Graphics Reference
In-Depth Information
Figure 5.7.
A nonsense object.
patches and so its definition would seem correct from a
local
point of view, but taken
in its entirety it clearly does not correspond to a real object. In early geometric mod-
eling systems, validity of a representation was the responsibility of the user, but this
has changed. It is no longer acceptable to assume human intervention to correct
errors. For one thing, a modeling system might have to feed its geometric data directly
to another system such as a robot and bad data might crash that system.
Here are some other informal properties of representation schemes:
(1) Robustness and numeric precision (see Section 5.10 for a discussion of this
topic)
(2) Compactness (for storing): “Verbose” representations may contain redundan-
cies that would make verifying validity harder. On the other hand, in the usual
trade-off, this may improve performance.
(3) Computational ease and applicability: No representation is best for everything.
To support a variety of applications, we could have multiple representations
for each object, but then one must maintain consistency.
(4) Ability to convert between different representation schemes: One may want to
pass data between different modelers, but even a single modeler may contain
more than one representation scheme.
Along with a formalization of the objects that constitute the domain of a modeler,
one should also specify and formalize the allowable operations and functions. This
formalization has only been carried out in a minimal way so far. We postpone this
largely ad hoc discussion to Section 5.7. Insofar as the usual definition of the term
“representation scheme” does not address operations and functions, it is an incom-
plete concept. The term “object representation scheme” would have been more appro-
priate because it is more accurate.
Representation schemes coupled with the user interface of a modeler have a great
influence on the way that a user will think about objects or shapes. One needs to dis-
tinguish between a
machine representation
and a
user representation
. The discussion
above has concentrated on the former, which may or may not be visible to the user,
but the latter is also very important and deals with the user interface. A driving force
behind generative modeling, which will be described in Section 5.3.5, had to do with
giving a modeler a desirable user representation. The issues involved with user rep-
resentations are similar to but not the same as those for machine representations.
Some important informal questions that a
user
representation must address are
