Enjoyable to see someone reasoning creatively about various ways to
solve this. In the end there are so many ways, each giving their own
feel. I would do generative landscapes by starting with Perlin noise
clouds, low pass filtering and then "flooding" the height-map with a
water table. That's basically how old generative landscapes like Bryce
used to work I think. For caves, pick a min and max plane, extrude to
get walls. As mentioned in the article checking connectivity was
always the PITA - and with 3D procedural mazes you have to also check
they're passable for the chosen engine's collision code.
That's how I learned about my favourite constant... Gerver's optimal
sofa constant...the maximum size sofa that can move around a
unit corner [1].
> The sofa problem is a so far unsolved geometrical problem that was described in 1966 by the Austrian-Canadian mathematician Leo Moser . It is a two-dimensional idealization of the practical problem of moving furniture around obstacles.
Doesn't seem to have much to do with the actual problem of moving furniture, where the third dimension is heavily exploited.
That's how I learned about my favourite constant... Gerver's optimal sofa constant...the maximum size sofa that can move around a unit corner [1].
[1] https://de.zxc.wiki/wiki/Sofaproblem