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

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

Most people are poor at knowing where the bottlenecks in their code will
be.  So my recommendation would be to use the geodesic distance and
only worry about finding a substitute if that proves too slow.

On 05/18/2014 12:33 PM, Edward Lam wrote:
> 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
>>