Pith Number

pith:GXHNEIKT

pith:2026:GXHNEIKTFU7XWEHICPBK5IKRFJ

not attested not anchored not stored refs resolved

OffsetAxis: UDF Mesh Reconstruction via Offset-Volume Medial Axis Extraction

Dominique Bechmann, Pierre Kraemer, Qijia Huang

Mesh extraction from unsigned distance fields reduces to medial axis extraction of the alpha-offset volume

arxiv:2605.15369 v1 · 2026-05-14 · cs.GR

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\pithnumber{GXHNEIKTFU7XWEHICPBK5IKRFJ}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

The 0-level set extraction problem can be restated as the extraction of the medial axis of the α-offset volume of the UDF. This formulation unlocks mature medial-axis machinery that naturally supports boundaries, non-manifold junctions and curves.

C2weakest assumption

That sampling the α-offset surface via ray casting and optimizing medial balls with a variant of Variational Medial Axis Sampling will produce clusters whose dual connectivity yields structurally coherent meshes across open, non-manifold, and curve-like topologies, including for imperfect neural or point-cloud-derived UDFs.

C3one line summary

OffsetAxis reconstructs meshes from unsigned distance fields by extracting the medial axis of the alpha-offset volume using ray casting and variational medial ball optimization.

References

18 extracted · 18 resolved · 2 Pith anchors

[1] ShapeNet: An Information-Rich 3D Model Repository 2015 · arXiv:1512.03012

[2] Stability of persistence diagrams 2025 · doi:10.1145/1064092.1064132

[3] Xu Cheng, Hou Fei, Wang Wencheng, Qin Hong, Zhang Zhebin, and Ying He 2022

[4] Computer Graphics Forum41, 2 (2022), 419–432 2022 · doi:10.1111/cgf.14484

[5] 2023 , publisher = 2023 · doi:10.1145/3618314

Formal links

2 machine-checked theorem links

Receipt and verification

First computed	2026-05-20T00:00:54.944626Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

35ced221532d3f7b10e813c2aea1512a40f43a38701558543b2012bdc97fb2d7

Aliases

arxiv: 2605.15369 · arxiv_version: 2605.15369v1 · doi: 10.48550/arxiv.2605.15369 · pith_short_12: GXHNEIKTFU7X · pith_short_16: GXHNEIKTFU7XWEHI · pith_short_8: GXHNEIKT

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/GXHNEIKTFU7XWEHICPBK5IKRFJ \
  | 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: 35ced221532d3f7b10e813c2aea1512a40f43a38701558543b2012bdc97fb2d7

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "d934f1d09b5b80377cab7689bcd54edc8520e294c39d50e2a1f1181682e22e3b",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cs.GR",
    "submitted_at": "2026-05-14T19:49:15Z",
    "title_canon_sha256": "7114fb56ac8947e2816192551be69379773b7f63cd1a8cce273418829e48be78"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.15369",
    "kind": "arxiv",
    "version": 1
  }
}