/****************************************************************************
*
* 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 */
