heading in a cartesian coordinate system question

[MikeAThon]

Understand that you are using a compass-style definition of headings, which differs from standard angular measurements used by most trig functions by direction (clockwise vs. counterclockwise) and by 90 degrees (or, pi/2 radians, since most trig functions use radians, not degrees).

With that understanding, look at the atan2() function. To get the compass heading in degrees from point b to point a, use the following:

double compass_heading = 90.0 - 57.29578 * atan2( by-ay, bx-ax );
if (compass_heading >= 360.0)
  compass_heading -= 360.;
if (compass_heading < 0.0)
  compass_heading += 360.;

In your case, where point a is at the origin, ay=ax=0, which simplifies the equation a bit.

To determine if the actual heading is "close enough" to the compass heading, just test against limits:

double limit = 30.0;  /* in degrees */
double actual_heading = /* whatever */;
if ( fabs( actual_heading - compass_heading ) < limit
{
  /* it's close enough
}
else
{
  /* it's not close enough */
}

fabs() is the floating point absolute value function.

Mike