Detecting if you are one kilometre from point of interest

I have an interesting question. I have a latitude value of 51.445376 and a longitude value of -0.190624 (as an example, say this was recieved by an androids location listener). This particular location (and it's values) is a point of i开发者_开发百科nterest and it is stored in my database. I am using a location listener on my android, and I will send the users current location to the server to detect if the user has come within a one kilometre radius of that particular point of interest. Does anyone know what algorithm to use to check if the users current longitude and latitude is within that one kilometre radius of the point of interests longitude and latitude? Or something I can see?

Perhaps someone could help me out, as my math is not the greatest in the world.

For geographic coordinates, use this function (public domain):

public static double distanceInKM(
           double latStart,double lonStart,
           double latEnd,double lonEnd
){
      latStart=Math.toRadians(latStart);
      latEnd=Math.toRadians(latEnd);
      return 6370.997*Math.acos(
              Math.cos(Math.toRadians(lonEnd - lonStart))*Math.cos(latStart)*
              Math.cos(latEnd)+Math.sin(latStart)*Math.sin(latEnd));
}

Calculating the shortest geographic path is called the "inverse geodesic problem", and this is discussed in C.F.F. Karney's article "Algorithms for geodesics, 2012. The method above shows a distance function based on the spherical law of cosines, which is a less accurate way to compute this path, especially because it assumes Earth is a perfect sphere.

This post from 2008 might be helpful.

It links to a MovableType description of how to use the Haversine formula to calculate the distance between two points on a sphere. It's important to note that it's not 100% accurate since the Earth is not a perfect sphere (it's equatorial radius is some 20km different from its polar radius) but should be sufficient for your needs.

The MovableType link also describes how to use an equi-rectangular projection (translation of lat/long to rectangular coordinates) and the pythagorean theorem to determine a rougher (but faster) approximation of the distance (good for small distances of ~1-2km.)

A simple solution: Simply find the distance, by first finding dx and dy.

Say I have point 1 (p1) and point 2 (p2)

dx = p2.x - p1.x; dy = p2.y - p1.y;

Now find the distance d as follows

d = sqrt(dx^2 + dy^2)

In a programming language like java, you can use the following lines:

double d = Math.sqrt(dx*dx + dy*dy);

Hope this helps as your starting point!

Note: x & y must be calculated accordingly for your lat&lon info. I was going to write a short code snippet but I saw someone else has a nice solution (I upvoted his response).