Abstract
Feature modeling systems usually employ a boundary representation (b-rep) to
store the shape information on a product. It has, however, been shown that a
b-rep has a number of shortcomings, and that a cellular model presents a
valuable alternative which can be profitably used for several purposes. Cellular
models store additional shape information on a feature, including the faces that
are not on the boundary of the product. The cellular model discussed in this
paper, for example represents a part as a connected set of volumetric
quasi-disjoint cells of arbitrary shape, and represents each feature as a
connected subset of these cells. The cellular subdivision is determined by the
property that two cells may never volumetrically overlap. To identify and
analyze features in the cellular model, each cell has as attribute an owner list
indicating which features it belongs to.
A major operation in each feature modeling system is boundary evaluation, which
computes the geometric model of a product, i.e. either the b-rep or the cellular
model, from the features that have been specified by the user. Because it has to
be executed each time a feature has been added, removed or modified, its
efficiency is very important.
This paper describes the boundary evaluation scheme for the cellular model
mentioned above. The two basic operations on the cellular model (adding a new
feature shape and removing an existing feature shape) are described in detail.
The effect of these operations is twofold: (i) they change the topology of the
cellular model, and (ii) they update the owner lists of its cellular entities
accordingly.
Subsequently, the efficiency of this scheme is compared to the efficiency of
boundary evaluation for a b-rep, on the basis of performance measurements for a
series of add, remove and modify feature operations. For the add feature
operation, boundary evaluation for the cellular model has the same performance
trend as boundary evaluation for a b-rep; for both, the time increases linearly
with the number of features already in the model. For the remove and modify
feature operations, however, boundary evaluation for the cellular model has a
constant cost that is in the same order of magnitude as the cost of an add
feature operation. Boundary evaluation for a b-rep, on the other hand, has a
cost that is linearly dependent on when the feature being removed or modified
was added to the model, and is very high compared to the cost of an add
operation.
It is concluded that boundary evaluation for a cellular model is in fact more
efficient than for a b-rep, which makes cellular models even more attractive as
an alternative for b-reps.
Keywords
Feature modeling, boundary representation, cellular model, incremental evaluation, performance measurements, computational geometry
Bidarra R, Neels WJ, and Bronsvoort WF (2003), Boundary evaluation for a cellular model. In: CD-ROM Proceedings of the 2003 ASME Design Engineering Technical Conferences & Computers and Information in Engineering Conference, 2-6 September, Chicago, USA. ASME, New York.