Imagine finding the highest point on Earth. The bounded space is easy to find. 5E8km^2.
How many points do you need to find it by brute force searching all of them? It looks like a 10m*10m square is good enough, perhaps 100m*100m is enough. That is 5E12 or 5E10 points.
Anyway, you need all of them to detect all the mountains and oceanic trenches.
Most of the times, the terrain is quite smooth and you can interpolate like in their example with the Gaussians. Well, except the Colorado Canyon, the Niagara Falls and a long list of sharp features.
Also, if you want to detect also buildings, you need like x100 more points.
And this is just a 2D problem. When you add dimensions, the problem grows like grid size ^ dimensions and the brute force approach is not feasible. There are a few ideas that are very nice in 1D, but in 100D they are just impossible in a sensible amount of time.
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Imagine finding the highest point on Earth. The bounded space is easy to find. 5E8km^2.
How many points do you need to find it by brute force searching all of them? It looks like a 10m*10m square is good enough, perhaps 100m*100m is enough. That is 5E12 or 5E10 points.
Anyway, you need all of them to detect all the mountains and oceanic trenches.
Most of the times, the terrain is quite smooth and you can interpolate like in their example with the Gaussians. Well, except the Colorado Canyon, the Niagara Falls and a long list of sharp features.
Also, if you want to detect also buildings, you need like x100 more points.
And this is just a 2D problem. When you add dimensions, the problem grows like grid size ^ dimensions and the brute force approach is not feasible. There are a few ideas that are very nice in 1D, but in 100D they are just impossible in a sensible amount of time.