|
| 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 2003-2017 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 | + |
| 20 | +#include "aftypes.h" |
| 21 | + |
| 22 | + |
| 23 | + /* |
| 24 | + * We are not using `af_angle_atan' anymore, but we keep the source |
| 25 | + * code below just in case... |
| 26 | + */ |
| 27 | + |
| 28 | + |
| 29 | +#if 0 |
| 30 | + |
| 31 | + |
| 32 | + /* |
| 33 | + * The trick here is to realize that we don't need a very accurate angle |
| 34 | + * approximation. We are going to use the result of `af_angle_atan' to |
| 35 | + * only compare the sign of angle differences, or check whether its |
| 36 | + * magnitude is very small. |
| 37 | + * |
| 38 | + * The approximation |
| 39 | + * |
| 40 | + * dy * PI / (|dx|+|dy|) |
| 41 | + * |
| 42 | + * should be enough, and much faster to compute. |
| 43 | + */ |
| 44 | + FT_LOCAL_DEF( AF_Angle ) |
| 45 | + af_angle_atan( FT_Fixed dx, |
| 46 | + FT_Fixed dy ) |
| 47 | + { |
| 48 | + AF_Angle angle; |
| 49 | + FT_Fixed ax = dx; |
| 50 | + FT_Fixed ay = dy; |
| 51 | + |
| 52 | + |
| 53 | + if ( ax < 0 ) |
| 54 | + ax = -ax; |
| 55 | + if ( ay < 0 ) |
| 56 | + ay = -ay; |
| 57 | + |
| 58 | + ax += ay; |
| 59 | + |
| 60 | + if ( ax == 0 ) |
| 61 | + angle = 0; |
| 62 | + else |
| 63 | + { |
| 64 | + angle = ( AF_ANGLE_PI2 * dy ) / ( ax + ay ); |
| 65 | + if ( dx < 0 ) |
| 66 | + { |
| 67 | + if ( angle >= 0 ) |
| 68 | + angle = AF_ANGLE_PI - angle; |
| 69 | + else |
| 70 | + angle = -AF_ANGLE_PI - angle; |
| 71 | + } |
| 72 | + } |
| 73 | + |
| 74 | + return angle; |
| 75 | + } |
| 76 | + |
| 77 | + |
| 78 | +#elif 0 |
| 79 | + |
| 80 | + |
| 81 | + /* the following table has been automatically generated with */ |
| 82 | + /* the `mather.py' Python script */ |
| 83 | + |
| 84 | +#define AF_ATAN_BITS 8 |
| 85 | + |
| 86 | + static const FT_Byte af_arctan[1L << AF_ATAN_BITS] = |
| 87 | + { |
| 88 | + 0, 0, 1, 1, 1, 2, 2, 2, |
| 89 | + 3, 3, 3, 3, 4, 4, 4, 5, |
| 90 | + 5, 5, 6, 6, 6, 7, 7, 7, |
| 91 | + 8, 8, 8, 9, 9, 9, 10, 10, |
| 92 | + 10, 10, 11, 11, 11, 12, 12, 12, |
| 93 | + 13, 13, 13, 14, 14, 14, 14, 15, |
| 94 | + 15, 15, 16, 16, 16, 17, 17, 17, |
| 95 | + 18, 18, 18, 18, 19, 19, 19, 20, |
| 96 | + 20, 20, 21, 21, 21, 21, 22, 22, |
| 97 | + 22, 23, 23, 23, 24, 24, 24, 24, |
| 98 | + 25, 25, 25, 26, 26, 26, 26, 27, |
| 99 | + 27, 27, 28, 28, 28, 28, 29, 29, |
| 100 | + 29, 30, 30, 30, 30, 31, 31, 31, |
| 101 | + 31, 32, 32, 32, 33, 33, 33, 33, |
| 102 | + 34, 34, 34, 34, 35, 35, 35, 35, |
| 103 | + 36, 36, 36, 36, 37, 37, 37, 38, |
| 104 | + 38, 38, 38, 39, 39, 39, 39, 40, |
| 105 | + 40, 40, 40, 41, 41, 41, 41, 42, |
| 106 | + 42, 42, 42, 42, 43, 43, 43, 43, |
| 107 | + 44, 44, 44, 44, 45, 45, 45, 45, |
| 108 | + 46, 46, 46, 46, 46, 47, 47, 47, |
| 109 | + 47, 48, 48, 48, 48, 48, 49, 49, |
| 110 | + 49, 49, 50, 50, 50, 50, 50, 51, |
| 111 | + 51, 51, 51, 51, 52, 52, 52, 52, |
| 112 | + 52, 53, 53, 53, 53, 53, 54, 54, |
| 113 | + 54, 54, 54, 55, 55, 55, 55, 55, |
| 114 | + 56, 56, 56, 56, 56, 57, 57, 57, |
| 115 | + 57, 57, 57, 58, 58, 58, 58, 58, |
| 116 | + 59, 59, 59, 59, 59, 59, 60, 60, |
| 117 | + 60, 60, 60, 61, 61, 61, 61, 61, |
| 118 | + 61, 62, 62, 62, 62, 62, 62, 63, |
| 119 | + 63, 63, 63, 63, 63, 64, 64, 64 |
| 120 | + }; |
| 121 | + |
| 122 | + |
| 123 | + FT_LOCAL_DEF( AF_Angle ) |
| 124 | + af_angle_atan( FT_Fixed dx, |
| 125 | + FT_Fixed dy ) |
| 126 | + { |
| 127 | + AF_Angle angle; |
| 128 | + |
| 129 | + |
| 130 | + /* check trivial cases */ |
| 131 | + if ( dy == 0 ) |
| 132 | + { |
| 133 | + angle = 0; |
| 134 | + if ( dx < 0 ) |
| 135 | + angle = AF_ANGLE_PI; |
| 136 | + return angle; |
| 137 | + } |
| 138 | + else if ( dx == 0 ) |
| 139 | + { |
| 140 | + angle = AF_ANGLE_PI2; |
| 141 | + if ( dy < 0 ) |
| 142 | + angle = -AF_ANGLE_PI2; |
| 143 | + return angle; |
| 144 | + } |
| 145 | + |
| 146 | + angle = 0; |
| 147 | + if ( dx < 0 ) |
| 148 | + { |
| 149 | + dx = -dx; |
| 150 | + dy = -dy; |
| 151 | + angle = AF_ANGLE_PI; |
| 152 | + } |
| 153 | + |
| 154 | + if ( dy < 0 ) |
| 155 | + { |
| 156 | + FT_Pos tmp; |
| 157 | + |
| 158 | + |
| 159 | + tmp = dx; |
| 160 | + dx = -dy; |
| 161 | + dy = tmp; |
| 162 | + angle -= AF_ANGLE_PI2; |
| 163 | + } |
| 164 | + |
| 165 | + if ( dx == 0 && dy == 0 ) |
| 166 | + return 0; |
| 167 | + |
| 168 | + if ( dx == dy ) |
| 169 | + angle += AF_ANGLE_PI4; |
| 170 | + else if ( dx > dy ) |
| 171 | + angle += af_arctan[FT_DivFix( dy, dx ) >> ( 16 - AF_ATAN_BITS )]; |
| 172 | + else |
| 173 | + angle += AF_ANGLE_PI2 - |
| 174 | + af_arctan[FT_DivFix( dx, dy ) >> ( 16 - AF_ATAN_BITS )]; |
| 175 | + |
| 176 | + if ( angle > AF_ANGLE_PI ) |
| 177 | + angle -= AF_ANGLE_2PI; |
| 178 | + |
| 179 | + return angle; |
| 180 | + } |
| 181 | + |
| 182 | + |
| 183 | +#endif /* 0 */ |
| 184 | + |
| 185 | + |
| 186 | + FT_LOCAL_DEF( void ) |
| 187 | + af_sort_pos( FT_UInt count, |
| 188 | + FT_Pos* table ) |
| 189 | + { |
| 190 | + FT_UInt i, j; |
| 191 | + FT_Pos swap; |
| 192 | + |
| 193 | + |
| 194 | + for ( i = 1; i < count; i++ ) |
| 195 | + { |
| 196 | + for ( j = i; j > 0; j-- ) |
| 197 | + { |
| 198 | + if ( table[j] >= table[j - 1] ) |
| 199 | + break; |
| 200 | + |
| 201 | + swap = table[j]; |
| 202 | + table[j] = table[j - 1]; |
| 203 | + table[j - 1] = swap; |
| 204 | + } |
| 205 | + } |
| 206 | + } |
| 207 | + |
| 208 | + |
| 209 | + FT_LOCAL_DEF( void ) |
| 210 | + af_sort_and_quantize_widths( FT_UInt* count, |
| 211 | + AF_Width table, |
| 212 | + FT_Pos threshold ) |
| 213 | + { |
| 214 | + FT_UInt i, j; |
| 215 | + FT_UInt cur_idx; |
| 216 | + FT_Pos cur_val; |
| 217 | + FT_Pos sum; |
| 218 | + AF_WidthRec swap; |
| 219 | + |
| 220 | + |
| 221 | + if ( *count == 1 ) |
| 222 | + return; |
| 223 | + |
| 224 | + /* sort */ |
| 225 | + for ( i = 1; i < *count; i++ ) |
| 226 | + { |
| 227 | + for ( j = i; j > 0; j-- ) |
| 228 | + { |
| 229 | + if ( table[j].org >= table[j - 1].org ) |
| 230 | + break; |
| 231 | + |
| 232 | + swap = table[j]; |
| 233 | + table[j] = table[j - 1]; |
| 234 | + table[j - 1] = swap; |
| 235 | + } |
| 236 | + } |
| 237 | + |
| 238 | + cur_idx = 0; |
| 239 | + cur_val = table[cur_idx].org; |
| 240 | + |
| 241 | + /* compute and use mean values for clusters not larger than */ |
| 242 | + /* `threshold'; this is very primitive and might not yield */ |
| 243 | + /* the best result, but normally, using reference character */ |
| 244 | + /* `o', `*count' is 2, so the code below is fully sufficient */ |
| 245 | + for ( i = 1; i < *count; i++ ) |
| 246 | + { |
| 247 | + if ( table[i].org - cur_val > threshold || |
| 248 | + i == *count - 1 ) |
| 249 | + { |
| 250 | + sum = 0; |
| 251 | + |
| 252 | + /* fix loop for end of array */ |
| 253 | + if ( table[i].org - cur_val <= threshold && |
| 254 | + i == *count - 1 ) |
| 255 | + i++; |
| 256 | + |
| 257 | + for ( j = cur_idx; j < i; j++ ) |
| 258 | + { |
| 259 | + sum += table[j].org; |
| 260 | + table[j].org = 0; |
| 261 | + } |
| 262 | + table[cur_idx].org = sum / (FT_Pos)j; |
| 263 | + |
| 264 | + if ( i < *count - 1 ) |
| 265 | + { |
| 266 | + cur_idx = i + 1; |
| 267 | + cur_val = table[cur_idx].org; |
| 268 | + } |
| 269 | + } |
| 270 | + } |
| 271 | + |
| 272 | + cur_idx = 1; |
| 273 | + |
| 274 | + /* compress array to remove zero values */ |
| 275 | + for ( i = 1; i < *count; i++ ) |
| 276 | + { |
| 277 | + if ( table[i].org ) |
| 278 | + table[cur_idx++] = table[i]; |
| 279 | + } |
| 280 | + |
| 281 | + *count = cur_idx; |
| 282 | + } |
| 283 | + |
| 284 | + |
| 285 | +/* END */ |
0 commit comments