ch22.txt

chapter: Gaming from One Place to Another
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typedef enum {
float lat;
float lon;
} Coordinate2D;
    
    
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float distanceGreatCircle(Coordinate2D startPoint, Coordinate2D endPoint){

    //Convert location from degrees to radians
    float lat1 = (M_PI/180.) * startPoint.lat;
    float lon1 = (M_PI/180.) * endPoint.longi;
    float lat2 = (M_PI/180.) * endPoint.lat;
    float lon2 = (M_PI/180.) * endPoint.longi;

    //Calculate deltas
float dLat = lat2 - lat1;
    float dLon = lon2 - lon1;

    //Calculate half chord legnth
float a = sin(dLat/2) * sin(dLat/2) + cos(lat1) * cos(lat2) * sin(dLon/2) 
                                                           * sin(dLon/2);

//Calculate angular distance
    float C = 2 * atan(sqrt(a)/sqrt(1-a));

//Find arclength
    float distance = 6371 * C; //6371 is radius of earth in km
    return distance;
}
    
    
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float initialBearing (Coordinate2D startPoint, Coordinate2D endPoint){
    //Convert location from degrees to radians
    float lat1 = (M_PI/180.) * startPoint.lat;
    float lon1 = (M_PI/180.) * startPoint.longi;
    float lat2 = (M_PI/180.) * endPoint.lat;
    float lon2 = (M_PI/180.) * endPoint.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
return bearing;
}
    
    
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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;
}
    
    
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float rhumbBearing ( Coordinate2D startPoint, Coordinate2D endPoint){
    //Convert location from degrees to radians
float lat1 = (M_PI/180.) * startPoint.lat;
    float lon1 = (M_PI/180.) * startPoint.longi;
    float lat2 = (M_PI/180.) * endPoint.lat;
    float lon2 = (M_PI/180.) * endPoint.longi;

    //Calculate deltas
float dLat = lat2 - lat1;
    float dLon = lon2 - lon1;

    //find delta phi
    float deltaPhi = log(tan(lat2/2+(M_PI)/4)/tan(lat1+M_PI/4))
    float q=(deltaPhi==0 ? dlat/deltaPhi : cos(lat1); //avoids division by 0

if (abs(dLon) > M_PI){
        dLon = (dLon>0 ? −(2*(M_PI-dLon):(2*M_PI+dLon));
}

float D = sqrt(dLat*dLat + q*q*dLon*dLo)* 6371;
float theta = atan2f(dLon, deltaPhi);

//now convert to compass heading
float bearing = theta * (180 / M_PI); //radians to degrees
bearing = ( bearing > 0 ? bearing : (360.0 + bearing)); //fix range

return bearing;
}
    
    
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