Calculation that calculates the new latitude and longitude based on a starting point, bearing and distance? - iphone

Question

Does anyone have a calculation that calculates the new
latitude and longitude based on a starting point, bearing and
distance?
I would greatly appreciate any help people might have.

Answer 1

I've used the code from Calculate new coordinate x meters and y degree away from one coordinate:
- (CLLocationCoordinate2D)coordinateFromCoord:(CLLocationCoordinate2D)fromCoord
atDistanceKm:(double)distanceKm
atBearingDegrees:(double)bearingDegrees
{
double distanceRadians = distanceKm / 6371.0;
//6,371 = Earth's radius in km
double bearingRadians = [self radiansFromDegrees:bearingDegrees];
double fromLatRadians = [self radiansFromDegrees:fromCoord.latitude];
double fromLonRadians = [self radiansFromDegrees:fromCoord.longitude];
double toLatRadians = asin(sin(fromLatRadians) * cos(distanceRadians)
+ cos(fromLatRadians) * sin(distanceRadians) * cos(bearingRadians) );
double toLonRadians = fromLonRadians + atan2(sin(bearingRadians)
* sin(distanceRadians) * cos(fromLatRadians), cos(distanceRadians)
- sin(fromLatRadians) * sin(toLatRadians));
// adjust toLonRadians to be in the range -180 to +180...
toLonRadians = fmod((toLonRadians + 3*M_PI), (2*M_PI)) - M_PI;
CLLocationCoordinate2D result;
result.latitude = [self degreesFromRadians:toLatRadians];
result.longitude = [self degreesFromRadians:toLonRadians];
return result;
}
- (double)radiansFromDegrees:(double)degrees
{
return degrees * (M_PI/180.0);
}
- (double)degreesFromRadians:(double)radians
{
return radians * (180.0/M_PI);
}
Or in Swift:
extension CLLocationCoordinate2D {
func adjusted(distance: Double, degrees: Double) -> CLLocationCoordinate2D {
let distanceRadians = distance / 6_371 // 6,371 == Earth's radius in km
let bearingRadians = degrees.radians
let fromLatRadians = latitude.radians
let fromLonRadians = longitude.radians
let toLatRadians = asin(sin(fromLatRadians) * cos(distanceRadians) + cos(fromLatRadians) * sin(distanceRadians) * cos(bearingRadians))
var toLonRadians = fromLonRadians + atan2(sin(bearingRadians)
* sin(distanceRadians) * cos(fromLatRadians), cos(distanceRadians)
- sin(fromLatRadians) * sin(toLatRadians))
// adjust toLonRadians to be in the range -180 to +180...
toLonRadians = fmod((toLonRadians + 3 * .pi), (2 * .pi)) - .pi
return CLLocationCoordinate2D(latitude: toLatRadians.degrees, longitude: toLonRadians.degrees)
}
}
extension CLLocationDegrees {
var radians: Double { self * .pi / 180 }
}
extension Double {
var degrees: CLLocationDegrees { self * 180 / .pi }
}

Answer 2

You will find all the calculations you could possibly want (including explanations etc) at http://www.movable-type.co.uk/scripts/latlong.html
The code you need is (in JavaScript) under the heading "Destination point given distance and bearing from start point". Excerpting:
var lat2 = Math.asin( Math.sin(lat1)*Math.cos(d/R) +
Math.cos(lat1)*Math.sin(d/R)*Math.cos(brng) );
var lon2 = lon1 + Math.atan2(Math.sin(brng)*Math.sin(d/R)*Math.cos(lat1),
Math.cos(d/R)-Math.sin(lat1)*Math.sin(lat2));
Where R = radius of the earth, d = distance (in same units), and lat/long are in radians (since that's what the sin function expects). You go from degrees to radians with
radians = pi * degrees / 180;
You should be able to take it from here. Do look at the link I gave for more info.