<title>Adaptive reconstruction of closed Bezier surfaces</title>
Bibliographic record
Abstract
This paper presents a technique for reconstructing smooth closed Bezier surfaces from coordinate measurements based on a Bernstein Basis Function (BBF) network. While various neural networks, such as the backpropagation network and radial basis function networks, have been effective in functional approximation and surface fitting these neural networks produce system dependent solutions that are not easily transferable to commercially available design software. The BBF network has an advantage over other networks by directly employing the same Bernstein polynomial basis functions that are used in describing Bezier surfaces. The BBF network is capable of implementing a close approximation to any continuous nonlinear mapping by forming a linear combination of nonlinear Bernstein polynomial basis functions. Changing the number of basis neurons in the network architecture is equivalent to modifying the degree of the Bernstein polynomials. Complex smooth surfaces can be reconstructed by using several simultaneously updated networks, each corresponding to a separate surface patch. A smooth transition between adjacent Bezier surface patches can be achieved by imposing additional positional C0 and tangential C1 continuity constraints on the weights during the adaptation process. Once adapted, the final weights of the networks correspond to the control points of the Bezier surface, and can therefore be used directly in commercial CAD software packages that utilize parametric modelers.
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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 | 0.001 | 0.002 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.014 | 0.007 |
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".