Pith Number

pith:CY3VJPLH

pith:2026:CY3VJPLHPERMKPEJG5NZLAOVH3

not attested not anchored not stored refs resolved

An improved boundary-focused adaptive quadtree algorithm for circle-polygon intersection area approximation

Baoshan Wang, Lan Li, Songyi Liu, Yongjun Wang, Zeping Yi

An adaptive quadtree algorithm approximates circle-polygon intersection areas in O(1/ε^{3/2}) time with O(ε) error.

arxiv:2605.15627 v1 · 2026-05-15 · cs.CG

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Record completeness

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Claims

C1strongest claim

Theoretical analysis shows that the algorithm achieves O(1/ε^{3/2}) computational complexity while maintaining an O(ε) error bound, improving upon the O(1/ε²) complexity of classical Monte Carlo and uniform grid methods for the same error tolerance ε.

C2weakest assumption

The curvature-multiplicity-guided adaptive sampling strategy, including the introduced minimum sample count and constant factor, correctly concentrates points on complex boundaries to achieve the stated O(ε) error without systematic bias or missed intersections in multi-circle cells.

C3one line summary

An adaptive quadtree algorithm with curvature-guided Monte Carlo sampling for multi-circle polygon intersections achieves O(1/ε^{3/2}) complexity at O(ε) error, outperforming classical methods in experiments.

References

35 extracted · 35 resolved · 0 Pith anchors

[1] A. P. de Almeida Rocha, A. Rodler, R. C. Oliveira, J. Virgone, N. Mendes, A pixel counting technique for sun patch assessment within building enclosures, Solar Energy 184 (2019) 173– 2019

[2] doi:https://doi.org/10.1016/j.solener.2019.03.081 2019 · doi:10.1016/j.solener.2019.03.081

[3] M. S. Shaikh, C. Wang, S. Xie, G. Zheng, X. Dong, S. Qiu, M. A. Ahmad, S. Raj, Cover- age and connectivity maximization for wireless sensor networks using improved chaotic grey wolf optimization, Scie 2025

[4] W. Wu, Z. Wang, L. Lin, X. Chang, L. Tian, An efficient coverage path planning method for UA V in complex concave regions, Scientific Reports 15 (2025) 37227. doi:https://doi. org/10.1038/s41598-025-2 2025 · doi:10.1038/s41598-025-20978-8

[5] Bogosel, V olume computation for meissner polyhedra and applications, Dis- crete & Computational Geometry 75 (2026) 48–72 2026

Formal links

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Receipt and verification

First computed	2026-05-20T00:01:08.863803Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

163754bd677922c53c89375b9581d53eeb98c76ebf411f4f077546518e89a363

Aliases

arxiv: 2605.15627 · arxiv_version: 2605.15627v1 · doi: 10.48550/arxiv.2605.15627 · pith_short_12: CY3VJPLHPERM · pith_short_16: CY3VJPLHPERMKPEJ · pith_short_8: CY3VJPLH

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/CY3VJPLHPERMKPEJG5NZLAOVH3 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 163754bd677922c53c89375b9581d53eeb98c76ebf411f4f077546518e89a363

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "587b8de304853e6d366ce5d882927d34e2c93fb7fb7368ce9f44d88e1b8ee5f3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.CG",
    "submitted_at": "2026-05-15T05:20:17Z",
    "title_canon_sha256": "f3780ffd7eb351741bf130f109bce3a179bde8a4fe6fce0bd16854cdf066d1db"
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    "kind": "arxiv",
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