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Record W2331493134 · doi:10.2514/6.2009-375

Eikonal Equation Based Front Propagation Technique and its Applications

2009· article· en· W2331493134 on OpenAlex
Yuanli Wang

Why this work is in the frame

A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.

fundA Canadian funder is recorded on the work.
no affNo Canadian affiliation: this work is invisible to an affiliation-only frame.
No Canadian affiliation. An affiliation-only frame, the usual design, would never have seen this work. It is one of the works that make the case for inverting the frame.

Bibliographic record

Venue47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and Aerospace Exposition · 2009
Typearticle
Languageen
FieldComputer Science
TopicComputational Geometry and Mesh Generation
Canadian institutionsnot available
FundersPolytechnique Montréal
KeywordsEikonal equationFast marching methodOffset (computer science)Front (military)Point (geometry)Finite difference methodMathematical analysisNormalBoundary (topology)Computer scienceGeometryBoundary value problemMathematicsAlgorithmSurface (topology)Physics

Abstract

fetched live from OpenAlex

This paper presents a new front propagation technique which is extended to the applications in Ge-ometryModeling andMeshGeneration. The propagation process proposed in this technique is directly inspired from marching technology, that is all the points located on the original front are propagated along their local normal directions. The main difference between the current method and traditional marching methods lies in the way that local normal direction is computed. Traditionally, the local nor-mal directions are computed using geometric information, such as the average (or weighted) normal of neighboring points or facets surrounding the point to be propagated. In this method, the local nor-mal directions are calculated using equation ~n = ∇φ/|∇φ. φ is the solution of the minimum distance equation, ∇φ · ∇φ = 1, which is a variation of the Eikonal equation. The benefit of calculating normal directions in such a way is that self-intersections are avoided in a natural way. This proposed front propagation method is validated from two aspects: accuracy and efficiency. The proposed front propa-gation technique is successfully applied in the applications of offset surface construction and boundary layer mesh generation. Nomenclature φ The minimum Euclidean distance between any arbitrary point of computational domain to the propagated front ~n Normal vector ∇ First derivative in space Γ The front to be propagated t The sweep counter I.

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.

Full frame distilled prediction

Teacher imitation

Not 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.

metaresearch head score (Codex)0.001
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesScience and technology studies
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Bench or experimental · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: none
Teacher disagreement score0.873
Threshold uncertainty score0.999

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0010.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0020.000
Scholarly communication0.0010.001
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0000.000

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.

Opus teacher head0.024
GPT teacher head0.271
Teacher spread0.247 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it