Geometric and Feature modelling

Boundary evaluation for a cellular model

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


download full paper


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.