Question

I got a point with latitude and longitude using decimals. The point is centered in a circle, the radius of the circle is x km. How do I find the all latitudes and longitudes which covers in the circle?

Answer 1

Probably the easiest answer is using pythagoras.

You got a point (x,y) which is the center of a circle of radius r.

‘How do I find the all latitudes and longitudes which covers in the circle?’ is almost infinite.

Instead you would rather want to check if a center point is within the radius of a circle (guessing you want to figure out what locations are within k km of point (x,y)).

Given point (x1,y1), you would do sqrt((x1-x)^2 + (y1-y)^2) (pythagoras theorem a^2 = b^2 + c^2) to find the distance from point (x,y) to point(x1,y1) and check if the distance is <= to radius r. Bounds are easily calculated (xmin = x-r, xmax = x+r etc.).

In terms of actual distance, you would probably need to use the Haversine formula:

a = sin²(Δlat/2) + cos(lat1).cos(lat2).sin²(Δlong/2)

c = 2.atan2(√a, √(1−a))

d = R.c

where R is earth’s radius (mean radius = 6,371km) (d is distance);
note that angles need to be in radians to pass to trig functions!

More on that here http://www.movable-type.co.uk/scripts/latlong.html