CONSTRUCTING CONSTRAINED DELAUNAY TETRAHEDRALIZATIONS OF VOLUMES BOUNDED BY PIECEWISE SMOOTH SURFACES
Bibliographic record
Abstract
This article presents an algorithm to construct constrained Delaunay tetrahedralizations of geometric domains bounded by piecewise smooth surfaces. Meshes are built from the bottom-up by first discretizing the boundary curves and then by sampling the smooth surfaces. The sampling procedure refines the Delaunay triangulation restricted to these surfaces, targeting topological violations and poor quality triangles. Unlike previously published algorithms adopting a similar approach, we propose to sample each smooth surface patch independently. This obviates the need for a boundary protection scheme around small dihedral angles in the input and can also lead to coarser constraining triangulations. Starting from a Delaunay tetrahedralization of the point samples, a combination of mesh reconfigurations and vertex insertions is then used to obtain a tetrahedralization constrained to the boundary surfaces. The algorithm is designed to produce tetrahedralizations that can be used in conjunction with a Delaunay refinement algorithm implemented on a Bowyer-Watson framework.
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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 | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.002 | 0.003 |
| Research integrity | 0.001 | 0.002 |
| 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".