Geometry Images of Arbitrary Genus in the Spherical Domain
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
Bibliographic record
Abstract
Abstract While existing spherical parameterization algorithms are limited to genus‐0 geometrical models, we believe a wide class of models of arbitrary genus can also benefit from the spherical domain. We present a complete and robust pipeline that can generate spherical geometry images from arbitrary genus surfaces where the holes are explicitly represented. The geometrical model, represented as a triangle mesh, is first made topologically equivalent to a sphere by cutting each hole along its generators, thus performing genus reduction. The resulting genus‐0 model is then parameterized on the sphere, where it is resampled in a way to preserve connectivity between holes and to reduce the visual impact of seams due to these holes. Knowing the location of each pair of boundary components in parametric space, our novel sampling scheme can automatically choose to scale down or completely eliminate the associated hole, depending on geometry image resolution, thus lowering the genus of the reconstructed model. We found our method to scale better than other geometry image algorithms for higher genus models. We illustrate our approach on remeshing, level‐of‐detail rendering, normal mapping and topology editing.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 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