Why CAD Data Repair Requires Discrete Algorithmic Techniques.
Karsten Weihe, Thomas Willhalm · 1998
We consider a problem of reconstructing a discrete structure from unstructured numerical data. The problem arises in the computer-aided design of machines, motor vehicles, and other technical devices. A CAD model consists of a set of surface pieces in the three-dimensional space (the socalled mesh elements). The neighbourhoods of these mesh elements, the topology of the model, must be reconstructed. The reconstruction is non-trivial because of erroneous gaps between neighboured mesh elements. However, a look at the real-world data from various applications strongly suggests that the pairs of neighboured mesh elements may be (nearly) correctly identified by some distance measure and some threshold. In fact, to our knowledge, this is the main strategy pursued in practice. In this paper, we make a first attempt to design systematic studies to support a claim of failure: we demonstrate empirically that human intuition is misleading here, and that this approach fails even for "i...