Source Code: /src/families/_2d/tests/discrepancy/
This is the same as the 1d discrepancy test, but in 2d.
Calculating discrepancy gets a lot more expensive each dimension you go up.
In 1d, it's an O(n^2) operation, but in 2d, it's an O(n^4) operation. This is because in 1d, you have to consider every pair of points (n^2), but in higher dimensions you have to do the same, but on each axis individually.
Intuition about discrepancy changes as you go up in dimension as well. What had low discrepancy in 1d may not have low discrepancy in 2d and higher. For instance, in 1d, regular sampling had the lowest discrepancy, but in 2d (and up), that isn't the case due to those long rows and columns of empty space between the sampling points.
Blue noise has lower discrepancy than regular sampling in 2d, as does regular jittered sampling. Neither of those things are true in 1d.
This difference in discrepancy also affects how well the sequences perform for integration.
tests done:
- CalculateDiscrepancy
