[Proj] Re: Distance measured in Mercator projection

Shannon Scott sscott at locationinc.com
Thu Jul 10 07:02:14 EDT 2008

Thank you all for your comments.
1m / cos (phi) was the formula I was looking for.

We have an application that maps data based on a search radius ( ie 5 
miles around Chicago ).
The maps show the search radius. We had been using UTM for the maps, so 
I was able to plot the search radius with this piece of code:
// convert miles to meters
bufdist = (miles * 1609.344);

// create circle
for (double i=0;i<360;i+=5) {
deltax = (Math.cos(i) * bufdist);
deltay = (Math.sin(i) * bufdist);
pntx = (centerPntx + deltax);
pnty = (centerPnty + deltay);
// plot point

The maps have been converted to work as a google map overlay, so we need 
to use the Mercator projection.
I have modified the way the search radius is calculated:
// convert miles to meters
bufdist = (miles * (Math.abs(1609.344 * (1/Math.cos(latrad)))));

and everything looks good.
Thanks again.

Ed McNierney wrote:
> Shannon -
> First, let me apologize for trying to respond (twice) when I was too 
> rushed to do so properly.
> Since you say you’re not very familiar with map projections, it might 
> be helpful for you to describe a little bit more about what you’re 
> trying to do. Daan’s and Chris’s comments are both correct but could 
> be confusing to a novice; the scale factor at a single point is the 
> same in all directions for a Mercator projection, but strictly 
> speaking only at that point. If you have another point in a different 
> place, the scale factor at that point will be different from the first 
> unless they’re at exactly the same latitude. So if you’re measuring 
> the distance between two points at a non-trivial distance apart, a 
> 500-mile line will, for example, change length on a Mercator map 
> depending on its angle with the Equator. What I was trying to say in 
> my first, poorly-worded reply, is that the set of points that are all 
> 500 miles from a center point on a Mercator map will NOT form a circle 
> on that map.
> If your question really is, “How can I measure the great circle 
> distance between two points given their Mercator coordinates” then 
> that’s rather tricky. And it will depend on how far apart those two 
> points are, and how accurate you need your answer to be.
> You will find incredibly talented professional expertise on this list, 
> but it’s hard for people to answer the question you didn’t ask. If you 
> can describe – in general terms, rather than specific ones – what 
> you’re trying to do and what questions you’re trying to answer, that 
> will make it easier. If there are constraints on your solution (e.g. 
> “I have to use Mercator so please don’t suggest an alternative 
> projection that would make the math easier”) let us know as well. Thanks.
> - Ed
> Ed McNierney
> 205 Indian Hill Road
> Groton, MA 01450
> ed at mcnierney.com
> +1 (978) 761-0049
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