[Proj] Re: Distance measured in Mercator projection

strebe at aol.com strebe at aol.com
Thu Jul 10 15:28:22 EDT 2008

Glad this works for you. Don't hesitate to ask for the more complicated formula if you need greater accuracy — the calculation you have will be off by a percent or two because it assumes a spherical earth.

-- daan Strebe



-----Original Message-----
From: Shannon Scott <sscott at locationinc.com>
To: PROJ.4 and general Projections Discussions <proj at lists.maptools.org>
Sent: Thu, 10 Jul 2008 4:02 am
Subject: Re: [Proj] Re: Distance measured in Mercator projection

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 depen
d 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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