地理位置-如何检查2个圆圈是否重叠

Question

Let's say we have 2 locations (latitude,longitude) and each location has a radius (it may be different from each other), making a circle. How to check if these 2 circles are overlapping?

Answer 1

Check if the distance between the centers is smaller than the sum of the radii.

Say for circles A and B with radius A _r and B _r respectively, and coordinates ( A _x , A _y ) and ( B _x , B _y ) respectively, the distance between the circles is

D = sqrt( (A _x - B _x ) ² + (A _y - B _y ) ² )

They overlap when

D < A _r + B _r

There's a catch, however: the centers of the circles are placed on a sphere. The shortest distance between them is a straight line, beneath the sphere's surface. The distance between them following the surface will be larger. For instance, the distance between the North and South pole is 2 Earth radii, but the path on the surface will be 2π Earth radii. Also, these circles don't overlap. So, the above equations only hold when the distances are relatively small.