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Record W2119490711 · doi:10.1142/s0218195900000085

EXACT AND OPTIMAL CONVEX HULLS IN 2D

2000· article· en· W2119490711 on OpenAlex

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.

affAt least one author lists a Canadian institution in the pinned OpenAlex snapshot.

Bibliographic record

VenueInternational Journal of Computational Geometry & Applications · 2000
Typearticle
Languageen
FieldComputer Science
TopicNumerical Methods and Algorithms
Canadian institutionsUniversity of Calgary
Fundersnot available
KeywordsConvex hullRoundingMathematicsHullFloating pointComputationConvex combinationInterval arithmeticAlgorithmConvex setRegular polygonCombinatoricsArithmeticConvex optimizationComputer scienceGeometryMathematical analysis

Abstract

fetched live from OpenAlex

We present an algorithm for computing the convex hull of a finite set of points. The algorithm is based on a version of Graham scan with the following additional features: • If the points are already (single precision) machine numbers, the computation is rounding-error free, that is, the computed hull is the hull that would have been computed if real arithmetic was available. • If the points are arbitrary numbers, the algorithm renders the smallest possible machine representable convex hull that includes the exact convex hull. • The computation time is still O(n log 2 n). • Only floating point arithmetic with double mantissa length is required. No mantissa splitting or other mantissa manipulations are needed; one only has to know the exponent parts of the numbers. Also, no fixed point accumulator is needed. • Single precision interval arithmetic is recommended for accelerating the computation, but is not necessary. • All of these aims are achieved with a new method for exact determination of the sign of a sum.

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)0.000
metaresearch head score (Gemma)0.000
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Other design · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.930
Threshold uncertainty score0.468

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.000
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.001
Science and technology studies0.0000.000
Scholarly communication0.0000.001
Open science0.0010.000
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 head0.011
GPT teacher head0.313
Teacher spread0.302 · 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