Circle of Radius 1 km around Given Latitude/LongitudeDate: 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/ |
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