Shape of High-Dimensional Regions
Two (and higher) dimensional shapes can be complex
How to construct and weight points in a grid that covers the region R?
- hard to formulate a methodical algorithm in a complex boundary
- usually do not have analytic expression for position of boundary
- complexity of shape can increase unimaginably as dimension of integral grows
We need to deal with 100+ dimensional integrals
Example: mean-square distance from origin