[Edu-sig] More Pythonic Soccer Ball Geometry (was HexaPent)

[kirby urner]

On 7/22/06, kirby urner <kirby.urner at gmail.com> wrote:

> Note that the tricks I use to build this data structure (globaldata)
> aren't necessarily going to scale when we move to the higher frequency
> hexapents (12 pentagons, more hexagons).

Actually, I'm thinking they scale pretty well.

Given a set of hexapent faces, say a list of 5- and 6-tuples, we name
each face after the corner vertices, just as we normally do in
geometry.  Tuples are hashable keys, so we could call (1,3,13,5,7) a
face (I'm just inventing the sequence), except to avoid duplicates
we'd take advantage of ordinality to make (1,3,5,7,13) the *unique*
reference to some pentagon.

>From this face data, we have the same ability to distill (a) all
unique edges (as vertex-pair tuples) and (b) all neighbors of a cell =
those with exactly one edge in common.

We can brute force our way through this if we're lazy and operating at
a low enough frequency.  Once developed, the resulting data structure
may be saved to a file for recycling.

So far, I haven't found a way to make Rick Bono's dome.exe (mentioned
earlier) output buckyballs (x3 frequency) in a format that conserves
faces as such.  However, I'm thinking Adrian's Packinon might well do
the job.

So using gm.py to automatically build a globaldata dictionary for a
higher frequency hexapent shouldn't be too problematic, using integers
for vertices, and tuples for edges and faces.  globaldata, recall,
keys each face to a list of neighboring faces, so we're talking all 5-
and 6-tuples.

A separate lookup function could then retrieve pre-rendered data from
a stash.  Walking the globe is one thing.  Doing so in real time --
well, that depends on what you're looking to see.

I haven't forgotten that we want a compass control as part of the GUI,
so that the 90-45 degree points mix with the 60-72 degree motif of the
hexapent.

Also, we of course want our labeled vertices to map to XYZ coordinate
data, or whatever info will help with the OpenGL or whatever.

Kirby