Posted on by Simon

Calculating the distance and bearing between two GPS points

I have been searching for a solution to calculate the distance and bearing of a target gps location for a while now. This page always popped up but my brain hurt every time I tried to convert this to lua.

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I am happy to say I have cracked it and here is my code.

function Geo_Angle( lat1, lon1, lat2, lon2)
  local dLon = math.rad(lon2-lon1);
  local y = math.sin(dLon) * math.cos(math.rad(lat2));
  local x = math.cos(math.rad(lat1)) * math.sin(math.rad(lat2)) - math.sin(math.rad(lat1)) * math.cos(math.rad(lat2)) * math.cos(dLon);
  local brng = math.deg(math.atan2(y, x));
  return ((brng + 360) % 360);
end

The distance code was created by roaminggamer else on the Corona forums (can’t find their name).

 
function Geo_Distance(lat1, lon1, lat2, lon2)
  if lat1 == nil or lon1 == nil or lat2 == nil or lon2 == nil then
    return nil
  end
  local dlat = math.rad(lat2-lat1)
  local dlon = math.rad(lon2-lon1)
  local sin_dlat = math.sin(dlat/2)
  local sin_dlon = math.sin(dlon/2)
  local a = sin_dlat * sin_dlat + math.cos(math.rad(lat1)) * math.cos(math.rad(lat2)) * sin_dlon * sin_dlon
  local c = 2 * math.atan2(math.sqrt(a), math.sqrt(1-a))
  -- 6378 km is the earth's radius at the equator.
  -- 6357 km would be the radius at the poles (earth isn't a perfect circle).
  -- Thus, high latitude distances will be slightly overestimated
  -- To get miles, use 3963 as the constant (equator again)
  local d = 6378 * c
  return d
end

Here is how I call the code

print("Bearing between Tamworth and Armidale: " .. tonumber(GeoAngle(-31.1063157, 150.9307341,-30.5143425, 151.66696439999998)))
print("Distance between Tamworth and Armidale: " .. tonumber(GeoDistance(-31.1063157, 150.9307341,-30.5143425, 151.66696439999998)) .. "km")

Results:

Corona Simulator[4155:693467] Bearing between Tamworth and Armidale: 47.07677793374
Corona Simulator[4155:693467] Distance between Tamworth and Armidale: 96.419986257454km

When comparing my results with this site my bearing results are within 0.18677793374 degree and 0.078686257454 km for distance (good enough for my simple augmented reality app).

I tried to trick it by putting the source/dest either side of GMT and it did not measure the longest route around the globe.

Corona Simulator[4288:936166] Bearing between -179 lon and 179 lon: 270
Corona Simulator[4288:936166] Distance between -179 lon and 179 lon: 222.6341993844km

Also putting a source/dest near each pole calculated the approximate right distance between the coordinates.

Corona Simulator[4288:936166] Bearing between -89 lat and 89 lat: 180°
Corona Simulator[4288:936166] Distance between 89 lat and 89 lat: 19814.443745211km

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