Open danlooo opened 1 year ago
Each hexagon naturally has 7 children. This is independent of the aperture:
Source: http://webpages.sou.edu/%7Esahrk/sqspc/pubs/autocarto14.pdf
Aperture 4 means that the area of a parent cell is 4 times larger than the area of a child cell.
Finding the children cell ids is trivial, i.e. the child cell with the same center coordinates of the parent + the 6 neighbors. Contrary, finding the parent cell results in ambiguities, i.e. there are multiple parent cells having the same minimal distance to the parent center points.
This has one major implication: If we compute the value of a parent cell by just using the values of its 7 child cells, points inside the ambiguous child hexagons will be counted for both parent cell neighbors. Since those ambigious hexagons have the same minimal distance to both parent hexagons, it makes sense to do so.
On a 2D plane, one can just aggregate hexagons into big pseudo-hexagons (hexagons + little spikes):
Source: http://webpages.sou.edu/~sahrk/sqspc/pubs/gdggs03.pdf
This is a complete-nested tessellation, i.e. there are no ambiguous child cells. However, we can not use this on a 3D shpere DGGS (Sahr et al. 2003) due to the following reasons:
Center of hexagonal cells are at the edge of their parent cell. This yields into having the same distance to both parent cell centers. This makes the 1:1 mapping to the parent cell ambigious. We need to fix this. This problem is only for hexagonal grids: