Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 1 | /***************************************************************************/ |
| 2 | /* */ |
| 3 | /* fttrigon.c */ |
| 4 | /* */ |
| 5 | /* FreeType trigonometric functions (body). */ |
| 6 | /* */ |
Werner Lemberg | 1ec3963 | 2004-11-24 07:08:21 +0000 | [diff] [blame^] | 7 | /* Copyright 2001, 2002, 2003, 2004 by */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 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 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 19 | #include <ft2build.h> |
Werner Lemberg | 80cfbd7 | 2003-12-26 07:26:08 +0000 | [diff] [blame] | 20 | #include FT_INTERNAL_OBJECTS_H |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 21 | #include FT_TRIGONOMETRY_H |
| 22 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 23 | |
| 24 | /* the following is 0.2715717684432231 * 2^30 */ |
| 25 | #define FT_TRIG_COSCALE 0x11616E8EUL |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 26 | |
| 27 | /* this table was generated for FT_PI = 180L << 16, i.e. degrees */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 28 | #define FT_TRIG_MAX_ITERS 23 |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 29 | |
| 30 | static const FT_Fixed |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 31 | ft_trig_arctan_table[24] = |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 32 | { |
Werner Lemberg | cf24d51 | 2001-06-18 14:23:45 +0000 | [diff] [blame] | 33 | 4157273L, 2949120L, 1740967L, 919879L, 466945L, 234379L, 117304L, |
| 34 | 58666L, 29335L, 14668L, 7334L, 3667L, 1833L, 917L, 458L, 229L, 115L, |
| 35 | 57L, 29L, 14L, 7L, 4L, 2L, 1L |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 36 | }; |
| 37 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 38 | /* the Cordic shrink factor, multiplied by 2^32 */ |
| 39 | #define FT_TRIG_SCALE 1166391785UL /* 0x4585BA38UL */ |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 40 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 41 | |
| 42 | #ifdef FT_CONFIG_HAS_INT64 |
| 43 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 44 | /* multiply a given value by the CORDIC shrink factor */ |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 45 | static FT_Fixed |
| 46 | ft_trig_downscale( FT_Fixed val ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 47 | { |
| 48 | FT_Fixed s; |
| 49 | FT_Int64 v; |
| 50 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 51 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 52 | s = val; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 53 | val = ( val >= 0 ) ? val : -val; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 54 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 55 | v = ( val * (FT_Int64)FT_TRIG_SCALE ) + 0x100000000UL; |
| 56 | val = (FT_Fixed)( v >> 32 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 57 | |
| 58 | return ( s >= 0 ) ? val : -val; |
| 59 | } |
| 60 | |
| 61 | #else /* !FT_CONFIG_HAS_INT64 */ |
| 62 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 63 | /* multiply a given value by the CORDIC shrink factor */ |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 64 | static FT_Fixed |
| 65 | ft_trig_downscale( FT_Fixed val ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 66 | { |
| 67 | FT_Fixed s; |
| 68 | FT_UInt32 v1, v2, k1, k2, hi, lo1, lo2, lo3; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 69 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 70 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 71 | s = val; |
| 72 | val = ( val >= 0 ) ? val : -val; |
| 73 | |
| 74 | v1 = (FT_UInt32)val >> 16; |
Werner Lemberg | 43ba084 | 2003-06-23 19:26:53 +0000 | [diff] [blame] | 75 | v2 = (FT_UInt32)val & 0xFFFFL; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 76 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 77 | k1 = FT_TRIG_SCALE >> 16; /* constant */ |
Werner Lemberg | 43ba084 | 2003-06-23 19:26:53 +0000 | [diff] [blame] | 78 | k2 = FT_TRIG_SCALE & 0xFFFFL; /* constant */ |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 79 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 80 | hi = k1 * v1; |
| 81 | lo1 = k1 * v2 + k2 * v1; /* can't overflow */ |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 82 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 83 | lo2 = ( k2 * v2 ) >> 16; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 84 | lo3 = ( lo1 >= lo2 ) ? lo1 : lo2; |
| 85 | lo1 += lo2; |
| 86 | |
| 87 | hi += lo1 >> 16; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 88 | if ( lo1 < lo3 ) |
| 89 | hi += 0x10000UL; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 90 | |
| 91 | val = (FT_Fixed)hi; |
| 92 | |
| 93 | return ( s >= 0 ) ? val : -val; |
| 94 | } |
| 95 | |
| 96 | #endif /* !FT_CONFIG_HAS_INT64 */ |
| 97 | |
| 98 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 99 | static FT_Int |
| 100 | ft_trig_prenorm( FT_Vector* vec ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 101 | { |
| 102 | FT_Fixed x, y, z; |
| 103 | FT_Int shift; |
| 104 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 105 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 106 | x = vec->x; |
| 107 | y = vec->y; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 108 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 109 | z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 110 | shift = 0; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 111 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 112 | if ( z < ( 1L << 27 ) ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 113 | { |
| 114 | do |
| 115 | { |
| 116 | shift++; |
| 117 | z <<= 1; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 118 | } while ( z < ( 1L << 27 ) ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 119 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 120 | vec->x = x << shift; |
| 121 | vec->y = y << shift; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 122 | } |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 123 | else if ( z > ( 1L << 28 ) ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 124 | { |
| 125 | do |
| 126 | { |
| 127 | shift++; |
| 128 | z >>= 1; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 129 | } while ( z > ( 1L << 28 ) ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 130 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 131 | vec->x = x >> shift; |
| 132 | vec->y = y >> shift; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 133 | shift = -shift; |
| 134 | } |
| 135 | return shift; |
| 136 | } |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 137 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 138 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 139 | static void |
| 140 | ft_trig_pseudo_rotate( FT_Vector* vec, |
| 141 | FT_Angle theta ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 142 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 143 | FT_Int i; |
| 144 | FT_Fixed x, y, xtemp; |
| 145 | const FT_Fixed *arctanptr; |
| 146 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 147 | |
| 148 | x = vec->x; |
| 149 | y = vec->y; |
| 150 | |
| 151 | /* Get angle between -90 and 90 degrees */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 152 | while ( theta <= -FT_ANGLE_PI2 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 153 | { |
| 154 | x = -x; |
| 155 | y = -y; |
| 156 | theta += FT_ANGLE_PI; |
| 157 | } |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 158 | |
| 159 | while ( theta > FT_ANGLE_PI2 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 160 | { |
| 161 | x = -x; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 162 | y = -y; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 163 | theta -= FT_ANGLE_PI; |
| 164 | } |
| 165 | |
| 166 | /* Initial pseudorotation, with left shift */ |
| 167 | arctanptr = ft_trig_arctan_table; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 168 | |
| 169 | if ( theta < 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 170 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 171 | xtemp = x + ( y << 1 ); |
| 172 | y = y - ( x << 1 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 173 | x = xtemp; |
| 174 | theta += *arctanptr++; |
| 175 | } |
| 176 | else |
| 177 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 178 | xtemp = x - ( y << 1 ); |
| 179 | y = y + ( x << 1 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 180 | x = xtemp; |
| 181 | theta -= *arctanptr++; |
| 182 | } |
| 183 | |
| 184 | /* Subsequent pseudorotations, with right shifts */ |
| 185 | i = 0; |
| 186 | do |
| 187 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 188 | if ( theta < 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 189 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 190 | xtemp = x + ( y >> i ); |
| 191 | y = y - ( x >> i ); |
| 192 | x = xtemp; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 193 | theta += *arctanptr++; |
| 194 | } |
| 195 | else |
| 196 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 197 | xtemp = x - ( y >> i ); |
| 198 | y = y + ( x >> i ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 199 | x = xtemp; |
| 200 | theta -= *arctanptr++; |
| 201 | } |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 202 | } while ( ++i < FT_TRIG_MAX_ITERS ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 203 | |
| 204 | vec->x = x; |
| 205 | vec->y = y; |
| 206 | } |
| 207 | |
| 208 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 209 | static void |
| 210 | ft_trig_pseudo_polarize( FT_Vector* vec ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 211 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 212 | FT_Fixed theta; |
| 213 | FT_Fixed yi, i; |
| 214 | FT_Fixed x, y; |
| 215 | const FT_Fixed *arctanptr; |
| 216 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 217 | |
| 218 | x = vec->x; |
| 219 | y = vec->y; |
| 220 | |
| 221 | /* Get the vector into the right half plane */ |
| 222 | theta = 0; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 223 | if ( x < 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 224 | { |
| 225 | x = -x; |
| 226 | y = -y; |
| 227 | theta = 2 * FT_ANGLE_PI2; |
| 228 | } |
| 229 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 230 | if ( y > 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 231 | theta = - theta; |
| 232 | |
| 233 | arctanptr = ft_trig_arctan_table; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 234 | |
| 235 | if ( y < 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 236 | { |
| 237 | /* Rotate positive */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 238 | yi = y + ( x << 1 ); |
| 239 | x = x - ( y << 1 ); |
| 240 | y = yi; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 241 | theta -= *arctanptr++; /* Subtract angle */ |
| 242 | } |
| 243 | else |
| 244 | { |
| 245 | /* Rotate negative */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 246 | yi = y - ( x << 1 ); |
| 247 | x = x + ( y << 1 ); |
| 248 | y = yi; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 249 | theta += *arctanptr++; /* Add angle */ |
| 250 | } |
| 251 | |
| 252 | i = 0; |
| 253 | do |
| 254 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 255 | if ( y < 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 256 | { |
| 257 | /* Rotate positive */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 258 | yi = y + ( x >> i ); |
| 259 | x = x - ( y >> i ); |
| 260 | y = yi; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 261 | theta -= *arctanptr++; |
| 262 | } |
| 263 | else |
| 264 | { |
| 265 | /* Rotate negative */ |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 266 | yi = y - ( x >> i ); |
| 267 | x = x + ( y >> i ); |
| 268 | y = yi; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 269 | theta += *arctanptr++; |
| 270 | } |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 271 | } while ( ++i < FT_TRIG_MAX_ITERS ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 272 | |
| 273 | /* round theta */ |
| 274 | if ( theta >= 0 ) |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 275 | theta = FT_PAD_ROUND( theta, 32 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 276 | else |
David Turner | 87c0d30 | 2003-12-24 01:10:46 +0000 | [diff] [blame] | 277 | theta = - FT_PAD_ROUND( -theta, 32 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 278 | |
| 279 | vec->x = x; |
| 280 | vec->y = theta; |
| 281 | } |
| 282 | |
| 283 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 284 | /* documentation is in fttrigon.h */ |
| 285 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 286 | FT_EXPORT_DEF( FT_Fixed ) |
| 287 | FT_Cos( FT_Angle angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 288 | { |
| 289 | FT_Vector v; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 290 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 291 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 292 | v.x = FT_TRIG_COSCALE >> 2; |
| 293 | v.y = 0; |
| 294 | ft_trig_pseudo_rotate( &v, angle ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 295 | |
Werner Lemberg | 5da9dd7 | 2001-12-16 08:17:33 +0000 | [diff] [blame] | 296 | return v.x / ( 1 << 12 ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 297 | } |
| 298 | |
| 299 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 300 | /* documentation is in fttrigon.h */ |
| 301 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 302 | FT_EXPORT_DEF( FT_Fixed ) |
| 303 | FT_Sin( FT_Angle angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 304 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 305 | return FT_Cos( FT_ANGLE_PI2 - angle ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 306 | } |
| 307 | |
| 308 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 309 | /* documentation is in fttrigon.h */ |
| 310 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 311 | FT_EXPORT_DEF( FT_Fixed ) |
| 312 | FT_Tan( FT_Angle angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 313 | { |
| 314 | FT_Vector v; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 315 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 316 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 317 | v.x = FT_TRIG_COSCALE >> 2; |
| 318 | v.y = 0; |
| 319 | ft_trig_pseudo_rotate( &v, angle ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 320 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 321 | return FT_DivFix( v.y, v.x ); |
| 322 | } |
| 323 | |
| 324 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 325 | /* documentation is in fttrigon.h */ |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 326 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 327 | FT_EXPORT_DEF( FT_Angle ) |
| 328 | FT_Atan2( FT_Fixed dx, |
| 329 | FT_Fixed dy ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 330 | { |
| 331 | FT_Vector v; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 332 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 333 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 334 | if ( dx == 0 && dy == 0 ) |
| 335 | return 0; |
| 336 | |
| 337 | v.x = dx; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 338 | v.y = dy; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 339 | ft_trig_prenorm( &v ); |
| 340 | ft_trig_pseudo_polarize( &v ); |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 341 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 342 | return v.y; |
| 343 | } |
| 344 | |
| 345 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 346 | /* documentation is in fttrigon.h */ |
| 347 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 348 | FT_EXPORT_DEF( void ) |
| 349 | FT_Vector_Unit( FT_Vector* vec, |
| 350 | FT_Angle angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 351 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 352 | vec->x = FT_TRIG_COSCALE >> 2; |
| 353 | vec->y = 0; |
| 354 | ft_trig_pseudo_rotate( vec, angle ); |
| 355 | vec->x >>= 12; |
| 356 | vec->y >>= 12; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 357 | } |
| 358 | |
| 359 | |
Werner Lemberg | 4f10745 | 2003-05-17 12:07:45 +0000 | [diff] [blame] | 360 | /* these macros return 0 for positive numbers, |
| 361 | and -1 for negative ones */ |
| 362 | #define FT_SIGN_LONG( x ) ( (x) >> ( FT_SIZEOF_LONG * 8 - 1 ) ) |
| 363 | #define FT_SIGN_INT( x ) ( (x) >> ( FT_SIZEOF_INT * 8 - 1 ) ) |
| 364 | #define FT_SIGN_INT32( x ) ( (x) >> 31 ) |
| 365 | #define FT_SIGN_INT16( x ) ( (x) >> 15 ) |
| 366 | |
| 367 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 368 | /* documentation is in fttrigon.h */ |
| 369 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 370 | FT_EXPORT_DEF( void ) |
| 371 | FT_Vector_Rotate( FT_Vector* vec, |
| 372 | FT_Angle angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 373 | { |
| 374 | FT_Int shift; |
| 375 | FT_Vector v; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 376 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 377 | |
Werner Lemberg | 4f10745 | 2003-05-17 12:07:45 +0000 | [diff] [blame] | 378 | v.x = vec->x; |
| 379 | v.y = vec->y; |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 380 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 381 | if ( angle && ( v.x != 0 || v.y != 0 ) ) |
| 382 | { |
| 383 | shift = ft_trig_prenorm( &v ); |
| 384 | ft_trig_pseudo_rotate( &v, angle ); |
| 385 | v.x = ft_trig_downscale( v.x ); |
| 386 | v.y = ft_trig_downscale( v.y ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 387 | |
Werner Lemberg | 4f10745 | 2003-05-17 12:07:45 +0000 | [diff] [blame] | 388 | if ( shift > 0 ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 389 | { |
Werner Lemberg | 4f10745 | 2003-05-17 12:07:45 +0000 | [diff] [blame] | 390 | FT_Int32 half = 1L << ( shift - 1 ); |
| 391 | |
| 392 | |
| 393 | vec->x = ( v.x + half + FT_SIGN_LONG( v.x ) ) >> shift; |
| 394 | vec->y = ( v.y + half + FT_SIGN_LONG( v.y ) ) >> shift; |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 395 | } |
| 396 | else |
| 397 | { |
| 398 | shift = -shift; |
| 399 | vec->x = v.x << shift; |
| 400 | vec->y = v.y << shift; |
| 401 | } |
| 402 | } |
| 403 | } |
| 404 | |
| 405 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 406 | /* documentation is in fttrigon.h */ |
| 407 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 408 | FT_EXPORT_DEF( FT_Fixed ) |
| 409 | FT_Vector_Length( FT_Vector* vec ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 410 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 411 | FT_Int shift; |
| 412 | FT_Vector v; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 413 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 414 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 415 | v = *vec; |
| 416 | |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 417 | /* handle trivial cases */ |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 418 | if ( v.x == 0 ) |
| 419 | { |
| 420 | return ( v.y >= 0 ) ? v.y : -v.y; |
| 421 | } |
| 422 | else if ( v.y == 0 ) |
| 423 | { |
| 424 | return ( v.x >= 0 ) ? v.x : -v.x; |
| 425 | } |
| 426 | |
| 427 | /* general case */ |
| 428 | shift = ft_trig_prenorm( &v ); |
| 429 | ft_trig_pseudo_polarize( &v ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 430 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 431 | v.x = ft_trig_downscale( v.x ); |
Werner Lemberg | 04728a8 | 2002-04-02 14:50:31 +0000 | [diff] [blame] | 432 | |
| 433 | if ( shift > 0 ) |
| 434 | return ( v.x + ( 1 << ( shift - 1 ) ) ) >> shift; |
| 435 | |
| 436 | return v.x << -shift; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 437 | } |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 438 | |
| 439 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 440 | /* documentation is in fttrigon.h */ |
| 441 | |
Werner Lemberg | f814d0f | 2001-06-27 16:18:10 +0000 | [diff] [blame] | 442 | FT_EXPORT_DEF( void ) |
| 443 | FT_Vector_Polarize( FT_Vector* vec, |
| 444 | FT_Fixed *length, |
| 445 | FT_Angle *angle ) |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 446 | { |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 447 | FT_Int shift; |
| 448 | FT_Vector v; |
| 449 | |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 450 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 451 | v = *vec; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 452 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 453 | if ( v.x == 0 && v.y == 0 ) |
| 454 | return; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 455 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 456 | shift = ft_trig_prenorm( &v ); |
| 457 | ft_trig_pseudo_polarize( &v ); |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 458 | |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 459 | v.x = ft_trig_downscale( v.x ); |
| 460 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 461 | *length = ( shift >= 0 ) ? ( v.x >> shift ) : ( v.x << -shift ); |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 462 | *angle = v.y; |
Werner Lemberg | 415235d | 2001-06-28 17:49:10 +0000 | [diff] [blame] | 463 | } |
David Turner | ebe85f5 | 2001-05-11 14:25:57 +0000 | [diff] [blame] | 464 | |
| 465 | |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 466 | /* documentation is in fttrigon.h */ |
| 467 | |
David Turner | 0d73b0c | 2002-06-26 23:45:21 +0000 | [diff] [blame] | 468 | FT_EXPORT_DEF( void ) |
| 469 | FT_Vector_From_Polar( FT_Vector* vec, |
| 470 | FT_Fixed length, |
| 471 | FT_Angle angle ) |
| 472 | { |
| 473 | vec->x = length; |
| 474 | vec->y = 0; |
| 475 | |
| 476 | FT_Vector_Rotate( vec, angle ); |
| 477 | } |
| 478 | |
| 479 | |
| 480 | /* documentation is in fttrigon.h */ |
| 481 | |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 482 | FT_EXPORT_DEF( FT_Angle ) |
David Turner | ac90c0e | 2002-07-01 21:35:17 +0000 | [diff] [blame] | 483 | FT_Angle_Diff( FT_Angle angle1, |
| 484 | FT_Angle angle2 ) |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 485 | { |
| 486 | FT_Angle delta = angle2 - angle1; |
David Turner | 0d73b0c | 2002-06-26 23:45:21 +0000 | [diff] [blame] | 487 | |
Werner Lemberg | 1ec3963 | 2004-11-24 07:08:21 +0000 | [diff] [blame^] | 488 | |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 489 | delta %= FT_ANGLE_2PI; |
David Turner | 20e3315 | 2003-01-07 22:54:02 +0000 | [diff] [blame] | 490 | if ( delta < 0 ) |
| 491 | delta += FT_ANGLE_2PI; |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 492 | |
| 493 | if ( delta > FT_ANGLE_PI ) |
| 494 | delta -= FT_ANGLE_2PI; |
David Turner | 0d73b0c | 2002-06-26 23:45:21 +0000 | [diff] [blame] | 495 | |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 496 | return delta; |
David Turner | 0d73b0c | 2002-06-26 23:45:21 +0000 | [diff] [blame] | 497 | } |
David Turner | b7e18ef | 2002-06-26 22:05:05 +0000 | [diff] [blame] | 498 | |
| 499 | |
Werner Lemberg | ec6ddd5 | 2001-05-12 18:04:08 +0000 | [diff] [blame] | 500 | /* END */ |