Comment by mrb | Hacker News Reader

Comment by mrb | Hacker News Reader

Hi Tom it's Marc, I'm glad to see you finished your sightline project ! Any clue why you report the longest sightline as "530.8 km" when it seems to be actually 538.1 km? That's what my code calculated (https://news.ycombinator.com/item?id=45512970) that's what Dr. Ulrich Deuschle also calculates (https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne...) You, Deuschle, and I all use the same DEM data (https://www.viewfinderpanoramas.org/Coverage%20map%20viewfin...) and the same refraction coeff (0.13), and nearly the same camera height (1.5m for me, 2.0m for Deuschle, and 1.65m for you—and these differing heights make no difference given the coarse DEM resolution). Something must be slighly off in your computations? Or do you think both Deuschle and I are wrong?

Edit: to be clear the difference stems from our coordinates. Our starting points are:

41.059167,77.683333 (me)

41.0181,77.6708 (you)

And our end points are:

36.295364,78.755593 (me)

36.314,78.7654 (you)

Also I calculate the distance assuming the Earth is spherical (which gives 538 km) not the standard geodesic (which would give 537 km).

And in the DEM data I measure the distance from the center of a cell to another (not the edge), while measuring from edge to edge may explain a difference of at most 0.1 km as the DEM resolution is 3 arcseconds.

So clearly we disagree on the coordinates of the exact actual sightline as we have a 7 km difference :-)

Edit #2: clearly the error is on your side. I should have checked this first, but the coordinates you give for the "To" point (41.0181,77.6708) land in a valley with the south view completely blocked so it's impossible to view 500+ km south as you claim. Look at where the marker lands on this Google Maps Terrain: https://maps.app.goo.gl/PgBWxi31WZC6vk3V9

Hey Marc, Ryan here. Tom may respond as well

There's two forms of interpolation going on here that I'm not sure you or Dr Dueschle are using. We interpolate a "band of sight" of single a degree for our azithmual projection, but uniquely we also rotate the DEM elevations around all the observers rather than the observer around to see all the elevations.

The effects of the first can be lessened by lowering the band of sight such that we only process half a degree at a time so that we make sure we get more coverage further away. We plan on running some more experiments by rotating to cover more points.

The algorithm is already fairly expensive to run against the whole world so we weren't particularly interested in that level of coverage for the full earth.

For total viewshed area, our algorithm comes in at roughly a percent or so difference which was what we used as our benchmark for correctness.

All this to say, no, we don't think you both are wrong, we've been looking at making ours more accurate. At a world scale that's quite computationally expensive, so we didn't use that methodology for our initial launch. We see our results as validation of yours, not as something we've disproved.

Edit: grammar

Ok that makes sense, thanks for the reply! Maybe document this "percent or so" error in the FAQ since it is about 16 times bigger than the (other?) ~0.0685% error you mention that can be caused by the AEQD reprojections.

Good idea, I'll add it to the FAQ later today. Under a section of "why don't these results match the other tools". The projection error is separate as you mentioned.

The error I've experienced hunting bugs tends to be within about .5-2%. That's a vibe, not an empirical "I've calculated the error to be 1.5%". We definitely expect that bound to tighten as we get access to more computational resources.

I do not think this is numerical however. I think it's more directly related to rasterization, interpolation, and not enough angle coverage. We have fairly good numerical and viewshed tests to double check we don't have weirdness going on there.

Reply to my edit #2: I realize the "To" point 41.0181,77.6708 is just the coordinate of the center of the 1°-wide horizon line. The actual farthest visible point according to your analysis is probably this peak in the west half of the 1° field of view: 41.014862, 77.647818 So I retract my comment about the error being "clearly" on your side. However this does indicate that we definitely calculate things differently. In my analysis Pik Dankova at 41.059542, 77.684808 which is a few km further can actually be seen and that's the source of our differences. I don't know who is right.

It sounds like we're just not casting enough rays then.

Ok! Ping me when you get it updated - I am very curious :-)

Sure!

Hey Marc!

I'm afraid I don't have a good answer. I'm sure with future runs will get closer to you and udeuschle.de

I thought of you when we saw Colombia appear so high up in the list, I remembered that's something you'd found too.

Is this a hobby lots of people have or something? And if so, what is it called? Cartography? I'm surprised to see folks debating this.

I suppose our hobby is related to the hobby of ground-to-ground long-distance observation. Except we don't perform the actual observation, just the math of where it is theoretically feasible :-) In my case, years ago, I did exactly the same as Tom and Ryan: I algorithmically searched for the longest sightline. It was a weekend project just to satisfy my curiosity. Then last year, Tom and I kinda connected informally over this hobby.

Fascinating, I'd never even thought of the longest sightline till now! Well cheers to you and Tom and Ryan, a thoughtful and smart bunch!! :)

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