Graphics Reference
In-Depth Information
of the declarations is accomplished by a constraint satisfaction algorithm, an infer-
ence engine, or unification, respectively. Three basic approaches are used for solving
the constraint problem: constraint graphs where the nodes are geometric entities
and the edges are the constraints, logical assertions, or algebraic equations that are
expressed symbolically and solved symbolically. None of the approaches are easy. See
[LiON02] for an example of feature mapping in a design-by-feature system.
In conclusion, many modelers are now supporting features. Overall, b-rep mod-
elers, in particular those that support nonmanifolds, seem better suited to the feature
recognition task than CSG modelers. The only advantage of the latter is in editing but
this can also be dealt with in a b-rep modeler. For example, consider an object with
slots of varying lengths. Changing the length of the slots may cause them to intersect.
With a CSG representation the history of any changes can be maintained relatively
easily, whereas with a boundary representation such changes might cause radical
changes in the relationships of facets. [Prat87b] mentions the following feature-
specific advantages of a boundary representation:
(1) Features are usually best described in terms of faces, edges, etc.
(2) Dimensioning and tolerancing of features need these low-level entities.
(3) CSG representations can be ambiguous. See Figure 5.33 again.
(4) Local operations for feature manipulation are available in the design stage.
Feature recognition algorithms for b-rep modelers divide into two types: those that
use purely surface information and those that use volume decompositions. The latter
seem to be a better approach but are not as developed yet.
[Prat87a] and [Prat87b] have a nice survey of work in feature based modeling
from 1980 to 1987.
Finally, since there are a number of feature-based modelers, it is important that
one can exchange data between them. One might also want to input some feature data
to an application program. STEP ( St andard for e xchange of p roduct data) is a set
of standards that resulted from an international effort to enable this exchange. See
[ShaM95] for an overview and additional references.
5.7
Functions and Algorithms
In addition to modeling objects, modelers must also be able to perform a variety of
operations on the objects that they have modeled. As indicated in the introduction,
modeling involves modeling maps as well as objects. Here is a sample of some queries
users may want to make and actions they may want to perform:
(1) Find physical propertie of objects:
center of mass, moments of inertia, area,
volume, . . .
(2) Find geometrical properties of objects:
distances between objects, collision
detection, intersections and other
Boolean set operations, . . .
(3) Perform geometrical operations:
rigid motions, . . .
(4) Numerical control related operations:
milling, lathing, . . .
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