[PROJ] Ellipsoidal distances, with different heights

[Even Rouault]

Or even simpler, compute geodesic distance on ellipsoid (a + h_mean, b + 
h_mean) where h_mean is the mean of h_start and h_end.  If h_start and 
h_end are small compared to a, I would expect whatever mean formula used 
to lead to similar results. At least this method is guaranteed to give 
the correct result when h_start = h_end = 0 ...

Le 28/08/2024 à 01:36, Even Rouault via PROJ a écrit :
> Nyall,
>
> I'm not sure there's a real definition to what you want to accomplish.
>
> I guess I would :
>
> - use the geod_position() of geodesic.h to compute a sufficient number 
> of intermediate positions
>
> - linearly interpolate the ellipsoidal height
>
> - convert the resulting (lon, lat, h) to geocentric (X, Y, Z) using 
> +proj=cart
>
> - use 3D Cartesian distance to compute each intermediate segment
>
> - sum them up
>
> A cheaper alternative might be to compute the geodesic distance 
> between the start and end points both on the ellipsoid (a + h_start, b 
> + h_start) and on the one (a + h_end, b + h_end), and compute some 
> sort of mean (arithmetic, geometry, ... ?) on those 2 distances.
>
> Even
>
>
> Le 28/08/2024 à 01:06, Nyall Dawson via PROJ a écrit :
>> Hi list,
>>
>> Let's say I have two points on an ellipsoid, with each point having a
>> different height above the ellipsoid. I want to calculate a kind of
>> "geodesic" between these points, where there's an assumption that the
>> gradient of the height-above-ellipsoid for the "geodesic" is constant.
>>
>> Is this mathematically solvable? Or, more to the point, is it possible
>> to calculate this using any of the methods exposed via geodesic.h?
>>
>> Nyall
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>
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