Re: [Geographiclib-users] Comparing distances between geographic coordinates

[Edward L. <e4...@ya...>]

Hi Charles,

Yes, I want the metric to correlate to real distances. Some of the hardware I'm looking at can be very underpowered (think 400 MHz clock speeds) which may (or may not) matter. I figured I'd ask anyway if there some proxy distance measure I could use that was faster to compute.

Thanks for your suggestion regardless.

-Edward

> On May 17, 2014, at 5:04 PM, Charles Karney <cha...@sr...> wrote:
> 
> Lots of distance metric will satisfy the triangle inequality
> 
> * geodesic distance on ellipsoid
> * Euclidean distance on ellipsoid
> * surface distance on sphere
> * Euclidean distance on sphere
> * a Manhattan distance |dlat| + |dlon|
> 
> etc.  However, I suspect you want a stronger condition, namely
> 
>  d(A,B) < d(A,C)
> 
> implies that B really is closer to A than C.  For this I recommend just
> using the true geodesic distance (e.g., from GeographicLib).  You can do
> a million such distance calculations in a couple of seconds.
> 
> On 05/17/2014 03:45 PM, Edward Lam wrote:
>> Hi,
>> 
>> I trying to write an app that performs route planning through a graph of
>> points given by their GPS latitude/longitude coordinates. So to do this,
>> I need to compare the relative distances between these points such that
>> the triangle inequality holds. What is the best/fastest way to do so?
>> 
>> There's a great deal of description on the web on how to compute
>> distances between two GPS coordinates ranging from approximate ones
>> based on the haversine formula via an idealized sphere to more accurate
>> ellipsoidal ones like the one in GeographicLib.
>> 
>> For this application, I don't need real distances between the points,
>> just some metric so that the triangle inequality holds. I'm tempted to
>> use the haversine formula since it is cheaper than the alternatives but
>> it has distortions depending on the chosen radius that may affect the
>> triangle inequality? Or am I over thinking this? Is there some
>> projection I can use that is both cheap and accurate?
>> 
>> Thanks,
>> -Edward
>