An Effective Approach to Approximating 2-D Free-Form Curve Offsets for B-Spline NC Tool Paths With Offset Error Globally Bounded
Bibliographic record
Abstract
The topic of representing the offset of a 2-D B-spline curve in the same form has been under research for a long time, and it has many industrial applications, especially, in NC tool path generation for pocketing. For B-spline tool paths, it is often required that the tool paths have fewer control points, lower base function degree, and higher geometric accuracy. However, the existing methods often generate the offsets of 2-D free-form curves in the form of B-spline curves with high function degree and many control points. Although these offsets are useful in computer-aided design, they are inappropriate for the use of CNC machining. To address the problems in order to generate high quality B-spline tool paths, this original work formulates an error function of the offset approximation and then constructs a NURBS curve to globally bound the errors. By checking the maximum coefficient of the bounding curve, the upper bound of all the approximated offset errors is found and the errors can be reduced by adding more offset points at the appropriate locations. The proposed new approach is more efficient, and the resulting offsets in B-spline are more accurate with fewer control points and lower function degree. It is useful to generate B-spline tool paths for CNC pocketing, and has potential for other applications in industry.
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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".