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.
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