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

[Charles K. <cha...@sr...>]

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
>