Near-linear time medial axis approximation of smooth curves in $\mathbb{R}^3$
Bibliographic record
Abstract
We present the first algorithm to approximate the medial axis $M_{\gamma}$ of a smooth, closed curve $\gamma \subset \mathbb{R}^3$ in near-linear time. Our algorithm works on a sufficiently dense \eps-sample and comes with a convergence guarantee for the non-discrete, but continuous approximation object. As our approach also works correctly for a set of curves, we discuss the following application of the medial axis: The medial axis of two curves $\gamma_1$ and $\gamma_2$ can be applied to compute piecewise-linear simplifications of $\gamma_1$ and $\gamma_2$. In particular, a controllable tradeoff between the degree of simplification and the degree of falsification of the summed Fr\'{e}chet distance between $\gamma_1$ and $\gamma_2$ is obtained. Finally, we show that for simplifying $\gamma_1$ and $\gamma_2$, our approximation, instead of $M_{\gamma}$, can be applied while guaranteeing the same result.
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 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 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| 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".