检查点是否在圆圈内 [英] Check if point is inside a circle

问题描述

我有一点用纬度/经度表示

I have a point expressed in lat/long

Position louvreMuseum = new Position( 48.861622, 2.337474 );

我有一个以米表示的半径值.我需要检查另一个点(也以 lat/long 表示)是否在圆圈内.

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.

如果我在平坦的表面上，我可以简单地使用公式

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

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

正如这些 SO answer 中深入解释的那样.

as deeply explained in these SO answer.

但是根据纬度/经度的用法，由于行星的球形性质，我不能使用该公式.

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

如何计算任何给定点到中心的距离以与半径进行比较?

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

推荐答案

计算两个坐标之间距离的函数(从这里转换为C# 回答):

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);
}

如果两点之间的距离小于半径，那么它在圆内.

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

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