
Geometry : 
Subject: Re: [geometry] Support for geographic coordinate system
From: Adam Wulkiewicz (adam.wulkiewicz_at_[hidden])
Date: 20141126 19:40:35
Hi Barend,
20141126 23:22 GMT+01:00 Barend Gehrels <barend_at_[hidden]>:
>
> Adam Wulkiewicz wrote On 26112014 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:
>
> http://barendgehrels.blogspot.nl/2011/06/sphericalsideformula.html
>
> Quoting, a.o.:
> "Summary: Using some highschool 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.
>
>
> Nope.
>
Do you have an idea how we could verify this?
Regards,
Adam
Geometry list run by mateusz at loskot.net