Bibliographic record
Abstract
A basic challenge in field-guided hexahedral meshing is to find a spatially-varying frame that is adapted to the domain geometry and is continuous up to symmetries of the cube. We introduce a fundamentally new representation of such 3D cross fields based on Cartan's method of moving frames. Our key observation is that cross fields and ordinary frame fields are locally characterized by identical conditions on their Darboux derivative. Hence, by using derivatives as the principal representation (and only later recovering the field itself), one avoids the need to explicitly account for symmetry during optimization. At the discrete level, derivatives are encoded by skew-symmetric matrices associated with the edges of a tetrahedral mesh; these matrices encode arbitrarily large rotations along each edge, and can robustly capture singular behavior even on coarse meshes. We apply this representation to compute 3D cross fields that are as smooth as possible everywhere but on a prescribed network of singular curves---since these fields are adapted to curve tangents, they can be directly used as input for field-guided mesh generation algorithms. Optimization amounts to an easy nonlinear least squares problem that behaves like a convex program in the sense that it always appears to produce the same result, independent of initialization. We study the numerical behavior of this procedure, and perform some preliminary experiments with mesh generation.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.012 | 0.003 |
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".