Buckminster Fuller shows the continents of the world laid out onto the faces of

an icosahedron in one of his books. I have such a printed map. It can be laid

out flat or tabbed together to form the wacky looking globe.

I guess you'll need triangle rotation and drag and drop in any software to lay

out the full spherical view from inside a heart. CAD software can provide a

half spherical view. I've done that. There might be something to do it more

recently. I laid out an extreme perspective in Visi Cad years ago. Just set the

one number to 90 degrees, and the whole visual field of half a sphere is

computed and displayed. It's a little disorienting. Only the connections with

various parts are correct. All the scales get distorted.

Quote:>What is the best way

Only you can decide what's best.

Quote:>as least distorted as possible,

The problem is that without a definition of distortion, we won't agree on what

is the least. And in any case, best is always for some reason. There's no

objectivity in it.

More than one way to skin a cat. Got a knife? What kind?

Hyperbolic geometry maps infinite space to a mere circle on the plane. But

that's two dimensional...

Teri and I used to play Action Biker, a Commodore 64 game. The play area in

that game is infinite, but connected at top and bottom. You can go in any

direction you want forever, but it gets boring because the scenery repeats

after a screen width or two. It turns out such a play area is topologically a

toroid, not a sphere. Topology is the geometry of connectedness or something

like that. You probably already know that. But that's the first step. Look for

the singularities on a sphere. You can't comb a hairy orange neatly. There's

always a whorl somewhere on it.

The regular polyhedra are the tetrachedron, octahedron, cube, dodecahedron, and

icosahedron. In Greek, that just means 4, 8, 6, 12, or 20 faces. They can be

subdivided. The whorl won't go away.

I guess you could lay out an infinite pattern of triangles on the screen and

map the 4, 8, or 20 sided polygons to them. The 4 sided tetrahedron could map

to one triangle with three on its edges. By repeating from those edges, you

might make a map that would help people navigate the spherical data set.

XY pixels are a pain for this. The pixels on a CRT are usually in triangles.

There are ways to scan a CRT in triangles, but once again, like that whorl,

you've got a problem. The triangles become redundant, while the whorl is a

singularity. Both are unavoidable problems. Be innovative. Try things.

Yours,

Doug Goncz

Experimental Machinist

Replikon Research

Seven Corners, VA 22044-0394

What I'm into:

Home Page (1999-11-24):

http://members.aol.com/DGoncz