6 ms·

Packing the world for longest lines of sight

141 points by tombh 1y ago

greggsy 1y ago
Related, there’s a Reddit post tracking the furthest photos of the Sydney skyline: https://www.reddit.com/r/sydney/comments/1lzke5t/the_actual_furthest_point_you_can_see_sydney/ https://www.reddit.com/r/sydney/comments/1lzke5t/the_actual_... Google Earth map: https://earth.google.com/web/@-32.84964163,149.89452785,590.94032059a,749464.65835959d,35y,360h,0t,0r/data=CgRCAggBMikKJwolCiExOE1QYVlNbC14dHkzYWZNVjdqWGtJcTRsVzVmaWFBcjcgAToDCgEwQgIIAEoHCKf_uhwQAQ https://earth.google.com/web/@-32.84964163,149.89452785,590....
- SpicyUme 1y ago
  There's a nearly 450 km photo of the Ecrins from the Pyrenees! https://beyondrange.wordpress.com/2016/08/03/pic-de-finestrelles-pic-gaspard-ecrins-443-km/ https://beyondrange.wordpress.com/2016/08/03/pic-de-finestre... That's a cool thing to track, I've been surprised by the places I've seen the Seattle skyline reflected on the water near sundown. No crazy distances, but there's a small time period where it flashes into view.
  - lloeki 1y ago
    On clear days from the Vosges mountains you can easily see the French Alps (and even part of Austrian Alps if lucky), and especially the Mont Blanc. e.g places like the Ballon D'Alsace, and even all the way up north to Donon or Nideck+Schneeberg†. Quite a bit shorter in distance (between 200 and 300km depending on where you sit) but visually stunning. I seem to recall in older times there used to be some light semaphore infrastructure to communicate over these distances. https://web.archive.org/web/20251008080738mp_/https://i72.servimg.com/u/f72/12/92/78/27/pict0016.jpg https://web.archive.org/web/20251008080738mp_/https://i72.se... https://www.vosgesmatin.fr/environnement/2023/12/19/quand-le-mont-blanc-se-dessine-au-loin-depuis-le-ballon-d-alsace https://www.vosgesmatin.fr/environnement/2023/12/19/quand-le... https://www.vosgesmatin.fr/environnement/2022/11/12/quand-le-mont-blanc-se-decouvre-depuis-le-ballon-d-alsace https://www.vosgesmatin.fr/environnement/2022/11/12/quand-le... † Which I hiked this year, unfortunately only had a phone so all I get is the memory of seeing the Mont Blanc from there.
    - DiggyJohnson 1y ago
      Panorama in the first of three links is stunning.
    - SpicyUme 1y ago
      Those are great pictures. And I've been near there! I've seen the Alps from near Saignelégier then we drove through Plombieres-les-Bains on the way north. On certain clear winter days I bet the mountains look bigger due to lensing.
- 7373737373 1y ago
  This had me find https://old.reddit.com/r/FromAfar/top/?t=all https://old.reddit.com/r/FromAfar/top/?t=all !
cozzyd 1y ago
If you consider atmospheric refraction it might be more complicated...
eszed 1y ago
Since you asked about alternate packing solutions: https://news.ycombinator.com/item?id=43305920 https://news.ycombinator.com/item?id=43305920 I don't know enough about the subject to have any useful suggestions, but I'd be interested in your take on how a project like yours would work differently if you were to choose a different solution.
- tombh 1y ago
  I'd heard of H3, they definitely sound like they could be related, but I think they're solving a different problem. I think H3 is for efficient storage of geographic data whereas I'm just trying to solve a classic packing problem, like this monstrosity https://www.reddit.com/r/math/comments/111ne5y/deeply_unsettling_asymmetric_patterns_in/ https://www.reddit.com/r/math/comments/111ne5y/deeply_unsett...
rendaw 1y ago
I was recently looking into this for roguelike-like visibility calculations. The term I came across was "isovist" not "viewshed", but they seem identical? The former appears to be used a lot in architecture. Calculating a 2d isovist is (relatively) simple, for 3d it seems much more complex. Is this simplified by the fact that it's dealing with a height map?
- pcthrowaway 1y ago
  Not sure what you mean by 2D isovist, but is it that 3D involves the curvature of the earth?
  - rendaw 1y ago
    Something like this: https://en.wikipedia.org/wiki/Isovist#/media/File:Isovist.svg https://en.wikipedia.org/wiki/Isovist#/media/File:Isovist.sv...
lsy 1y ago
I'm sure it's nearly an academic distinction, but: > Basically, for any given region, we find its highest point and assume that there is a perfectly placed sibling peak of the same height that is mutually visible. Shouldn't you always add 335km to the horizon distance to account for the possibility of Everest (i.e. a taller sibling peak) being on the other side of the horizon?
- tennysont 1y ago
  You're right, but all lines of sight are mutual, so we will notice this oversight when checking the other peak. This seems poorly explained, but I think the author was in a hurry to get to the main algorithm, and sped through the intro.
- tombh 1y ago
  Author here. I really appreciate this question because it's the entire reason I wrote the post. I feel like this is a unique problem and so I'm sure I'm not considering all the possibilities. I _think_ your suggestion is covered by the fact that I'm basing the size of the tile on the single highest point that it contains. The steps are: 1. Take any point and calculate the furthest theoretical distance it could see if there were another point at just the perfect distance away for mutual visibility. Note how there could of course be an Everest, but I don't check because step 2 should solve that. 2. Based on that furthest theoretical distance I create a tile of that exact width around the point and then check to see what the new highest point is within that tile _and_ its surroundings. "Surroundings" here means a border region around the tile of the same width as the tile itself. These surroundings don't get viewsheds calculated for them, they're just auxiliary data. 3. If a higher point is found, then increase the width based on that new highest point and repeat step 2. If no higher point is found then the tile is ready.
temptemptemp111 1y ago
[dead]
dolmen 1y ago
Does the source dataset includes with enough precision human made buildings? Will it allow to determine the farthest point theorically visible from the top of the Eiffel Tower?
- tombh 1y ago
  The underlying data isn't that accurate, but I think with a tool like https://www.heywhatsthat.com https://www.heywhatsthat.com you can set the coordinates and elevation manually and create a custom viewshed.
mungoman2 1y ago
As proposed in the article, calculating the area weights all points in the viewshed equally. I wonder if it makes sense to give more weight to far-away points? Or maybe less weight? Not sure! But would be interesting to explore and see if it gives anything.
- tombh 1y ago
  I'm the author. Well there's actually a term in the kernel to normalise the surface area of each visible point by a factor of tan(1 radian): https://github.com/tombh/total-viewsheds/blob/main/crates/kernels/vulkan-and-cpu/src/kernel.rs#L163 https://github.com/tombh/total-viewsheds/blob/main/crates/ke... I don't know if that's related to what you're thinking about?
7373737373 1y ago
I've been wondering about using OpenStreetMap data to achieve something similar, like getting the longest uninterrupted (by buildings) distance between two viewpoints (the Nikon Coolpix P900/P1000/P1100 cameras or a telescope are pretty good for this due to their extreme focal lengths), or maybe something like "most ice cream shop dense area" https://wiki.openstreetmap.org/wiki/Key:amenity https://wiki.openstreetmap.org/wiki/Key:amenity Putting the typical airplane cruise altitude (10km) into the distance to horizon calculator https://www.ringbell.co.uk/info/hdist.htm https://www.ringbell.co.uk/info/hdist.htm results in a "reverse" distance of 357km to the horizon. So that's how far typical airplanes can be seen when standing at sea level!
- 7373737373 1y ago
  The answer to the ice cream question (for places where ice cream can be bought) appears to be Buenos Aires! https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7B%7Bbbox%7D%7D%29%5B%22amenity%22%3D%22ice_cream%22%5D%3B%0Aout%20body%3B%0A&C=-34.639705%3B-58.416417%3B12&R= https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7... (for any circular area centered around such a shop with 10km radius) For ice cream shops specifically, Kraków? https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7B%7Bbbox%7D%7D%29%5B%22shop%22%3D%22ice_cream%22%5D%3B%0Aout%20body%3B%0A&C=50.058902%3B19.954179%3B14&R= https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7...
mrb 1y ago
Oh that project is right up my alley, as I did the same! Back in 2021, for fun, I wrote an algorithm to find the longest sightline on earth. And I did find a previously undiscovered sightline. My code was relatively unoptimized, it ran for 95 days on an 8-core 16-thread AMD Ryzen 5750G to crunch all the data. I have never published my code or results. I should really do it... I downloaded a digital earth model of about 30 gigabytes from http://www.viewfinderpanoramas.org/Coverage%20map%20viewfinderpanoramas_org3.htm http://www.viewfinderpanoramas.org/Coverage%20map%20viewfind... which had a resolution of 3 seconds, so I had the elevation of each 90x90 meters "tile" of land. I wrote a simple algo in C that: finds potential viewpoints (mountain peaks or plateaus above a minimum ), calculates the longest sightline 360° around you, taking into account an atmospheric refraction coefficient (I used 0.13 which seems to be a default used by some panorama tools like https://www.udeuschle.de https://www.udeuschle.de). It's really basic trigonometry: look one tile ahead of you, and the next one, etc, until you find the one with the highest vertical angle of view. Stop one sightline exploration when reaching a certain maximum distance (750 km in my implementation) when it becomes mathematically impossible to find a visible tile beyond this distance. And I found the longest sightline: In Kyrgyzstan from Pik Dankova (41.059167,77.683333) which is at 5977.5 meters (in my DEM data), you can see 538.1 km into China if you look toward bearing 169.7° (roughly south) as you see some distant minor peak at 36.295364,78.75593 which is 6444.0 meters high. However this sightline is already known. But it's only theoretical. No one ever encountered good enough atmospheric clear-sky conditions to observe it from Pik Dankova. Using the panorama tool maintained by this cool German guy, you can verify it: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=newstandard&data=lon:77.684167$$$lat:41.059167$$$alt:auto$$$altcam:2$$$hialt:false$$$resolution:600$$$azimut:169.7$$$sweep:1$$$leftbound:169.2$$$rightbound:170.2$$$split:2$$$splitnr:1$$$tilt:-2.14166666666667$$$tiltsplit:false$$$elexagg:1$$$range:750$$$colorcoding:false$$$colorcodinglimit:493$$$title:Pik+Dankova$$$description:$$$email:$$$language:ge$$$screenwidth:2560$$$screenheight:1414 https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... However one notable finding my tool gave me was it discovered the second longest sightline that is competely unknown up until this day AFAIK: In Colombia, from Pico Cristóbal Colón (10.838333,-73.687500) which is at 5668.5 meters (in my DEM data), you can see 502.6 km over the plains of the Caribbean region all the way to the Colombian Andes if you look toward bearing 206.2° (roughly south-south-west) as you see some distant peak at 6.777286,-75.692304 which is 3347.0 meters high. Here you can verify it here: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=newstandard&data=lon:-73.6875$$$lat:10.838333$$$alt:auto$$$altcam:2$$$hialt:false$$$resolution:600$$$azimut:206.2$$$sweep:1$$$leftbound:205.7$$$rightbound:206.7$$$split:2$$$splitnr:1$$$tilt:-2.29166666666667$$$tiltsplit:false$$$elexagg:1.2$$$range:750$$$colorcoding:false$$$colorcodinglimit:502$$$title:Pico%20Crist%C3%B3bal%20Col%C3%B3n$$$description:$$$email:$$$language:ge$$$screenwidth:2304$$$screenheight:1440 https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... I am not sure if this Comlombian sighline has ever been observed. As I said I should really publish my code and results. And at some point I would like to optimize it and re-run it using a higher-precision DEM with 30x30 meters tiles instead of 90x90 meters. I think there are a few 30-meter DEMs available but I need to find the highest-quality one.
hdersch 1y ago
"Viewsheds" of any location can be calculated and matched with photographs using "GeoImageViewer", an application I wrote a couple of years ago. Any feature in the image can be interactively identified in a mapview and vice versa, including the boundary of the viewshed. As has been mentioned in the comments, it is essential to include atmospheric refraction in the calculation, at least for distances above ~100km. [1] https://hdersch.github.io/Viewing.html https://hdersch.github.io/Viewing.html
- redfloatplane 1y ago
  Wow, this is really an incredible bit of work! Very impressive stuff, I look forward to using it!
- shrx 1y ago
  There's also https://www.heywhatsthat.com/ https://www.heywhatsthat.com/
- tombh 1y ago
  What a fantastic tool. I'm the author of the post. Do you have any knowledge about how refraction can vary? I was wondering about calculating the world twice, once with a lower refraction bound and then again with an upper.
  - hdersch 1y ago
    Atmospheric refraction is due to the vertical gradients of atmospheric pressure, temperature, and composition of the atmosphere, all of which are usually not precisely known, and which vary with time, so one gets larger lines of sights at certain times. For my application I used the standard formulas for astronomical refraction (-> many weblinks) with constant medium gradients. If I recall correctly this results in ~100m height correction for features in 100km distance and ~400m in 200km distance (features appear higher than without atmospheric refraction). For your application it would make sense to use two extreme values for the gradients to get maximum and minimum, as you suggested.
    - 1y ago
me_vinayakakv 1y ago
Nice work! Do the tiles point to actual heatmap?
- tombh 1y ago
  Each tile's heatmap takes hours to crunch, so I haven't done them all yet. Here's a sneak peek of the UK though https://mastodon.social/@tombh/115330398582193988 https://mastodon.social/@tombh/115330398582193988
anovikov 1y ago
Ofc my home country's name was misspelled :/
- tombh 1y ago
  Kyrgyzstan? Damn, I'm sorry. I've update the article now.
  - anovikov 1y ago
    Thank you! I kind of understood that from those mountains one could see really far away, but had no idea it was THAT far.
mrb 1y ago
Nitpick: "resolution of 3 arc-seconds (~100m²)" This resolution is equivalent to tiles of 8500 m² not 100 m². I think the author confused tile edge length (92 meters exactly) with tile area.
- tombh 1y ago
  Damn, that's the second time I've confused those 2 concepts. The distinction is significant. I updated the article, thanks.
Theodores 1y ago
You have a very interesting project. What happens if you put your maps and elevation data on a 'sphere', to model the world as 3D? You can then leverage a GPU to render a view from one vertex to then determine what is furthest away yet visible from that vertex. The vertices can then be given some type of heatmap colour and an interactive tool made. A full GIS tool isn't needed for this, with Blender and three.js there are all of the tools needed.
- tombh 1y ago
  This is pretty much what I'm already doing. The kernel is written on the GPU and just does raw visibility calculations.
reassess_blind 1y ago
A kid once asked me “How far can humans see?”. I told him you can see the Andromeda Galaxy 2.5 million light years away, but when he said he meant on Earth I didn’t know the answer.
lostlogin 1y ago
> I find these TVS heatmaps eerily beautiful. The first one somehow looked like something violent going on. Limbs? Bodies?
liamph 1y ago
It is interesting to also consider dry land which is below sea level. "For an average height person standing on a beach, their horizon is around 4.5km away." For an average height person standing at sea level, near a large depression such as the Dead Sea, for example, you may be able to see land at a much greater distance. I doubt if this factor would impact your findings for the longest sight lines on Earth, but perhaps for some local findings. Also, applying the same concept to other planets has some surprising results. The tallest mountain in the solar system, Olympus Mons, has very gentle slopes. So gentle that from the peak all you can see is Olympus Mons itself.
- tombh 1y ago
  Yes! These are very much the kinds of questions I'm interested in. The search for the single longest line of sight on Earth is just an excuse to play around in this space.
TCHAD235 1y ago
Samsung
kcexn 1y ago
I don't think I'm understanding the properties of a viewshed tile. Each tile is sized so that the viewshed size (in square metres) of every point within the tile can be found just from elevation data within the tile itself? But that doesn't seem right from the example you gave, because along the edge at the mouth of the river, the viewshed presumably includes the rest of the river outside of the tile as well?

141 points by tombh 1y ago

Related, there’s a Reddit post tracking the furthest photos of the Sydney skyline: https://www.reddit.com/r/sydney/comments/1lzke5t/the_actual_furthest_point_you_can_see_sydney/ https://www.reddit.com/r/sydney/comments/1lzke5t/the_actual_... Google Earth map: https://earth.google.com/web/@-32.84964163,149.89452785,590.94032059a,749464.65835959d,35y,360h,0t,0r/data=CgRCAggBMikKJwolCiExOE1QYVlNbC14dHkzYWZNVjdqWGtJcTRsVzVmaWFBcjcgAToDCgEwQgIIAEoHCKf_uhwQAQ https://earth.google.com/web/@-32.84964163,149.89452785,590....

SpicyUme 1y ago
There's a nearly 450 km photo of the Ecrins from the Pyrenees! https://beyondrange.wordpress.com/2016/08/03/pic-de-finestrelles-pic-gaspard-ecrins-443-km/ https://beyondrange.wordpress.com/2016/08/03/pic-de-finestre... That's a cool thing to track, I've been surprised by the places I've seen the Seattle skyline reflected on the water near sundown. No crazy distances, but there's a small time period where it flashes into view.
- lloeki 1y ago
  On clear days from the Vosges mountains you can easily see the French Alps (and even part of Austrian Alps if lucky), and especially the Mont Blanc. e.g places like the Ballon D'Alsace, and even all the way up north to Donon or Nideck+Schneeberg†. Quite a bit shorter in distance (between 200 and 300km depending on where you sit) but visually stunning. I seem to recall in older times there used to be some light semaphore infrastructure to communicate over these distances. https://web.archive.org/web/20251008080738mp_/https://i72.servimg.com/u/f72/12/92/78/27/pict0016.jpg https://web.archive.org/web/20251008080738mp_/https://i72.se... https://www.vosgesmatin.fr/environnement/2023/12/19/quand-le-mont-blanc-se-dessine-au-loin-depuis-le-ballon-d-alsace https://www.vosgesmatin.fr/environnement/2023/12/19/quand-le... https://www.vosgesmatin.fr/environnement/2022/11/12/quand-le-mont-blanc-se-decouvre-depuis-le-ballon-d-alsace https://www.vosgesmatin.fr/environnement/2022/11/12/quand-le... † Which I hiked this year, unfortunately only had a phone so all I get is the memory of seeing the Mont Blanc from there.
  - DiggyJohnson 1y ago
    Panorama in the first of three links is stunning.
  - SpicyUme 1y ago
    Those are great pictures. And I've been near there! I've seen the Alps from near Saignelégier then we drove through Plombieres-les-Bains on the way north. On certain clear winter days I bet the mountains look bigger due to lensing.
7373737373 1y ago
This had me find https://old.reddit.com/r/FromAfar/top/?t=all https://old.reddit.com/r/FromAfar/top/?t=all !

cozzyd 1y ago

If you consider atmospheric refraction it might be more complicated...

eszed 1y ago

Since you asked about alternate packing solutions: https://news.ycombinator.com/item?id=43305920 https://news.ycombinator.com/item?id=43305920 I don't know enough about the subject to have any useful suggestions, but I'd be interested in your take on how a project like yours would work differently if you were to choose a different solution.

tombh 1y ago
I'd heard of H3, they definitely sound like they could be related, but I think they're solving a different problem. I think H3 is for efficient storage of geographic data whereas I'm just trying to solve a classic packing problem, like this monstrosity https://www.reddit.com/r/math/comments/111ne5y/deeply_unsettling_asymmetric_patterns_in/ https://www.reddit.com/r/math/comments/111ne5y/deeply_unsett...

rendaw 1y ago

I was recently looking into this for roguelike-like visibility calculations. The term I came across was "isovist" not "viewshed", but they seem identical? The former appears to be used a lot in architecture. Calculating a 2d isovist is (relatively) simple, for 3d it seems much more complex. Is this simplified by the fact that it's dealing with a height map?

pcthrowaway 1y ago
Not sure what you mean by 2D isovist, but is it that 3D involves the curvature of the earth?
- rendaw 1y ago
  Something like this: https://en.wikipedia.org/wiki/Isovist#/media/File:Isovist.svg https://en.wikipedia.org/wiki/Isovist#/media/File:Isovist.sv...

lsy 1y ago

I'm sure it's nearly an academic distinction, but: > Basically, for any given region, we find its highest point and assume that there is a perfectly placed sibling peak of the same height that is mutually visible. Shouldn't you always add 335km to the horizon distance to account for the possibility of Everest (i.e. a taller sibling peak) being on the other side of the horizon?

tennysont 1y ago
You're right, but all lines of sight are mutual, so we will notice this oversight when checking the other peak. This seems poorly explained, but I think the author was in a hurry to get to the main algorithm, and sped through the intro.
tombh 1y ago
Author here. I really appreciate this question because it's the entire reason I wrote the post. I feel like this is a unique problem and so I'm sure I'm not considering all the possibilities. I _think_ your suggestion is covered by the fact that I'm basing the size of the tile on the single highest point that it contains. The steps are: 1. Take any point and calculate the furthest theoretical distance it could see if there were another point at just the perfect distance away for mutual visibility. Note how there could of course be an Everest, but I don't check because step 2 should solve that. 2. Based on that furthest theoretical distance I create a tile of that exact width around the point and then check to see what the new highest point is within that tile _and_ its surroundings. "Surroundings" here means a border region around the tile of the same width as the tile itself. These surroundings don't get viewsheds calculated for them, they're just auxiliary data. 3. If a higher point is found, then increase the width based on that new highest point and repeat step 2. If no higher point is found then the tile is ready.

temptemptemp111 1y ago

[dead]

dolmen 1y ago

Does the source dataset includes with enough precision human made buildings? Will it allow to determine the farthest point theorically visible from the top of the Eiffel Tower?

tombh 1y ago
The underlying data isn't that accurate, but I think with a tool like https://www.heywhatsthat.com https://www.heywhatsthat.com you can set the coordinates and elevation manually and create a custom viewshed.

mungoman2 1y ago

As proposed in the article, calculating the area weights all points in the viewshed equally. I wonder if it makes sense to give more weight to far-away points? Or maybe less weight? Not sure! But would be interesting to explore and see if it gives anything.

tombh 1y ago
I'm the author. Well there's actually a term in the kernel to normalise the surface area of each visible point by a factor of tan(1 radian): https://github.com/tombh/total-viewsheds/blob/main/crates/kernels/vulkan-and-cpu/src/kernel.rs#L163 https://github.com/tombh/total-viewsheds/blob/main/crates/ke... I don't know if that's related to what you're thinking about?

7373737373 1y ago

I've been wondering about using OpenStreetMap data to achieve something similar, like getting the longest uninterrupted (by buildings) distance between two viewpoints (the Nikon Coolpix P900/P1000/P1100 cameras or a telescope are pretty good for this due to their extreme focal lengths), or maybe something like "most ice cream shop dense area" https://wiki.openstreetmap.org/wiki/Key:amenity https://wiki.openstreetmap.org/wiki/Key:amenity Putting the typical airplane cruise altitude (10km) into the distance to horizon calculator https://www.ringbell.co.uk/info/hdist.htm https://www.ringbell.co.uk/info/hdist.htm results in a "reverse" distance of 357km to the horizon. So that's how far typical airplanes can be seen when standing at sea level!

7373737373 1y ago
The answer to the ice cream question (for places where ice cream can be bought) appears to be Buenos Aires! https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7B%7Bbbox%7D%7D%29%5B%22amenity%22%3D%22ice_cream%22%5D%3B%0Aout%20body%3B%0A&C=-34.639705%3B-58.416417%3B12&R= https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7... (for any circular area centered around such a shop with 10km radius) For ice cream shops specifically, Kraków? https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7B%7Bbbox%7D%7D%29%5B%22shop%22%3D%22ice_cream%22%5D%3B%0Aout%20body%3B%0A&C=50.058902%3B19.954179%3B14&R= https://overpass-turbo.eu/?Q=%5Bout%3Ajson%5D%3B%0Anode%28%7...

mrb 1y ago

Oh that project is right up my alley, as I did the same! Back in 2021, for fun, I wrote an algorithm to find the longest sightline on earth. And I did find a previously undiscovered sightline. My code was relatively unoptimized, it ran for 95 days on an 8-core 16-thread AMD Ryzen 5750G to crunch all the data. I have never published my code or results. I should really do it... I downloaded a digital earth model of about 30 gigabytes from http://www.viewfinderpanoramas.org/Coverage%20map%20viewfinderpanoramas_org3.htm http://www.viewfinderpanoramas.org/Coverage%20map%20viewfind... which had a resolution of 3 seconds, so I had the elevation of each 90x90 meters "tile" of land. I wrote a simple algo in C that: finds potential viewpoints (mountain peaks or plateaus above a minimum ), calculates the longest sightline 360° around you, taking into account an atmospheric refraction coefficient (I used 0.13 which seems to be a default used by some panorama tools like https://www.udeuschle.de https://www.udeuschle.de). It's really basic trigonometry: look one tile ahead of you, and the next one, etc, until you find the one with the highest vertical angle of view. Stop one sightline exploration when reaching a certain maximum distance (750 km in my implementation) when it becomes mathematically impossible to find a visible tile beyond this distance. And I found the longest sightline: In Kyrgyzstan from Pik Dankova (41.059167,77.683333) which is at 5977.5 meters (in my DEM data), you can see 538.1 km into China if you look toward bearing 169.7° (roughly south) as you see some distant minor peak at 36.295364,78.75593 which is 6444.0 meters high. However this sightline is already known. But it's only theoretical. No one ever encountered good enough atmospheric clear-sky conditions to observe it from Pik Dankova. Using the panorama tool maintained by this cool German guy, you can verify it: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=newstandard&data=lon:77.684167$$$lat:41.059167$$$alt:auto$$$altcam:2$$$hialt:false$$$resolution:600$$$azimut:169.7$$$sweep:1$$$leftbound:169.2$$$rightbound:170.2$$$split:2$$$splitnr:1$$$tilt:-2.14166666666667$$$tiltsplit:false$$$elexagg:1$$$range:750$$$colorcoding:false$$$colorcodinglimit:493$$$title:Pik+Dankova$$$description:$$$email:$$$language:ge$$$screenwidth:2560$$$screenheight:1414 https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... However one notable finding my tool gave me was it discovered the second longest sightline that is competely unknown up until this day AFAIK: In Colombia, from Pico Cristóbal Colón (10.838333,-73.687500) which is at 5668.5 meters (in my DEM data), you can see 502.6 km over the plains of the Caribbean region all the way to the Colombian Andes if you look toward bearing 206.2° (roughly south-south-west) as you see some distant peak at 6.777286,-75.692304 which is 3347.0 meters high. Here you can verify it here: https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=newstandard&data=lon:-73.6875$$$lat:10.838333$$$alt:auto$$$altcam:2$$$hialt:false$$$resolution:600$$$azimut:206.2$$$sweep:1$$$leftbound:205.7$$$rightbound:206.7$$$split:2$$$splitnr:1$$$tilt:-2.29166666666667$$$tiltsplit:false$$$elexagg:1.2$$$range:750$$$colorcoding:false$$$colorcodinglimit:502$$$title:Pico%20Crist%C3%B3bal%20Col%C3%B3n$$$description:$$$email:$$$language:ge$$$screenwidth:2304$$$screenheight:1440 https://www.udeuschle.de/panoramas/panqueryfull.aspx?mode=ne... I am not sure if this Comlombian sighline has ever been observed. As I said I should really publish my code and results. And at some point I would like to optimize it and re-run it using a higher-precision DEM with 30x30 meters tiles instead of 90x90 meters. I think there are a few 30-meter DEMs available but I need to find the highest-quality one.

hdersch 1y ago

"Viewsheds" of any location can be calculated and matched with photographs using "GeoImageViewer", an application I wrote a couple of years ago. Any feature in the image can be interactively identified in a mapview and vice versa, including the boundary of the viewshed. As has been mentioned in the comments, it is essential to include atmospheric refraction in the calculation, at least for distances above ~100km. [1] https://hdersch.github.io/Viewing.html https://hdersch.github.io/Viewing.html

redfloatplane 1y ago
Wow, this is really an incredible bit of work! Very impressive stuff, I look forward to using it!
shrx 1y ago
There's also https://www.heywhatsthat.com/ https://www.heywhatsthat.com/
tombh 1y ago
What a fantastic tool. I'm the author of the post. Do you have any knowledge about how refraction can vary? I was wondering about calculating the world twice, once with a lower refraction bound and then again with an upper.
- hdersch 1y ago
  Atmospheric refraction is due to the vertical gradients of atmospheric pressure, temperature, and composition of the atmosphere, all of which are usually not precisely known, and which vary with time, so one gets larger lines of sights at certain times. For my application I used the standard formulas for astronomical refraction (-> many weblinks) with constant medium gradients. If I recall correctly this results in ~100m height correction for features in 100km distance and ~400m in 200km distance (features appear higher than without atmospheric refraction). For your application it would make sense to use two extreme values for the gradients to get maximum and minimum, as you suggested.
  - 1y ago

me_vinayakakv 1y ago

Nice work! Do the tiles point to actual heatmap?

tombh 1y ago
Each tile's heatmap takes hours to crunch, so I haven't done them all yet. Here's a sneak peek of the UK though https://mastodon.social/@tombh/115330398582193988 https://mastodon.social/@tombh/115330398582193988

anovikov 1y ago

Ofc my home country's name was misspelled :/

tombh 1y ago
Kyrgyzstan? Damn, I'm sorry. I've update the article now.
- anovikov 1y ago
  Thank you! I kind of understood that from those mountains one could see really far away, but had no idea it was THAT far.

mrb 1y ago

Nitpick: "resolution of 3 arc-seconds (~100m²)" This resolution is equivalent to tiles of 8500 m² not 100 m². I think the author confused tile edge length (92 meters exactly) with tile area.

tombh 1y ago
Damn, that's the second time I've confused those 2 concepts. The distinction is significant. I updated the article, thanks.

Theodores 1y ago

You have a very interesting project. What happens if you put your maps and elevation data on a 'sphere', to model the world as 3D? You can then leverage a GPU to render a view from one vertex to then determine what is furthest away yet visible from that vertex. The vertices can then be given some type of heatmap colour and an interactive tool made. A full GIS tool isn't needed for this, with Blender and three.js there are all of the tools needed.

tombh 1y ago
This is pretty much what I'm already doing. The kernel is written on the GPU and just does raw visibility calculations.

reassess_blind 1y ago

A kid once asked me “How far can humans see?”. I told him you can see the Andromeda Galaxy 2.5 million light years away, but when he said he meant on Earth I didn’t know the answer.

lostlogin 1y ago

> I find these TVS heatmaps eerily beautiful. The first one somehow looked like something violent going on. Limbs? Bodies?

liamph 1y ago

It is interesting to also consider dry land which is below sea level. "For an average height person standing on a beach, their horizon is around 4.5km away." For an average height person standing at sea level, near a large depression such as the Dead Sea, for example, you may be able to see land at a much greater distance. I doubt if this factor would impact your findings for the longest sight lines on Earth, but perhaps for some local findings. Also, applying the same concept to other planets has some surprising results. The tallest mountain in the solar system, Olympus Mons, has very gentle slopes. So gentle that from the peak all you can see is Olympus Mons itself.

tombh 1y ago
Yes! These are very much the kinds of questions I'm interested in. The search for the single longest line of sight on Earth is just an excuse to play around in this space.

TCHAD235 1y ago

Samsung

kcexn 1y ago

I don't think I'm understanding the properties of a viewshed tile. Each tile is sized so that the viewshed size (in square metres) of every point within the tile can be found just from elevation data within the tile itself? But that doesn't seem right from the example you gave, because along the edge at the mouth of the river, the viewshed presumably includes the rest of the river outside of the tile as well?