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auto_arc_tan() version 5


Integer Version (using an arc tangent look-up table). See version 1 for more information.
// N.B. There is a 16 bit version of this routine below this one.

long auto_arc_tan( long v_dx, long v_dy )
   {
   // AUTOMATIC ARC TANGENT ROUTINE returning an Signed 32 bit  value.
   //  (c) Jon P
   //
   // Version 5.0     Speed-up routine with a look-up table rather than a formula.
   //  
   #define ARC_TANGENT_TABLE_SIZE 129
   #define ARC_TANGENT_ONE 512 
   static unsigned char arc_tangent_table[ ARC_TANGENT_TABLE_SIZE ] =
      {
       0,  1,  2,  3,  4,  5,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
      17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31,
      32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41,
      42, 42, 43, 43, 44, 44, 44, 45, 45, 45, 45, 46, 46, 46, 46, 46,
      46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 45, 45, 45, 44,
      44, 44, 43, 43, 43, 42, 42, 41, 41, 40, 39, 39, 38, 38, 37, 36,
      35, 35, 34, 33, 32, 31, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22,
      21, 19, 18, 17, 16, 15, 14, 12, 11, 10,  8,  7,  6,  4,  3,  1,
       0
      };    // ...This array was made by ATAN_TBL.BAS      JonP
   register long grad, ang, abs_dx, abs_dy, half;
   
   abs_dx = v_dx;
   if ( abs_dx < 0 ) abs_dx = 0 - abs_dx;
   abs_dy = v_dy;
   if ( abs_dy < 0 ) abs_dy = 0 - abs_dy;
   
   // find the gradient between 0 and "1 in 1" (or 0 and 512 in this impelmentation)....
   if ( abs_dy <= abs_dx )
      {
      if ( abs_dx == 0 )
         { //exact angle can be returned... also this prevents divide by 0 error...
         if ( v_dy >= 0 )
            return 0;
         else
            return 2048;
         }
      grad = abs_dy;
      grad <<= 9;
      grad /= abs_dx;
      half = 1;
      }
   else
      {
      if ( abs_dy == 0 )
         { //exact angle can be returned... also this prevents divide by 0 error...
         if ( v_dx >= 0 )
            return 1024;
         else
            return 3072;
         }
      grad = abs_dx;
      grad <<= 9;
      grad /= abs_dy;
      half = 0;
      }


   // We now have a gradient between 0 and "1 in 1" (0 to 512).
   // Access the arc tangent look-up table to convert the gradient to
   // an angle between 0 and 45 degrees (0 to 512)...

   ang = arc_tangent_table[grad>>2] + grad;


   if ( v_dx >= 0 )
      {
      if ( v_dy >= 0 )
         {
         if ( half ) ang = 1024 - ang;
         }
      else
         {
         if ( half )
            ang += 1024;
         else
            ang = 2048 - ang;
         }
      }
   else
      {
      if ( v_dy >= 0 )
         {
         if ( half )
            ang += 3072;
         else
            ang = 4096 - ang;
         }
      else
         {
         if ( half )
            ang = 3072 - ang;
         else
            ang += 2048;
         }
      }
   
   // The next line is for testing only....
   // printf( "\ndx %d   dy %d    = ang %d ", v_dx, v_dy, ang );

   return ang;
   }




short auto_arc_tan_s16( long v_dx, long v_dy )
   {
   // AUTOMATIC ARC TANGENT ROUTINE returning an Signed 16 bit value.
   // (c) Jon P
   //
   // Version 5.0     Speed-up routine with a look-up table rather than a formula.
   //
   
   #define ARC_TANGENT_TABLE_SIZE 129
   #define ARC_TANGENT_ONE 512 
   static unsigned char arc_tangent_table[ ARC_TANGENT_TABLE_SIZE ] =
      {
       0,  1,  2,  3,  4,  5,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,
      17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 28, 29, 30, 31,
      32, 32, 33, 34, 35, 35, 36, 37, 37, 38, 39, 39, 40, 40, 41, 41,
      42, 42, 43, 43, 44, 44, 44, 45, 45, 45, 45, 46, 46, 46, 46, 46,
      46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 46, 45, 45, 45, 44,
      44, 44, 43, 43, 43, 42, 42, 41, 41, 40, 39, 39, 38, 38, 37, 36,
      35, 35, 34, 33, 32, 31, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22,
      21, 19, 18, 17, 16, 15, 14, 12, 11, 10,  8,  7,  6,  4,  3,  1,
       0
      };    // ...This array was made by ATAN_TBL.BAS      JonP
   register long grad, abs_dx, abs_dy, half;
   register short ang;
   

   abs_dx = v_dx;
   if ( abs_dx < 0 ) abs_dx = 0 - abs_dx;
   abs_dy = v_dy;
   if ( abs_dy < 0 ) abs_dy = 0 - abs_dy;
   
   // find the gradient between 0 and "1 in 1" (or 0 and 512 in this impelmentation)....
   if ( abs_dy <= abs_dx )
      {
      if ( abs_dx == 0 )
         { //exact angle can be returned... also this prevents divide by 0 error...
         if ( v_dy >= 0 )
            return 0;
         else
            return 2048;
         }
      grad = abs_dy;
      grad <<= 9;
      grad /= abs_dx;
      half = 1;
      }
   else
      {
      if ( abs_dy == 0 )
         { //exact angle can be returned... also this prevents divide by 0 error...
         if ( v_dx >= 0 )
            return 1024;
         else
            return 3072;
         }
      grad = abs_dx;
      grad <<= 9;
      grad /= abs_dy;
      half = 0;
      }


   // We now have a gradient between 0 and "1 in 1" (0 to 512).
   // Access the arc tangent look-up table to convert the gradient to
   // an angle between 0 and 45 degrees (0 to 512)...

   ang = arc_tangent_table[grad>>2] + grad;


   if ( v_dx >= 0 )
      {
      if ( v_dy >= 0 )
         {
         if ( half ) ang = 1024 - ang;
         }
      else
         {
         if ( half )
            ang += 1024;
         else
            ang = 2048 - ang;
         }
      }
   else
      {
      if ( v_dy >= 0 )
         {
         if ( half )
            ang += 3072;
         else
            ang = 4096 - ang;
         }
      else
         {
         if ( half )
            ang = 3072 - ang;
         else
            ang += 2048;
         }
      }
   
   // The next line is for testing only....
   // printf( "\ndx %d   dy %d    = ang %d ", v_dx, v_dy, ang );

   return ang;
   }