Game Development Reference
In-Depth Information
A negative angle involves starting at 0° and rotating in the decreasing-heading direction,
but compasses aren't labeled with negative values! To fix this, the line that has the com‐
ment “fix range” is using a ternary operator to say that if the bearing is less than 0, return
the value the compass would read. For example, if the bearing were −10°, then the
compass bearing is −10° + 360° = 350°. If the value is positive, then it just returns the
same value.
To find the final bearing, we simply take the initial bearing going from the end point to
the start point and then reverse it. The code is produced as follows:
float finalBearing (Coordinate2D startPoint, Coordinate2D endPoint){
//Convert location from degrees to radians
float lat1 = (M_PI/180.) * endPoint.lat;
float lon1 = (M_PI/180.) * endPoint.longi;
float lat2 = (M_PI/180.) * startPoint.lat;
float lon2 = (M_PI/180.) * startPoint.longi;
//Calculate deltas
float dLat = lat2 - lat1;
float dLon = lon2 - lon1;
//Calculate bearing in radians
float theta = atan2f( sin(dlon) * cos(lat2), cos(lat1)*sin(lat2)-sin(lat1)*cos(lat2)
*cos(dlon));
//Convert to compass bearing
float bearing = theta * (180 / M_PI); //radians to degrees
bearing = ( bearing > 0 ? bearing : (360.0 + bearing)); //fix range
bearing = ((bearing + 180) % 360) //reverse heading
return bearing;
}
The difference here is that we have flipped lat1 , long1 and lat2 , long2 while converting
the locations to radians. Also, before we return the bearing value, we reverse it by adding
180° degrees to it. The modulo operator ( % ) ensures that values over 360° are rolled over
into compass coordinates. For example, if we calculate a bearing of 350° and add 180°
to it, we get 530° degrees. If you start at 0° and go around 530°, you'll end up at 170°.
The modulo operator will result in the bearing being calculated with this correct com‐
pass value.
Rhumb Line
As discussed before, it is sometimes preferable to take a longer path of constant heading,
called a rhumb line, as compared to constantly changing your heading to follow a great
circle path. The rhumb line will be longer than the great circle, and the distance you are
from the great circle route at any moment is called the cross track error . To cross the
Atlantic is about 5% longer if you follow a rhumb line. The extreme example of going
from the East Coast of the United States to China is about 30% longer. However, such
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