Hi Barend,

2014-11-26 23:22 GMT+01:00 Barend Gehrels <barend@xs4all.nl>:

Adam Wulkiewicz wrote On 26-11-2014 21:25:

Of course in all formulas some approximation of a globe is used. My assessment is based on a fact that SSF assume thet a globe is a sphere

Ah, so you did not read my blog, and apparently also not my statements that SSF can be used on a spheroid.

Of course I did read it.
So I repeat it again, there it goes:


Quoting, a.o.:
"Summary: Using some high-school mathematics I presented an algorithm and a formula to calculate at which side a point is with resepect to a segment, on a sphere or on the Earth"

Beside the summary, it has a whole paragraph about the Ellipsoid.

Because this is exact, and Vincenty is an approximation (close to reality, but still, an approximation), I now just assume that these results are correct and the Vincenty approximation is off within ranges of 0.6.

I assume that, until it is proven that it is the other way round...

The paragraph about the Earth, corresponding planes, etc. would be true only if a shape of spherical geodesic and ellipsoidal one was the same. In other words, it would be true if all intermediate points of a segment was going through the same coordinates. Are you sure that this is the case? I'm not. My test seems to prove that this is not true or at least that a method (Vincenty) which is known for giving precise results for an ellipsoid gives different results than SSF. Of course this is more visible for greater flattening.

If SSF was only applicable for 100% spheres, the error would be much larger. Compare Haversine/Vincenty, it can be off many kilometers.

Yes, it's not surprising that the distance may be more influenced. I'm guessing that in the case of distance more important is the difference between major an minor axes than the actual shape of the shortest path. Still it doesn't mean that a side is calculated correctly.
Note: it is different from distance, where an exact mathematical formula for ellips or spheroid just does not exist.

AFAIU it's the same for ellipsoid. And greater the flattening, greater the difference. See the picture for flattening = 0.5.
and Vincenty that it's a spheroid. So the approximation is closer to reality. And the greater the flattening, the greater the difference between SSF and Vincenty. I'm not considering precision, numerical errors, stability etc.
As for the Vincenty formula here: http://www.icsm.gov.au/gda/gdav2.3.pdf states:
"Vincenty's formulae (Vincenty, 1975) may be used for lines ranging from a few cm to nearly 20,000 km, with millimetre accuracy."
Calculation done with SSF is probably also precise but it uses a sphere model, that's all.


 Do you have an idea how we could verify this?