Graphics Reference
In-Depth Information
trivial cases. With the typical set of primitives, the
best that one could do for such objects, as for
example an airplane wing, is get a
very
inefficient
approximation.
(4) The definition of what is a “face” is more
complicated.
Some modelers were hybrid systems that used the best features of boundary and
CSG representations. In fact, the user interfaces for modelers are reasonably standard
and hide the actual representation that is used. It is like with a database program
where the user usually does not really know (or care) whether it is truly relational or
not. The only way one might get an inkling of the representation on which a modeler
is based is by the speed and ease of completing certain queries. For example, bound-
ary representations have an easier time with queries that deal with faces. A hybrid
system does have problems however:
(1) It must be able to convert between the different representation and the b-rep-
to-CSG conversion is very hard.
(2) It must maintain consistency between representations. This limits its cover-
age. For example, if a b-rep object came from a CSG representation and one
modifies it using a parametric surface for blending, the original CSG struc-
ture can probably not be kept consistent with it. See [ShaV95].
Initially, the typical operators in b-rep modelers were the set operations basic to
CSG, but gradually more and more operations were introduced into modelers, oper-
ations, such as local blending operations, that were not easy to implement in a CSG
modeler. This has caused pure CSG modelers to disappear, probably also because of
the many advantages to using spline surfaces, especially NURBS surfaces, and the fact
that there is no general b-rep-to-CSG algorithm. The result is that most modelers are
now b-rep based. Volume-based modelers will also probably become more prevalent
in the future with faster computers and large amounts of memory. Nevertheless, CSG
has had a fundamental impact on the way that one views geometric modeling. CSG
can be viewed as an abstract description of objects and so, whether or not a modeler
is based on it, the user interfaces will continue to support it. It should be pointed out
that the parametric modeling systems that developed did not entirely avoid the prob-
lems found in the dual b-rep/csg-rep systems. When a slot in the middle of a block is
moved to the edge of the block, it and the associated blend will disappear. Shapiro
and Vossler ([ShaV95]) argue that such difficulties are caused by the fact that the
concept “parametric family” is not well-defined. A designer may not be able to predict
whether certain parameterizations will remain valid throughout the design process.
A lot more work needs to be done in this area if one wants a design process that does
not require human intervention in the parametric structure of an object.
A modeler's ability to edit a model is extremely important to a user. Finding a good
way to do this is the basis of a lot of current research. We briefly discussed the medial
axis representation. Another approach called Erep is described in [GHSV93]. Its goal
is to be an editable, high-level textual representation for feature based solid model-
ing. It is a representation that is independent of the underlying modeler.
