Distance Calculation Between a Point and a NURBS Surface
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Bibliographic record
Abstract
In this paper, we consider the computation of an Euclidean shortest path between a point and a modelled curve or surface in three-dimensional space, which is one of the fundamental problems in robotics and many other areas. A new accurate algorithm for the distance-calculation between a point and a NURBS curve and its extension to the case of a point and a NURBS surface is presented. The algorithm consists of two steps, and is crucially based on appropriate projections and subdivision techniques. To solve a nonlinear polynomial system derived from the classical formulation of the distance problem, the well-known Newton-type algorithms or subdivision-based techniques first considered by Sherbrooke and Patrikalakis are used. Their modifications in conjunction with a low subdivision depth in the presented algorithms yield a verified enclosure of the solution.
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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 | 0.001 |
| 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 it