Mathematical tips needed

Eleas · Post by **Eleas** » 2007-02-18 09:07am

So I've been playing Master of Orion 2 lately, and it's inspired me into creating some sort of mini-game or proto-game. What I wanted to create is a utility (not a game, per se, just the bare-bones version of what in MoO2 would be the planet screen) that would look at the planet from the outside. Now unlike MoO2, where the planet is a single entity, this planet would consist of polygons of roughly uniform area). There would only be five or six different sizes of planet, and the usefulness of a planet would of course be proportional to the amount of space one could exploit.

That's not the issue, though; it can easily be accomplished once the primary problem is settled. The issue being rather the same problem Buckminster Fuller took on; how do I split a sphere into x amount of polygons (pentagons and hexagons, for preference; I'd prefer it if it's possible to move step by step across the grid in a flexible way)? The good thing is, there's only going to be around six different sizes, and there's some latitude about sizes that could be chosen.

So, is there a comparatively easy way to solve this? Being just a dabbler in mathematics, the only method I see myself is the brute-force one in which I fire up 3D Studio Max and do it manually, and that seems somehow very inelegant.

Steel · Post by **Steel** » 2007-02-18 11:22am

How about you just draw on the lines of lattitude and longitude?

That, depending how many of them you draw on gives you a whole bunch of (spherical) polygons. If you put on the lines every 30 degrees for a smally, 20 for meduim and 10 for large or something, that gives you a large number of simple regions. You would make all the small ones near the poles into one region or something, and could tweak it as you like

Eleas · Post by **Eleas** » 2007-02-18 01:32pm

Steel wrote:How about you just draw on the lines of lattitude and longitude?

That, depending how many of them you draw on gives you a whole bunch of (spherical) polygons. If you put on the lines every 30 degrees for a smally, 20 for meduim and 10 for large or something, that gives you a large number of simple regions. You would make all the small ones near the poles into one region or something, and could tweak it as you like

A simple solution, which is a good thing to my mind. I'll try it and see what comes out of it.

Post by **Lagmonster** » 2007-02-18 05:08pm

Not to be simplistic, but you might take a peek at a soccer ball - they're split into pentagons and hexagons, no?

Eleas · Post by **Eleas** » 2007-02-18 05:47pm

Lagmonster wrote:Not to be simplistic, but you might take a peek at a soccer ball - they're split into pentagons and hexagons, no?

Be simplistic. That's a fucking wonderful idea! Thank you.

Psychodelica · Post by **Psychodelica** » 2007-02-22 05:47pm

Well, Eleas. It seems you're coming along fine. Don't drop this project, I beg you!

Bärta: Edited spelling

Eleas · Post by **Eleas** » 2007-02-22 08:32pm

Psychodelica wrote:Well, Eleas. It seems you're coming along fine. Don't drop this project, I beg you!

Worry not, it's coming along. I've successfully, with the help of a certain once-bearded fellow we both know, delineated and eliminated various points. As for now, some things seem obvious.

First, what I need is the 3d model of a sphere. It appears there are actual programs out there that are able to generate instant hexagonally segmented spheres (I heard Maya and 3dSM were among them). I then need to create a very simple table that matches each facing to an ID number, and after that, it gets fairly straightforward.

I've decided that these steps are enough for the first build. Things like actually displaying the 3d model, let alone anything more complex, will have to wait until further versions. I'd rather get there by crawling than sprint and fall.