I have a region in n-dimensional space. I know nothing about this region, save these things:
- To start, I am given the coordinates of a single point that I know is within the region
- The region is contiguous
- I can perform a computation on any point to determine whether or not it's also inside this region
By utilizing #3, what is the most efficient algorithm for proving, to a given sampling resolution, that my high-dimensional region is bounded?
(The region I am personally studying lies on a hypertorus, but I will also accept an answer that just applies to normal Euclidean hyperspace.)