Circle of Radius 1 km around Given Latitude/Longitude

Date: 08/27/2002 at 20:50:24
From: Simla
Subject: Circle of radius 1 Km around given latitude and longitude

Hi,

I need feed points for a circle of radius 1 km with center at a given 
latitude and longitude. Eight or more points should be enough for the 
program. Could you tell me what formula I should use and how to get 
the points? Will I use spherical geometry?

Thanks,
Simla

Date: 08/28/2002 at 10:24:41
From: Doctor Rick
Subject: Re: Circle of radius 1 Km around given latitude and longitude

Hi, Simla.

Another inquirer wanted just four points (north, east, south, and 
west), but the answer I gave will allow you to calculate as many as 
you want - just choose headings such as 45 degrees.

   Finding Points on the Earth 
   http://mathforum.org/library/drmath/view/51816.html 

Since you are only concerned with short distances (1 km), a flat-earth 
approximation is probably sufficient, so you might also look here:

   Transformation between (x,y) and (longitude, latitude)
   http://mathforum.org/library/drmath/view/51833.html 

Here I explain how to convert latitude and longitude to x and y 
coordinates in a flat-earth approximation:

  x = R*(a2-a1)*(pi/180)*cos(b1)
  y = R*(b2-b1)*pi/180

You want to do the reverse. First find the (x,y) coordinates of a 
bunch of points on the circle using the usual Cartesian equation of a 
circle centered at the origin:

  x^2 + y^2 = r^2

Then you have to convert these (x,y) coordinates to the latitude and 
longitude of each point. I don't give this transformation in the page 
above, but it's easy enough to solve the equations for x and y to get 
a2 and b2:

  a2 = a1 + (x*180)/(R*pi*cos(b1))
  b2 = b1 + (y*180)/(R*pi)

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/