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geometrygpscoordinatesradius

Formula to determine whether a radius is within another radius

I want to define an operation to computer whether a radius is within another one.
My radiuses are defined by tuples (latitude, longitude, radius), with a radius in meters.
In other words, I want to be able to check whether a circle is within another circle, with an application to GPS coordinates.
I need an algorithm in pseudo-code that could be reused in many cases.

The closest formula I've found is the https://en.wikipedia.org/wiki/Haversine_formula

Solution

  • Let circle radii are R and r.
    Calculate distance d between circle centers using haversine formula.
    Compare d with radii:

    d > R + r:  circles don't intersect
Abs(R-r) <= d <= R + r: circles do intersect
Abs(R-r) > d : one circle lies inside another