Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!umich!samsung!cs.utexas.edu!asuvax!enuxha!hollasch
From: hollasch@enuxha.eas.asu.edu (Steve R. Hollasch)
Newsgroups: comp.graphics
Subject: Re: 4D Visualization (If you think you do it, you probably don't)
Summary: Further explanation of my intent.
Message-ID: <487@enuxha.eas.asu.edu>
Date: 9 Feb 90 22:01:58 GMT
References: <99@emtek.UUCP> <16033@well.sf.ca.us> <6162@eos.UUCP>
Organization: Arizona State Univ, Tempe
Lines: 54

In article <6162@eos.UUCP>, eugene@eos.UUCP (Eugene Miya) writes:
> >Try projecting to stereoscopic 3D, I've got a SGI program that does a 4 or 5
> >demension (sic) cube into stereo. Real nice to what it spin!!
> 
> But there are several issues:
> 1) tesseracts are PROJECTIONS of 4D hypercubes, they are not the cube itself.

    Granted, but you could also argue that an image of a normal 3D
solid object is merely a projection, and not the object itself.
What's the point?  With the 3D object you can gain insight into
clearance, structure and so on.  More importantly (for me at least),
you can spot trends, maximum regions, minimum regions, and the like.
Heck, if you go backpacking, you don't disregard your topo map because
it's not the true 3D object, do you?

> 3) DO NOT SUBSTITUTE TIME FOR A FOURTH PHYSICAL DIMENSION ...

    I'm not.

> 4) See the problem is we are plotting on 2-D surfaces.  Our retinas are
> also 2-D.

    Hmmmm.  Are you arguing that the actual 3D object is not useful?

> The problem is one of these hardest problems in mathematics: take a
> globe of the earth and "squash it" on a 2-D screen.  So far it can't
> be done without compromising something: area, distance, etc.  You
> see people ask for coordinates of the earth.  Cute to look at basically
> (like the cube above) impractical for nearly everything else.  A real
> 3-D globe can be used to determine distances between say NY and Tokyo
> (know what a great circle is?) which Mercator and other projections
> can't handle.

    So, you project an image of the globe to the screen, and you now
have before you a virtual 3D globe.  Provide for user manipulation of
this globe, and very soon (s)he'll be able to estimate relative sizes,
distances, and the like.  This is a good example of "bumping-up" a
dimension to gain insight into the actual data.

> But I still think graphics will never replace globes.

    I'm sure you've seen the dataglove & visual helmet combination
pioneered by NASA as a means to model "real space".  Why can't this as
effective as walking around to a globe and rotating it?  Or would our
2D retinas hold us up?  =)

> You trust your eyes too much when your eyes can be disceived.
> Meanwhile, I will hack and search for software. 8)

    Eyes can be deceived quite easily, but they one of the best ways
that humans have to rapidly and intuitively grasp many of the
properties of objects, and to quickly isolate interesting regions.  I
will choose visual information over tactile or aural information (are
you thinking of another method of perception?) almost every time.