curvature op• Data kinds: points → signal
• Call: import fullseye as fs; fs.ledger.mean_curvature(points, k=25, normals=None) (to call the implementation directly, import curvature3d; curvature3d.mean_curvature(points, k=25, normals=None); from the registry, ops3d.get("mean_curvature"))
Mean curvature H = (k1+k2)/2. → (N,). A quantity that depends on the orientation.
normals (oriented reference normals, (N,3)): when omitted, a convex-side heuristic is used (the concave/convex sign of an open surface is undefined). Passing oriented normals aligns with the global orientation and yields the correct sign.
Notes:
• The computation is the same as principal_curvatures (PCA normal of the k+1 neighbourhood + local quadric surface fit) and returns (k1 + k2) / 2. Units are 1/length.
• The sign follows the convention convex = positive, and corresponds to global concave/convex only when normals is passed. When omitted, H of an open surface is always on the convex side (equivalent to the absolute value).
• Points with fewer than 5 neighbours get 0. k is truncated to N-1.
• A sphere of radius R gives 1/R, a cylinder 1/(2R), a plane 0. A saddle point (k1 = -k2) also gives 0, but gaussian_curvature is negative there, so the two can be told apart.
• normals must be (N,3) with finite, non-zero rows (ValueError). Deterministic.
• blas_threads_and_memory — Why matrix decompositions are slow — BLAS threads, caches, memory layout
• 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.
• curvature_shape_index — py -3.11 examples_3d/curvature_shape_index.py
• minimal_surfaces — py -3.11 examples_3d/minimal_surfaces.py
signal as input)curvature)principal_curvatures · gaussian_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).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.