Section: Scientific Foundations

Geometric Uncertainties

Although geometric uncertainties are related to robustness and tolerance, there are a number of extra issues well worth deeper investigations.

Geometric arrangements are full of special cases. The most notable ones are: cases of touch, overlapping, containment, etc.; cases of parallelism, perpendicularity, coincidence, etc.; axes of symmetrical data, data clustering, dense or sparse data, etc.; cases of degeneracy, discontinuity, inconsistencies, etc.; problems with cracks, excess material, lack of detail, etc. In just about any code that deals with geometry, the number of special cases is significantly larger than the general ones.

Data explosion is the result of careless selection of the methods, e.g. parameter space-based sampling, and improper implementation, e.g. recursive algorithms. Some of the relevant issues are: sampling: over sampling, sampling in incorrect places, etc; procedural definitions, e.g. lofting a large set of curves may result in an explosion of control points; excess data on input may get magnified further to fill available memory; improper data structures, e.g. arrays of fixed size holding very little data; and non-compacted data bases used for further processing.

Last but not least, although CAD processes are supposed to produce valid and "made to order" models, the reality is that most (if not all) models are rough and require post-processing, i.e. beautification. Some of the most frequently needed tasks are: removing unwanted edges, corners, cracks, etc.; removing bumps, oscillations, curvature extremes, etc.; healing incorrect models, e.g. removing holes in triangulations; smoothing, fairing, re-shaping, etc. (See more detaila in the very interesting paper of G. Farin in Journal of Computer-Aided Design, 2007, Elsevier Publisher.).