# Algorithm to achieve 1m of displacement as Degrees of Latitude and Longitude

### North/South Deltas:

This conversion is static no matter where you are on earth

=> 1Lat = 110.574km
1Lat = 110574m
1m = 0.00000904371732957115 Lat
therefore a delta can be calculated by the following algorithm:

const METERS_TO_LATITUDE = 0.00000904371732957115

const latitudeDelta = meters => meters * METERS_TO_LATITUDE


### East/West Deltas

This is not as straight forward. Degrees of Longitude (Lon) have to be calculated based on positioning on Earth. For example: 1Lon at the earth’s equator is much further a distance than 1Lon at either of the poles. This means we have to take into account the Latitude position to calculate 1Lon

The shortened algorithm looks like: 1Lon = 111.320km * cos(Lat)

First, we’ll convert it to meters:
1Lon = 111320m * cos(Lat)

Latitude is expressed in degrees, however we’ll need to convert it first to radians.

The standard algorithm to convert to radians is:
radians = degrees * π/180

which gives us:
1Lon = 111320m * cos(Lat*π/180)

However, we need to solve for meters:
111320m = cos(Lat * π/180)
1m = cos(Lat * π/180) / 111320

Which means, the following should be the correct algorithm:

const {PI, cos} = Math

const d2r = d => d * PI / 180

const longitudeDelta = (meters, lat) => meters * (cos(d2r(lat)) / 11320)


If this is true, we can also create some extra helper methods:

// all functions return a [LonLat] pair... keeping with the mathematical
// convention of supplying the x value first

const calculateDeltas = ( [ dx, dy ], lat) => (
[ longitudeDelta(dx, lat), latitudeDelta(dy) ]
)

const translateGeoPoint = ([ lon, lat ], [ dx, dy ]) => {
const deltas = calculateDeltas(lat, [ dx, dy ])
return [ lon + deltas, lat + deltas ]
}


I believe this is correct… if not, I’ll update this doc with further findings.