Medial Axis Transform of Planar Shapes With Free-Form Curve Boundary
Bibliographic record
Abstract
Medial axis transform (MAT) is a very useful shape interrogation tool in NC tool path generation for pocket milling. This paper presents a new, efficient approach to calculating MATs of planar profiles with boundaries of free-form curves. The proposed approach is mainly based on profile boundary tracing and decomposition. By studying the basic elements of MAT and their geometric properties, several algorithms of finding contact circles are developed. The boundary tracing algorithm can handle profiles with/without internal holes. For a profile without internal holes, it is continuously divided into simpler sub-profiles while travelling along the boundary, and a tree data structure is adopted to keep track of the boundary decomposition process. For a profile with internal holes, it is divided into several simple profiles without internal holes. After generating the MAT of each simple profile, the completed MAT can be found by combining these MATs. This proposed approach is implemented and some illustrative samples are presented to demonstrate its advantages.
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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".