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here. In particular, the global illumination models discussed in the earlier chapter still
were implemented in a local space.
Finally, this brings us to another point. Current modeling systems (other than
those involved with volume rendering) only represent objects. Systems should really
also model the entire space ( R 3 ) that these objects exist in. Since the objects are really
imbedded objects, if one modeled the complimentary space one would have a lot more
information. For example, visible surface determination would theoretically become
less expensive because one could basically “walk” from the viewpoint to an object to
see if something blocked it rather than having to check a ray against all the objects
in a scene. The fact that one can do precisely that in volume rendering makes that
approach very attractive and guarantees that it will become more important in the
future, especially since the hardware issues that have made this approach impracti-
cal are going away.
Section 16.2 is a slight digression from the main topic of this chapter, although
the material is related. We discuss current virtual reality programs that try to immerse
a user into computer generated worlds which are representations of either actual or
totally artificial environments. Section 16.3 describes what geometrically intelligent
modeling systems might look like. Section 16.4 describes the idea behind the SPACE
program that accompanies this topic. Section 16.5 touches on some software that cur-
rently exists and which implements some aspects of what we have been talking about
here, suggesting future directions for geometric modeling.
16.2
Virtual Reality
The term “virtual reality” (VR) is used to mean many things, ranging from visions that
one may never be able to achieve to more down-to-earth applications that are start-
ing to have a profound influence. If one wants to create a virtual, meaning computer-
generated, world, one clearly has to be able to model this world. It is therefore
appropriate to say something about it in a topic on geometric modeling; however,
there is much more to VR than just modeling and so we shall limit ourselves to some
general comments. The interested reader is referred to [Broo99] and [VFLL00], where
one can find lots of other references to work in the field. Those papers and others in
the IEEE Computer Graphics and Applications journal also describe many examples
of applications in VR. We shall not describe them here.
The idea of virtual environments (VE) using head-mounted displays (HMD) goes
back to the early 1960s ([HalM63]). Ivan Sutherland ([Suth65]) considered the com-
puter screen as a window into a virtual world. However, actually getting anything to
work took some time because it was harder than initially expected. Before 1990 the
results were very limited and existed mainly at a few laboratories. The first two IEEE
conferences on VR took place in 1993. One was the Virtual Reality Annual International
Symposium (VRAIS '93) and the other was a symposium at the Visualization '93
conference. As Brooks ([Broo99]) points out, between 1994 and 1999 the technology
moved from “it almost works” to “it barely works.” Vehicle simulators and entertain-
ment applications were not counted in that analysis. Although very successful, the
former were not really built on VR technology and the latter made lower demands and
the experience achieved was an end in itself and not thought of as a tool.
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