Check if point is inside a circle

Question

I have a point expressed in lat/long

Position louvreMuseum = new Position( 48.861622, 2.337474 );

and I have a radius value expressed in meters. I need to check if another point, also expressed in lat/long, is inside the circle.

If I were on a flat surface I can simply use the formula

(x - center_x)^2 + (y - center_y)^2 <= radius^2

as deeply explained in these SO answer.

However as per the latitude/longitude usage I can not use that formula because of the spherical nature of the planet.

How can I calculate a distance from any given point to the center to be compared with the radius?

Solution

Function to calculate the distance between two coordinates (converted to C# from this answer):

double GetDistance(double lat1, double lon1, double lat2, double lon2) 
{
    var R = 6371; // Radius of the earth in km
    var dLat = ToRadians(lat2-lat1);
    var dLon = ToRadians(lon2-lon1); 
    var a = 
        Math.Sin(dLat/2) * Math.Sin(dLat/2) +
        Math.Cos(ToRadians(lat1)) * Math.Cos(ToRadians(lat2)) * 
        Math.Sin(dLon/2) * Math.Sin(dLon/2);

    var c = 2 * Math.Atan2(Math.Sqrt(a), Math.Sqrt(1-a)); 
    var d = R * c; // Distance in km
    return d;
}

double ToRadians(double deg) 
{
    return deg * (Math.PI/180);
}

If the distance between the two points is less than the radius, then it is within the circle.

Comments

[Jonesopolis]

sounds like a math question, not a programming question

[Lorenzo]

@Jonesopolis: Right. Is a Math question that shall be correctly coded in a program

[A.S.H]

I googled distance using earth coordinates and found so many answers

[A.S.H]

Here is a detailed one: andrew.hedges.name/experiments/haversine