gaussian_curvature — 3D `curvature` op

• Data kinds: points → signal

• Call: import fullseye as fs; fs.ledger.gaussian_curvature(points, k=25) (to call the implementation directly, import curvature3d; curvature3d.gaussian_curvature(points, k=25); from the registry, ops3d.get("gaussian_curvature"))

Usage

Gaussian curvature K = k1·k2 (invariant to flipping the normal). → (N,).

> The detailed description below is the original text — the summary and the headings are translated.

補足:

• `principal_curvatures と同じ局所二次曲面フィットで k1 * k2 を返す。符号は法線の向きに依らないため normals` 引数を持たない(向き付けは常に近傍重心ヒューリスティクス)。

• 単位は 1/長さ²。半径 R の球なら `1/R²`、円柱・平面は 0、鞍点は負(k1 と k2 が異符号)。

• `k` は近傍点数(既定 25、N-1 に切り詰め)。近傍が 5 点未満の点は 0。

• 楕円点(K>0)/放物点(K=0)/双曲点(K<0)の分類に使う。凸凹の区別は `mean_curvature か shape_index に normals` を渡して行う。

• 入力は (N,3) の点群。決定論的。

Background guides (the physics and conventions behind this op)

• blas_threads_and_memory — 行列分解が遅い理由の知識 — BLAS スレッド・キャッシュ・メモリ配置

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

Runnable examples (verified samples that actually call this op)

• curvature_grasp — py -3.11 examples_3d/curvature_grasp.py

• curvature_shape_index — py -3.11 examples_3d/curvature_shape_index.py

Ops the type connects to (they accept `signal` as input)

fuse_to_voxel

Same category (`curvature`)

principal_curvatures · mean_curvature · shape_index · estimate_normals

*Provenance: curvature3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

gaussian_curvature — 3D curvature op