3 ms·
> Unfortunately, we can’t make use of this intuition in a formal way because of the coastline paradox. I wonder if you could create some "relaxed" definitions
by xg15 4y ago
> Unfortunately, we can’t make use of this intuition in a formal way because of the coastline paradox.
I wonder if you could create some "relaxed" definitions of "convex" that would be able to capture shape properties only at certain scales. Something like "every polygon from points which are between x and y meters from the coastline and at least z meters from each other is convex".
- fwlr 4y agoDraw a convex polygon which satisfies the conditions 1. Every point on the edge of the polygon is in water 2. Every point on the land in question is inside the polygon And then sample some very large n points uniformly/randomly from inside the polygon, reporting whether you hit land or water. The closer to 100% land your sampling gets, the more “convex-like” the land in question is. Basically, draw a convex bounding polygon around the land and ask how much of that bounding polygon does the land fill up.