How do I figure out the grid references necessary to create a circular 1 mile radius around one location?

For instance:

Grid Reference: SO 47904 87484

X (Eastings): 347904

Y (Northings): 287484

I know the approach has something to do with referencing the number of degrees from the original point for instance 10. Then subtracting the output by the number of metres in the radius size (a mile, so 1609.344).

But I've forgot the actual approach. What is it, thanks?

  • What kind of technology/framework are you using? OpenLayers? ArcMap? QGIS? – Catlover Mar 3 '14 at 0:21
  • I am simply using O.S framework, the same format utilized on www.streetmap.co.uk/ – user2960091 Mar 3 '14 at 0:24
  • How did you actually draw the circle in the end? This exactly what I am trying to do? – user61459 Oct 28 '15 at 14:42

X and Y are in meters (if this is the UK national grid), so compute X' = round(X + 1609.344 cos(θ)) and Y' = round(X + 1609.344 sin(θ)), for θ ∈ [−π, π], and convert the results to grid references. There's small error in this approach (X and Y differ from true distances by a scale factor which differs slightly from one).

  • Could you please run through this explanation with an example? Also at what point does the number of degrees come into it? (as making radius around point) – user2960091 Mar 3 '14 at 1:17
  • I'm not sure what I can add...? Did you try working out the results for X' and Y'? Perhaps you need to know that theta could be given in degrees, and then, of course, theta is in [-180d, 180d] (but you need to make sure that this is compatible with the way you're computing sine and cosine). – cffk Mar 3 '14 at 1:54
  • The confusion might be in the mathematical terms used in @cffk's answer. If you want to draw a circle, work out how many points you want to draw it with, then, divide the whole circle (2 * pi) into angles that make up the whole circle, then use simple trigonometry to work out the X, Y differences for each point (dX = radius * cos(angle)) and (dY = radius * sin(angle)) then add them to your origin point. – Alex Leith Mar 3 '14 at 4:50

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