4 ms·
> simplex noise scales O(n) Typo? Simplex noise scales at O(n^2), not O(n).
by MillenialMan 5y ago
> simplex noise scales O(n)
Typo? Simplex noise scales at O(n^2), not O(n).
- ginko 5y agoHm, not a typo, I thought it was O(n) since that's how simplices scale with dimensions. Where does the extra *n come from? I guess identifying the right simplex isn't free.. Right, the gradients will still have more dimensions to evaluate.
- MillenialMan 5y agoO(n) measures the number of vector operations, but each one operates over a vector, so there are n^2 arithmetic operations. This is also true for perlin noise - there are 2^n vector operations, but the arithmetic complexity is O(n.2^n). Obviously this ignores the parallelizability of the algorithms, which is probably the more important factor at this point, and the ability to be hardware accelerated. (Edit: the complexity is outlined on page 20 of the original simplex noise paper[1]. Just ctrl+f "complexity") [1] https://www.csee.umbc.edu/~olano/s2002c36/ch02.pdf https://www.csee.umbc.edu/~olano/s2002c36/ch02.pdf