Barend Gehrels wrote:
Adam Wulkiewicz wrote On 23-11-2014 13:54:
Barend Gehrels wrote:
Adam Wulkiewicz wrote On 7-11-2014 0:00:
Barend Gehrels wrote:
Adam Wulkiewicz wrote On 6-11-2014 17:06:

Basically, to support this CS we need a distance strategy and side strategy. They're already implemented (more or less) though in the extensions so not officially released yet. To release them we need to think about the interface first. The geographical strategies should have an interface similar to the one used in spherical strategies.


- a spherical side strategy is just used by default which I guess should be changed. I think the most precise would be a strategy finding the side using the geographic courses found using the inverse Vincenty's formula but this requires some testing

As far as I know, the spherical side strategy works for the geographic Earth too, please indicate if that is not the case.

See also

But I might be wrong, it is good to research this.

I feel that Vincenty's formula should give different results in some edge cases because the shape of geodesic on ellipsoid is different than on a sphere but I must perform some tests to be sure.

I'm curious about this.

I've made some quick test where I compared the result of spherical side formula and a side found by comparison of azimuths calculated using Vincenty's formula. The method comparing azimuths is very simple and probably not good enough to be released nevertheless the error is too small to be seen in this case. The difference between spherical and geographical geodesic seems to be a lot greater.

Thanks! But...
What is the conclusion?
- SSF can only be used for spherical and not for geographic (all non-spheres)?

It can be used but will give wrong results for spheroids. SSF gives the same results as Vincenty for sphere/flattening=0.

- the method comparing azimuths (you mentioned is probably not good enough) is not sufficient?

It's because the further the Point the calculation becomes less accurate. A "real" cross-track distance should probably be calculated and compared with EPS (if needed), similar to side_by_cross_track (or side_by_azimuth). However even there the distance nor radius isn't taken into account and without it we can't calculate a value of XTD. But maybe it's sufficient to do it this way... At least for doubles, I'm guessing that for floats it'd be different.

I cannot completely read that from your story, but the color-descriptions indicate the Vincenty azimuth comparisons are OK? It looks good indeed.

Most importantly they give different results. The difference is marked with bright colors. Some users may be ok with spherical calculations some may not.

It's also possible that I made something wrong. In that case don't hesitate to point it out :)

bgd::vincenty_inverse<double> vi2(lon_s1 * bg::math::d2r, lon_s1 * bg::math::d2r,
the second lon should be lat. Makes no difference for this test because both are 51, but for other tests it should be changed.

you skip collinear cases?

Do you mean, when a point is on a segment? The epsilon is so small that all test points are missing the segment (at least for double).

Btw, in spherical_side_formula EPS isn't used in the final result calculation:

return dist > zero ? 1
     : dist < zero ? -1
     : 0;

AFAIU dist should be compared with 0 using math::equals(). Do you agree? Or is there a reason why it's implemented like this?

Here is the code and the results:

Can you give a coordinate-pair where the deviation is large (probably easy to read from the graph)?

For the Earth the width of the erroreous part around lon=11.3, lat=17.3 is more or less 1.7 km but this is for this very long segment (-51 -51, 51 51). For a 1 deg segment (11 17, 12 18) (153km long) the width of the erroreous fragment is around 0.6m. So the difference seems to be relativaly small. I didn't check it for coordinates closer to poles.