Re: Star Maps

On Wed, 13 Oct 1999, Laserlight wrote:

> >> > Phillip Pournelle wrote:
> >>
> >> >	   Unfortunately, the three D view is not effective
> for a campaign map.  Is
> >> > it possible to generate a 2D map, perhaps on a hex
> sheet, where there are
> >> > distortions of the star's actual position,  but
> positioned to create a sense
> >> > of how far apart they would be for  a strategic view?
> 
> You can determine which plane (x, y, z) has the smallest
> difference from minimum to maximum value and make that your
> "z" on your 2D map, then just plot your other two
> coordinates as the x and y and ignore the z.

in principle, the plane of projection needn't be any of the zy, xz or yz
planes (is that how you name planes?); they have no significnt physical
meaning, they're just convenient. thus, you could pick any plane and
project the 3d map onto that; that way, you could absolutely minimise
the
total vertical height covered by the map. i'm not sure how you'd
calculate
which it was, although some sort of 3D generalisation of linear
regression
(planar regression?) might do the trick. i'm also not sure how you'd do
the projection. i suspect linear algebra is involved, and so my mind is
refusing to think about this any more until i've had lunch.

> Or you can use graduated circles to depict the Z.  Say your
> Z covers from +5 to -5 parsecs--use a large circle to
> represent +5, a medium at 0, and a tiny one at -5, plus
> intermediate diameters to taste.  I don't much like this
> because I don't have the patience to draw circles.

i like this idea - you could use this in concert with a snazzy
projection
method for extra supa dope results.

also, for large maps, you could split the space into layers, and draw
separate maps for each layer. this may not be very usable, though.

> Or you can pick the three most important points on your map
> (in my case, Alarish, New Arabia, and Huy Braseal, the
> latter because it's closest to everything else), plot those
> three distances correctly, and fit everything else in as
> best you can.

one way to do this would be to pick a plane which passes through all
three
points (in 3-space, there is exactly one plane which passes through 3
points [1]) and project onto that. this should be easier than the
full-blown height-minimiser.

i still think a Kohonen map is the way to go ... :)

tom

[1] unless they're in a line