Path: utzoo!utgpu!jarvis.csri.toronto.edu!clyde.concordia.ca!uunet!snorkelwacker!usc!elroy.jpl.nasa.gov!ames!amelia!eos!eugene
From: eugene@eos.UUCP (Eugene Miya)
Newsgroups: comp.graphics
Subject: Re: 4D Visualization (If you think you do it, you probably don't)
Message-ID: <6162@eos.UUCP>
Date: 9 Feb 90 11:41:39 GMT
References: <99@emtek.UUCP> <16033@well.sf.ca.us>
Reply-To: eugene@eos.UUCP (Eugene Miya)
Organization: NASA Ames Research Center, Calif.
Lines: 70

>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!!

This isn't a flame on this poor fellow, but I've got an Iris 4D and I'll
love to look at your program, but I seriously doubt you have a 4D cube.
Prove me wrong with your software, send it to me, I love being proved wrong.
It educates me.  I learn, but I'm supposed to be a scientist, and that means
being skeptical.  I'd also be interested in knowing how you get a 5th
Dimension without spinning a 60s record [Up Up and Away....] 8)

Going back to the CACM paper which was noted in a posting some months ago,
the authors from Bell Labs pointed out n>3 D has real problems in display.
Their paper had the rotation of a tesseract (which I suspect you are doing).
Lots of programs do this.

But there are several issues:
1) tesseracts are PROJECTIONS of 4D hypercubes, they are not the cube itself.
Most scientists need the Cube.  Suppose I have a function f in Complex 
space C bar which I want to map the Complex space C bar.  Well C bar 
consists of a real and imagery component-> 2 dimensions. Plotting
the mapping can be 4-D!  I also don't want |f(c)| (Euclidean distance of
the function for 3-D.
Now why would any one want to study such things?  Hydrodynamics,
particle physics, in my case to help a friend study gravitational lenses.
2) Cubes okay.  I've other data.  Points I want to plot, rays I wish to
trace, etc.
3) DO NOT SUBSTITUTE TIME FOR A FOURTH PHYSICAL DIMENSION.  Animation
is a form of Blinn's Chi-Ting.  (See why in 1).  I might need time for
something else like Time.
4) See the problem is we are plotting on 2-D surfaces.  Our retinas are
also 2-D.

Let me illustrate a problem which computer screens and even stereo
glasses will NEVER BE ABLE to solve.  You can solve it with smart
software, but see lack of understanding on the part of some computer
people is why I go into my diatribes about the some of bogus people
in scientific visualization.

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.

Other solutions try to use color, and other qualitative cues: not great
when you need the 4th D to be a spatial one.  I've see attempts
and I'm trying myself.

You can't put a tape measure to a floating visual 3-D orbis, BUT you can
do it in software.  Guess how?  I predict it will be with second generation
graphics software developed for scientists to go beyond mere looking.
But I still think graphics will never replace globes.

Also fortunately we have the CAD folk working with the numerically
controlled milling people.  We have the cartographers who make maps.

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

Another gross generalization from

--eugene miya, NASA Ames Research Center, eugene@aurora.arc.nasa.gov
  resident cynic at the Rock of Ages Home for Retired Hackers:
  "You trust the `reply' command with all those different mailers out there?"
  "If my mail does not reach you, please accept my apology."
  {ncar,decwrl,hplabs,uunet}!ames!eugene
  Do you expect anything BUT generalizations on the net?