Created
June 22, 2012 11:35
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optimized atan2 approximation
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#include <stdio.h> | |
#include <stdlib.h> | |
#include <math.h> | |
float atan2_approximation1(float y, float x); | |
float atan2_approximation2(float y, float x); | |
int main() | |
{ | |
float x = 1; | |
float y = 0; | |
for( y = 0; y < 2*M_PI; y+= 0.1 ) | |
{ | |
for(x = 0; x < 2*M_PI; x+= 0.1) | |
{ | |
printf("atan2 for %f,%f: %f \n", y, x, atan2(y, x)); | |
printf("approx1 for %f,%f: %f \n", y, x, atan2_approximation1(y, x)); | |
printf("approx2 for %f,%f: %f \n \n", y, x, atan2_approximation2(y, x)); | |
getch(); | |
} | |
} | |
return 0; | |
} | |
float atan2_approximation1(float y, float x) | |
{ | |
//http://pubs.opengroup.org/onlinepubs/009695399/functions/atan2.html | |
//Volkan SALMA | |
const float ONEQTR_PI = M_PI / 4.0; | |
const float THRQTR_PI = 3.0 * M_PI / 4.0; | |
float r, angle; | |
float abs_y = fabs(y) + 1e-10f; // kludge to prevent 0/0 condition | |
if ( x < 0.0f ) | |
{ | |
r = (x + abs_y) / (abs_y - x); | |
angle = THRQTR_PI; | |
} | |
else | |
{ | |
r = (x - abs_y) / (x + abs_y); | |
angle = ONEQTR_PI; | |
} | |
angle += (0.1963f * r * r - 0.9817f) * r; | |
if ( y < 0.0f ) | |
return( -angle ); // negate if in quad III or IV | |
else | |
return( angle ); | |
} | |
#define PI_FLOAT 3.14159265f | |
#define PIBY2_FLOAT 1.5707963f | |
// |error| < 0.005 | |
float atan2_approximation2( float y, float x ) | |
{ | |
if ( x == 0.0f ) | |
{ | |
if ( y > 0.0f ) return PIBY2_FLOAT; | |
if ( y == 0.0f ) return 0.0f; | |
return -PIBY2_FLOAT; | |
} | |
float atan; | |
float z = y/x; | |
if ( fabs( z ) < 1.0f ) | |
{ | |
atan = z/(1.0f + 0.28f*z*z); | |
if ( x < 0.0f ) | |
{ | |
if ( y < 0.0f ) return atan - PI_FLOAT; | |
return atan + PI_FLOAT; | |
} | |
} | |
else | |
{ | |
atan = PIBY2_FLOAT - z/(z*z + 0.28f); | |
if ( y < 0.0f ) return atan - PI_FLOAT; | |
} | |
return atan; | |
} |
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very nice, indeed.