Mitered offset of a mesh using QEM and vertex split
Bibliographic record
Abstract
In this paper, we present a mitered offsetting method of a triangular mesh. Though our main target application is machining tool path generation, it can also be applied to shelling/hollowing of solid objects, collision avoidance in robot path planning, and so on. Previous literature on mesh offsetting mostly suggest inserting a portion of a cylinder (or a ball) in order to fill the gap between offset faces adjacent to a sharp edge (or a sharp vertex, respectively). The gap filling elements (cylinders or balls) are approximated by a number of small triangles depending on the offset error tolerance. Those small gap filling triangles not only increase tool path computation time, but also cause harmful effect in the accuracy of the machined result around the sharp edges. In this research, we try to reduce the number of gap filling triangles while meeting the given tolerance by introducing the concept of mitered offset, which is popularly used in 2D profile machining practice. We borrowed and modified the notion of quadric error metric (QEM) from the mesh simplification area. A modified version of QEM is used for robust computation of the offset vertex position which minimizes the sum of squared distance error from the faces around the original mesh vertex. If the error is within tolerance, the offset vertex is accepted. Otherwise, the offset vertex is split repeatedly until the error is acceptable. Vertex split occurs at the sharp features. A rigorous foundation is given to the mitered offset of 3D mesh with sharp features as well as smooth regions. The experimental results indicate that only a small number of triangles are added in offset mesh.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".