Re: Star Maps

>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.
 
To determine plane that will provide the least z-axis distortion
(i.e., the plane that is nearest to containing all the stars),
by minimizing the mean squared distance from a plane to the stars.
Without actually doing this, I think this would also minimize the
apparent errors in the x- and y-axis relative locations of the
stars. All inter-star paths not parallel to the resultant plane
would still be foreshortened, however.
 
- Sam
________________________________________
Samuel Reynolds
Spinward Stars: http://www.spinwardstars.com/
Reynolds Virtual Workshop: http://www.primenet.com/~reynol
reynol@primenet.com
samuel_reynolds@csgsystems.com