| 377 | for ( i = 1; i < count; i++ ) |
| 378 | { |
| 379 | for ( j = i; j > 0; j-- ) |
| 380 | { |
| 381 | if ( table[j].org > table[j - 1].org ) |
| 382 | break; |
| 383 | |
| 384 | swap = table[j]; |
| 385 | table[j] = table[j - 1]; |
| 386 | table[j - 1] = swap; |
| 387 | } |
| 388 | } |
| 389 | } |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 390 | |
| 391 | |
| 392 | #ifdef TEST |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 393 | |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 394 | #include <stdio.h> |
| 395 | #include <math.h> |
| 396 | |
| 397 | int main( void ) |
| 398 | { |
| 399 | int angle; |
| 400 | int dist; |
| 401 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 402 | |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 403 | for ( dist = 100; dist < 1000; dist++ ) |
| 404 | { |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 405 | for ( angle = AF_ANGLE_PI; angle < AF_ANGLE_2PI * 4; angle++ ) |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 406 | { |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 407 | double a = ( angle * 3.1415926535 ) / ( 1.0 * AF_ANGLE_PI ); |
| 408 | int dx, dy, angle1, angle2, delta; |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 409 | |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 410 | |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 411 | dx = dist * cos( a ); |
| 412 | dy = dist * sin( a ); |
| 413 | |
| 414 | angle1 = ( ( atan2( dy, dx ) * AF_ANGLE_PI ) / 3.1415926535 ); |
| 415 | angle2 = af_angle_atan( dx, dy ); |
| 416 | delta = ( angle2 - angle1 ) % AF_ANGLE_2PI; |
David Turner | e664efa | 2004-06-04 17:41:59 +0000 | [diff] [blame] | 417 | if ( delta < 0 ) |
| 418 | delta = -delta; |
| 419 | |
| 420 | if ( delta >= 2 ) |
| 421 | { |
| 422 | printf( "dist:%4d angle:%4d => (%4d,%4d) angle1:%4d angle2:%4d\n", |
| 423 | dist, angle, dx, dy, angle1, angle2 ); |
| 424 | } |
| 425 | } |
| 426 | } |
| 427 | return 0; |
| 428 | } |
Werner Lemberg | f13516c | 2005-03-03 17:09:08 +0000 | [diff] [blame] | 429 | |
| 430 | #endif /* TEST */ |
| 431 | |
| 432 | |
| 433 | /* END */ |