Packing the world for longest lines of sight

Summary

Packing The World For Longest Lines Of Sight 05 October 2025 I have a side project to find the longest line of sight on the planet using a novel Total Viewshed algorithm. At a resolution of 3 arc-seconds (~100m²), the planet contains around 4.5 billion elevation samples. Now obviously we don’t need to calculate the visibility between literally every single one of those, so how do we begin to cut it up? That’s what I’ll explore in this post. Theoretical Longest Lines Of Sight A viewshed is all the things that you can see from any given point. Here is an example from my home country, Wales, looking across a large estuary towards England: Notice how it seems that this viewshed is pretty much completely contained within the screenshot. I say “seems” because what if there’s some gigantic off-screen mountain that, even though it’s far away, its peak can be seen for hundreds of kilometres all around? The fact is that there is only one way to know whether you’ve found the true boundaries of a viewshed — going to the edge of where the Earth curves. You may already know this bit of trivial knowledge: for an average height person standing on a beach, their horizon is around 4.5km away. So extending that example to Mount Everest, if it were unobstructed and looking at only sea, its horizon would be about 335km in the distance. Now we can add one more little case to this: what if there were another Mount Everest at exactly the right distance, such that it could see the same horizon, but from the other side? This would also mean that the peaks of these 2 Everests would be mutually visible. And so this is how we can construct theoretical maximums for viewsheds. 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. Here’s a list of some of these maximums: 8848m 670km (height of Everest) 6km 553km 4km 452km 2km 319km 1km 226km 0.5km 160km 1.65m 9km (height of an average human) ...