A Discrete Approach to Multiresolution Curves and Surfaces
Bibliographic record
Abstract
Subdivision surfaces have been widely adopted in modeling in part because they introduce a separation between the surface and the underlying basis functions. Such a separation allows for simple schemes that work on general topology surfaces. Multiresolution representations based on subdivision, however, incongruently return to continuous functional spaces in their construction and analysis. In this paper, we investigate a discrete approach to multiresolution construction for a variety of subdivision schemes, based only on the subdivision rules. Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between locally adjacent detail terms. In this way, all detail information is recoverable for reconstruction, and a decomposition approach is implied by the constraint. The construction is demonstrated with case studies in Dyn-Levin-Gregory curves and Catmull-Clark surfaces, each of which our method produces results as good as earlier methods. It is further shown that our construction can be interpreted as biorthogonal wavelet systems.
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How this classification was reachedexpand
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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".