ABF++: fast and robust angle based flattening
Why this work is in the frame
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Bibliographic record
Abstract
Conformal parameterization of mesh models has numerous applications in geometry processing. Conformality is desirable for remeshing, surface reconstruction, and many other mesh processing applications. Subject to the conformality requirement, these applications typically benefit from parameterizations with smaller stretch. The Angle Based Flattening (ABF) method, presented a few years ago, generates provably valid conformal parameterizations with low stretch. However, it is quite time-consuming and becomes error prone for large meshes due to numerical error accumulation. This work presents ABF++, a highly efficient extension of the ABF method, that overcomes these drawbacks while maintaining all the advantages of ABF. ABF++ robustly parameterizes meshes of hundreds of thousands and millions of triangles within minutes. It is based on three main components: (1) a new numerical solution technique that dramatically reduces the dimension of the linear systems solved at each iteration, speeding up the solution; (2) a new robust scheme for reconstructing the 2D coordinates from the angle space solution that avoids the numerical instabilities which hindered the ABF reconstruction scheme; and (3) an efficient hierarchical solution technique. The speedup with (1) does not come at the expense of greater distortion. The hierarchical technique (3) enables parameterization of models with millions of faces in seconds at the expense of a minor increase in parametric distortion. The parameterization computed by ABF++ are provably valid, that is they contain no flipped triangles. As a result of these extensions, the ABF++ method is extremely suitable for robustly and efficiently parameterizing models for geometry-processing applications.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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 it