Path: utzoo!utgpu!jarvis.csri.toronto.edu!mailrus!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: I think we're agreeing from different directions  =)
Message-ID: <493@enuxha.eas.asu.edu>
Date: 11 Feb 90 01:23:35 GMT
References: <99@emtek.UUCP> <16033@well.sf.ca.us> <6162@eos.UUCP> <6174@eos.UUCP>
Organization: Arizona State Univ, Tempe
Lines: 42

>                            ... You see a maximum, but display in science
> requires frames of reference, what is the max value, not just that it exists.
> You want value(max), or value(max), or |value(max)-value(min)|.
> 
> The problem with trends is the following: you can't simply predict
> something on the basis of solely using imagery.  ...
>
> Bottom line, you have to have additional information to predict or
> understanding trends.
> 
> Bottom line: visualization just does not go far enough.

    I think I better understand your viewpoint; it seems that you
oppose visualization as the endpoint in data analysis.  For the most
part, I agree with you -- visualization does not allow you to make
accurate predictions about the nature of the data, nor does it allow
you to predict the response to external conditions.  For the most part,
visualization is the beginning of serious data analysis -- it
allows you to quickly spot "interesting" regions for further
analysis.

    However, I think that there ARE exceptions to this view.  In some
cases visualization is the final analysis of a set of data.  Consider, 
for example, the fact that not all higher-dimensional data are based
on a particular 3D space with associated scalar (or vector) values.
One great example of this is the use of visualization to map upper
derivatives of mathematical functions.  Doctor Farin, a professor
here who specializes in CAGD, has recently published a book on this
subject that has some very interesting pictures of mathematically-
defined (B-spline and the like) surfaces.  The images, however, are
based on the C2 properties of this surface, not on the physical view
of the surface itself.  The end result is such that poor knot
selection (easily with an error of .1 mm on an automobile hood)
can produce C2 oscillations that would otherwise not be noticable,
even if you had the hood in front of you (although some VERY
experienced people can look at reflections of the hood and tell that
its C2 properties are not too slick).

    These sorts of applications really benefit from visualization.
It is easy to think of these sorts of applications that extend to
hyperspace and further.  In this respect, visualization is definitely
useful because it has no base in the "real" world.