Difference between revisions of "Notes:Grid iteration"
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See [[Modulo operator]] for a definition of {{M|\text{Mod}(a,b)}} | See [[Modulo operator]] for a definition of {{M|\text{Mod}(a,b)}} | ||
==2D grid== | ==2D grid== | ||
| + | [[File:2dGridReproduction small 4by5.gif|thumbnail|Notice the 21st point is back at the origin and the sequence repeats. [https://wiki.unifiedmathematics.com/index.php?title=File:2dGridReproduction_small_4by5.gif Direct link]]] | ||
* {{MM|\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)}} | * {{MM|\text{Mix}_x(k,m,n):\eq \text{Floor}\left(\text{Mod}\big(\text{Mod}(k,mn),m\big)\right)}} | ||
* {{MM|\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m} }} | * {{MM|\text{Mix}_y(k,m,n):\eq \frac{\text{Mod}(k,mn)-\text{Mod}\big(\text{Mod}(k,mn),m\big)}{m} }} | ||
Revision as of 18:28, 7 January 2018
See Modulo operator for a definition of Mod(a,b)
2D grid
Notice the 21st point is back at the origin and the sequence repeats. Direct link
- Mixx(k,m,n):=Floor(Mod(Mod(k,mn),m))
- Mixy(k,m,n):=Mod(k,mn)−Mod(Mod(k,mn),m)m
Then
- Points of the form:
- (Mixx(k,m,n),Mixy(k,m,n)) span an m×n grid, for k from 0 to mn−1
3D grid
Suppose we have an ℓ×m×n grid,
