Uncertainty Management in Feature-Based Geometric Modelling and Data Exchange
Bibliographic record
Abstract
If it is desired to obtain answers with correct topological form, then the problem of computing regularized Boolean operations in solid modelling is ill-conditioned. To say that the answer has correct topological form here means that not only is the computed model topologically well-formed, but also that it has the same topological form as the true (exact) result (i.e., the exact and computed objects are linked by a homeomorphism). That the problem is ill-conditioned means that small changes in the problem data (smaller than the uncertainty in this data) can cause the true result of the operation to change topological form, so that the true result corresponding to the new data is not just erroneous, but different in kind. The ill condition implies that the resulting computational difficulty cannot be resolved by designing better numerical algorithms. It is shown in this paper, however, that in at least one situation, there is enough information available to resolve the problem of correct topological form even though the available information does not eliminate the uncertainty involved. The situation referred to is that of feature-based design, where information concerning attachment of features is available. It is shown here how to produce a posteriori guarantees on topological form in the case when the faces of the solids and features are defined by logically-locally-planar Bézier patches. This case is general enough to cover, by means of representation conversion, many practical representation methods. Our approach is based on existing methods for the production of consistent trimmed surfaces, and existing methods permitting a posteriori verification that the patches forming the faces do not have self-intersections or extraneous intersections. The main contribution of the paper is to observe that uncertainty can affect the results of computing Boolean intersections at different levels of severity and that, in certain important practical situations, although the uncertainty cannot be removed, its effects can be rendered almost completely harmless.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.014 | 0.044 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.003 |
| Bibliometrics | 0.003 | 0.004 |
| Science and technology studies | 0.002 | 0.004 |
| Scholarly communication | 0.008 | 0.013 |
| Open science | 0.005 | 0.011 |
| Research integrity | 0.004 | 0.003 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".