ref: de2d90af6e9b9b719dc152828e26e00d2781bff0
dir: /src/autofit/afangles.c/
/***************************************************************************/ /* */ /* afangles.c */ /* */ /* Routines used to compute vector angles with limited accuracy */ /* and very high speed. It also contains sorting routines (body). */ /* */ /* Copyright 2003, 2004, 2005 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" #if 1 /* 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; } #else /* 0 */ /* * a python script used to generate the following table * import sys, math units = 256 scale = units/math.pi comma = "" print "" print "table of arctan( 1/2^n ) for PI = " + repr( units / 65536.0 ) + " units" r = [-1] + range( 32 ) for n in r: if n >= 0: x = 1.0 / ( 2.0 ** n ) # tangent value else: x = 2.0 ** ( -n ) angle = math.atan( x ) # arctangent angle2 = angle * scale # arctangent in FT_Angle units # determine which integer value for angle gives the best tangent lo = int( angle2 ) hi = lo + 1 tlo = math.tan( lo / scale ) thi = math.tan( hi / scale ) errlo = abs( tlo - x ) errhi = abs( thi - x ) angle2 = hi if errlo < errhi: angle2 = lo if angle2 <= 0: break sys.stdout.write( comma + repr( int( angle2 ) ) ) comma = ", " * * end of python script */ /* this table was generated for AF_ANGLE_PI = 256 */ #define AF_ANGLE_MAX_ITERS 8 #define AF_TRIG_MAX_ITERS 8 static const FT_Fixed af_angle_arctan_table[9] = { 90, 64, 38, 20, 10, 5, 3, 1, 1 }; static FT_Int af_angle_prenorm( FT_Vector* vec ) { FT_Fixed x, y, z; FT_Int shift; x = vec->x; y = vec->y; z = ( ( x >= 0 ) ? x : - x ) | ( (y >= 0) ? y : -y ); shift = 0; if ( z < ( 1L << 27 ) ) { do { shift++; z <<= 1; } while ( z < ( 1L << 27 ) ); vec->x = x << shift; vec->y = y << shift; } else if ( z > ( 1L << 28 ) ) { do { shift++; z >>= 1; } while ( z > ( 1L << 28 ) ); vec->x = x >> shift; vec->y = y >> shift; shift = -shift; } return shift; } static void af_angle_pseudo_polarize( FT_Vector* vec ) { FT_Fixed theta; FT_Fixed yi, i; FT_Fixed x, y; const FT_Fixed *arctanptr; x = vec->x; y = vec->y; /* Get the vector into the right half plane */ theta = 0; if ( x < 0 ) { x = -x; y = -y; theta = AF_ANGLE_PI; } if ( y > 0 ) theta = -theta; arctanptr = af_angle_arctan_table; if ( y < 0 ) { /* Rotate positive */ yi = y + ( x << 1 ); x = x - ( y << 1 ); y = yi; theta -= *arctanptr++; /* Subtract angle */ } else { /* Rotate negative */ yi = y - ( x << 1 ); x = x + ( y << 1 ); y = yi; theta += *arctanptr++; /* Add angle */ } i = 0; do { if ( y < 0 ) { /* Rotate positive */ yi = y + ( x >> i ); x = x - ( y >> i ); y = yi; theta -= *arctanptr++; } else { /* Rotate negative */ yi = y - ( x >> i ); x = x + ( y >> i ); y = yi; theta += *arctanptr++; } } while ( ++i < AF_TRIG_MAX_ITERS ); #if 0 /* round theta */ if ( theta >= 0 ) theta = FT_PAD_ROUND( theta, 2 ); else theta = -FT_PAD_ROUND( -theta, 2 ); #endif vec->x = x; vec->y = theta; } /* cf. documentation in fttrigon.h */ FT_LOCAL_DEF( AF_Angle ) af_angle_atan( FT_Fixed dx, FT_Fixed dy ) { FT_Vector v; if ( dx == 0 && dy == 0 ) return 0; v.x = dx; v.y = dy; af_angle_prenorm( &v ); af_angle_pseudo_polarize( &v ); return v.y; } FT_LOCAL_DEF( AF_Angle ) af_angle_diff( AF_Angle angle1, AF_Angle angle2 ) { AF_Angle delta = angle2 - angle1; delta %= AF_ANGLE_2PI; if ( delta < 0 ) delta += AF_ANGLE_2PI; if ( delta > AF_ANGLE_PI ) delta -= AF_ANGLE_2PI; return delta; } #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_widths( FT_UInt count, AF_Width table ) { FT_UInt i, j; AF_WidthRec swap; 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; } } } #ifdef TEST #include <stdio.h> #include <math.h> int main( void ) { int angle; int dist; for ( dist = 100; dist < 1000; dist++ ) { for ( angle = AF_ANGLE_PI; angle < AF_ANGLE_2PI * 4; angle++ ) { double a = ( angle * 3.1415926535 ) / ( 1.0 * AF_ANGLE_PI ); int dx, dy, angle1, angle2, delta; dx = dist * cos( a ); dy = dist * sin( a ); angle1 = ( ( atan2( dy, dx ) * AF_ANGLE_PI ) / 3.1415926535 ); angle2 = af_angle_atan( dx, dy ); delta = ( angle2 - angle1 ) % AF_ANGLE_2PI; if ( delta < 0 ) delta = -delta; if ( delta >= 2 ) { printf( "dist:%4d angle:%4d => (%4d,%4d) angle1:%4d angle2:%4d\n", dist, angle, dx, dy, angle1, angle2 ); } } } return 0; } #endif /* TEST */ /* END */