| /**************************************************************************** |
| * |
| * afangles.c |
| * |
| * Routines used to compute vector angles with limited accuracy |
| * and very high speed. It also contains sorting routines (body). |
| * |
| * Copyright (C) 2003-2021 by |
| * David Turner, Robert Wilhelm, and Werner Lemberg. |
| * |
| * This file is part of the FreeType project, and may only be used, |
| * modified, and distributed under the terms of the FreeType project |
| * license, LICENSE.TXT. By continuing to use, modify, or distribute |
| * this file you indicate that you have read the license and |
| * understand and accept it fully. |
| * |
| */ |
| |
| |
| #include "aftypes.h" |
| |
| |
| /* |
| * We are not using `af_angle_atan' anymore, but we keep the source |
| * code below just in case... |
| */ |
| |
| |
| #if 0 |
| |
| |
| /* |
| * The trick here is to realize that we don't need a very accurate angle |
| * approximation. We are going to use the result of `af_angle_atan' to |
| * only compare the sign of angle differences, or check whether its |
| * magnitude is very small. |
| * |
| * The approximation |
| * |
| * dy * PI / (|dx|+|dy|) |
| * |
| * should be enough, and much faster to compute. |
| */ |
| FT_LOCAL_DEF( AF_Angle ) |
| af_angle_atan( FT_Fixed dx, |
| FT_Fixed dy ) |
| { |
| AF_Angle angle; |
| FT_Fixed ax = dx; |
| FT_Fixed ay = dy; |
| |
| |
| if ( ax < 0 ) |
| ax = -ax; |
| if ( ay < 0 ) |
| ay = -ay; |
| |
| ax += ay; |
| |
| if ( ax == 0 ) |
| angle = 0; |
| else |
| { |
| angle = ( AF_ANGLE_PI2 * dy ) / ( ax + ay ); |
| if ( dx < 0 ) |
| { |
| if ( angle >= 0 ) |
| angle = AF_ANGLE_PI - angle; |
| else |
| angle = -AF_ANGLE_PI - angle; |
| } |
| } |
| |
| return angle; |
| } |
| |
| |
| #elif 0 |
| |
| |
| /* the following table has been automatically generated with */ |
| /* the `mather.py' Python script */ |
| |
| #define AF_ATAN_BITS 8 |
| |
| static const FT_Byte af_arctan[1L << AF_ATAN_BITS] = |
| { |
| 0, 0, 1, 1, 1, 2, 2, 2, |
| 3, 3, 3, 3, 4, 4, 4, 5, |
| 5, 5, 6, 6, 6, 7, 7, 7, |
| 8, 8, 8, 9, 9, 9, 10, 10, |
| 10, 10, 11, 11, 11, 12, 12, 12, |
| 13, 13, 13, 14, 14, 14, 14, 15, |
| 15, 15, 16, 16, 16, 17, 17, 17, |
| 18, 18, 18, 18, 19, 19, 19, 20, |
| 20, 20, 21, 21, 21, 21, 22, 22, |
| 22, 23, 23, 23, 24, 24, 24, 24, |
| 25, 25, 25, 26, 26, 26, 26, 27, |
| 27, 27, 28, 28, 28, 28, 29, 29, |
| 29, 30, 30, 30, 30, 31, 31, 31, |
| 31, 32, 32, 32, 33, 33, 33, 33, |
| 34, 34, 34, 34, 35, 35, 35, 35, |
| 36, 36, 36, 36, 37, 37, 37, 38, |
| 38, 38, 38, 39, 39, 39, 39, 40, |
| 40, 40, 40, 41, 41, 41, 41, 42, |
| 42, 42, 42, 42, 43, 43, 43, 43, |
| 44, 44, 44, 44, 45, 45, 45, 45, |
| 46, 46, 46, 46, 46, 47, 47, 47, |
| 47, 48, 48, 48, 48, 48, 49, 49, |
| 49, 49, 50, 50, 50, 50, 50, 51, |
| 51, 51, 51, 51, 52, 52, 52, 52, |
| 52, 53, 53, 53, 53, 53, 54, 54, |
| 54, 54, 54, 55, 55, 55, 55, 55, |
| 56, 56, 56, 56, 56, 57, 57, 57, |
| 57, 57, 57, 58, 58, 58, 58, 58, |
| 59, 59, 59, 59, 59, 59, 60, 60, |
| 60, 60, 60, 61, 61, 61, 61, 61, |
| 61, 62, 62, 62, 62, 62, 62, 63, |
| 63, 63, 63, 63, 63, 64, 64, 64 |
| }; |
| |
| |
| FT_LOCAL_DEF( AF_Angle ) |
| af_angle_atan( FT_Fixed dx, |
| FT_Fixed dy ) |
| { |
| AF_Angle angle; |
| |
| |
| /* check trivial cases */ |
| if ( dy == 0 ) |
| { |
| angle = 0; |
| if ( dx < 0 ) |
| angle = AF_ANGLE_PI; |
| return angle; |
| } |
| else if ( dx == 0 ) |
| { |
| angle = AF_ANGLE_PI2; |
| if ( dy < 0 ) |
| angle = -AF_ANGLE_PI2; |
| return angle; |
| } |
| |
| angle = 0; |
| if ( dx < 0 ) |
| { |
| dx = -dx; |
| dy = -dy; |
| angle = AF_ANGLE_PI; |
| } |
| |
| if ( dy < 0 ) |
| { |
| FT_Pos tmp; |
| |
| |
| tmp = dx; |
| dx = -dy; |
| dy = tmp; |
| angle -= AF_ANGLE_PI2; |
| } |
| |
| if ( dx == 0 && dy == 0 ) |
| return 0; |
| |
| if ( dx == dy ) |
| angle += AF_ANGLE_PI4; |
| else if ( dx > dy ) |
| angle += af_arctan[FT_DivFix( dy, dx ) >> ( 16 - AF_ATAN_BITS )]; |
| else |
| angle += AF_ANGLE_PI2 - |
| af_arctan[FT_DivFix( dx, dy ) >> ( 16 - AF_ATAN_BITS )]; |
| |
| if ( angle > AF_ANGLE_PI ) |
| angle -= AF_ANGLE_2PI; |
| |
| return angle; |
| } |
| |
| |
| #endif /* 0 */ |
| |
| |
| FT_LOCAL_DEF( void ) |
| af_sort_pos( FT_UInt count, |
| FT_Pos* table ) |
| { |
| FT_UInt i, j; |
| FT_Pos swap; |
| |
| |
| for ( i = 1; i < count; i++ ) |
| { |
| for ( j = i; j > 0; j-- ) |
| { |
| if ( table[j] >= table[j - 1] ) |
| break; |
| |
| swap = table[j]; |
| table[j] = table[j - 1]; |
| table[j - 1] = swap; |
| } |
| } |
| } |
| |
| |
| FT_LOCAL_DEF( void ) |
| af_sort_and_quantize_widths( FT_UInt* count, |
| AF_Width table, |
| FT_Pos threshold ) |
| { |
| FT_UInt i, j; |
| FT_UInt cur_idx; |
| FT_Pos cur_val; |
| FT_Pos sum; |
| AF_WidthRec swap; |
| |
| |
| if ( *count == 1 ) |
| return; |
| |
| /* sort */ |
| for ( i = 1; i < *count; i++ ) |
| { |
| for ( j = i; j > 0; j-- ) |
| { |
| if ( table[j].org >= table[j - 1].org ) |
| break; |
| |
| swap = table[j]; |
| table[j] = table[j - 1]; |
| table[j - 1] = swap; |
| } |
| } |
| |
| cur_idx = 0; |
| cur_val = table[cur_idx].org; |
| |
| /* compute and use mean values for clusters not larger than */ |
| /* `threshold'; this is very primitive and might not yield */ |
| /* the best result, but normally, using reference character */ |
| /* `o', `*count' is 2, so the code below is fully sufficient */ |
| for ( i = 1; i < *count; i++ ) |
| { |
| if ( table[i].org - cur_val > threshold || |
| i == *count - 1 ) |
| { |
| sum = 0; |
| |
| /* fix loop for end of array */ |
| if ( table[i].org - cur_val <= threshold && |
| i == *count - 1 ) |
| i++; |
| |
| for ( j = cur_idx; j < i; j++ ) |
| { |
| sum += table[j].org; |
| table[j].org = 0; |
| } |
| table[cur_idx].org = sum / (FT_Pos)j; |
| |
| if ( i < *count - 1 ) |
| { |
| cur_idx = i + 1; |
| cur_val = table[cur_idx].org; |
| } |
| } |
| } |
| |
| cur_idx = 1; |
| |
| /* compress array to remove zero values */ |
| for ( i = 1; i < *count; i++ ) |
| { |
| if ( table[i].org ) |
| table[cur_idx++] = table[i]; |
| } |
| |
| *count = cur_idx; |
| } |
| |
| |
| /* END */ |
