gridTools

[Curtis Lemay]

Wait a minute. I've figured out how to do it. The thing is, you can only divide the hexes up by even numbers (2, 4, 6, etc.). But, it occurred to me that once you've divided by 6, you can then double back up to get to 3. Sure enough, that works. In the attached screenshot, the red super hexes are every six TOAW hexes apart. Then, the blue hexes are every two TOAW hexes apart. Therefore, the blue super hexes are 1/3 the size of the red super hexes. Sure enough, there are 10 red hexes and 90 blue ones.

I think you actually have to create the 1/6 size grid first before decimating it into the 1/3 size one, since the direct relationship between the red and blue hexes is irregular.

[Martin_Goliath]

Sorry for not responding earlier - I have not been near a computer for the past week.

Colin & Bob: your series of posts really made my day by opening my eyes for new possibilities that seem to enable (almost) unrestricted hex sizes with the method I am working on [8D].

Your discussion on how to subdivide hexes to get a finer grid had me look closer on a research paper available at the site where I got the DGGRID program. The way the grid is constructed in that software seems to be by subdivisions of the type you discuss. They use two different ways to subdivide (see attached pic).

The aperture 3 grid gives 1 + 6/3 = 3 new hexes from one original (green) hex. After some geometry the scale relation is found to be D = sqrt(3)*d ~ 1.732 d. In other words, an aperture-3 subdivision gives you hexes that are 1/1.732 ~ 0.577 the original size (e.g. 10 km/hex becomes 5.77 km/hex).

The aperture 4 grid gives 1 + 6/2 = 4 new hexes from one original hex. Here, the scale relation is easily seen to be D = 2 d. Thus, an aperture-4 subdivision gives hexes half the original size.

In the DGGRID program, the starting hex size is set to 7674 km. Then a number of aperture-3 subdivisions are applied to generate a sequence of aperture-3 grids of successively finer resolution. Alternately, a sequence of aperture-4 subdivisions are applied, resulting in another set of grids. For some reason, the software does not mix the two types of subdivision (maybe it has to do with the purpose of generating a global grid), resulting in the rather limited set of available hex sizes.

However, at least for non-global grids, I see no reason why the two types of subdivision cannot be mixed. That way, all grids relevant for TOAW can be generated with reasonable accuracy. For instance, starting from the 15 km/hex grid (which happens to be DGGRID's aperture-4 grid of resolution 9), applying two consequtive aperture-3 subdivisions would give a 5 km/hex grid.

I think it is fairly straight-forward to implement this, once DGGRID has generated a coarse grid to start out from. (Also, it seems more elegant than the other grid generation ideas I have been sketching on lately!)

[ColinWright]

ORIGINAL: MarGol

Sorry for not responding earlier - I have not been near a computer for the past week.

Colin & Bob: your series of posts really made my day by opening my eyes for new possibilities that seem to enable (almost) unrestricted hex sizes with the method I am working on [8D].

Your discussion on how to subdivide hexes to get a finer grid had me look closer on a research paper available at the site where I got the DGGRID program. The way the grid is constructed in that software seems to be by subdivisions of the type you discuss. They use two different ways to subdivide (see attached pic).

The aperture 3 grid gives 1 + 6/3 = 3 new hexes from one original (green) hex. After some geometry the scale relation is found to be D = sqrt(3)*d ~ 1.732 d. In other words, an aperture-3 subdivision gives you hexes that are 1/1.732 ~ 0.577 the original size (e.g. 10 km/hex becomes 5.77 km/hex).

The aperture 4 grid gives 1 + 6/2 = 4 new hexes from one original hex. Here, the scale relation is easily seen to be D = 2 d. Thus, an aperture-4 subdivision gives hexes half the original size.

In the DGGRID program, the starting hex size is set to 7674 km. Then a number of aperture-3 subdivisions are applied to generate a sequence of aperture-3 grids of successively finer resolution. Alternately, a sequence of aperture-4 subdivisions are applied, resulting in another set of grids. For some reason, the software does not mix the two types of subdivision (maybe it has to do with the purpose of generating a global grid), resulting in the rather limited set of available hex sizes.

However, at least for non-global grids, I see no reason why the two types of subdivision cannot be mixed. That way, all grids relevant for TOAW can be generated with reasonable accuracy. For instance, starting from the 15 km/hex grid (which happens to be DGGRID's aperture-4 grid of resolution 9), applying two consequtive aperture-3 subdivisions would give a 5 km/hex grid.

I think it is fairly straight-forward to implement this, once DGGRID has generated a coarse grid to start out from. (Also, it seems more elegant than the other grid generation ideas I have been sketching on lately!)

Don't go away. Whatever you just said, we need you.