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"))
Gaussian curvature K = k1·k2 (invariant to flipping the normal). → (N,).
Notes:
• Returns k1 * k2 from the same local quadric surface fit as principal_curvatures. The sign does not depend on the normal orientation, so there is no normals argument (orientation always uses the neighbourhood-centroid heuristic).
• Units are 1/length². A sphere of radius R gives 1/R², a cylinder or plane 0, a saddle point negative (k1 and k2 have opposite signs).
• k is the number of neighbours (default 25, truncated to N-1). Points with fewer than 5 neighbours get 0.
• Used to classify elliptic points (K>0) / parabolic points (K=0) / hyperbolic points (K<0). To tell convex from concave, pass normals to mean_curvature or shape_index.
• Input is an (N,3) point cloud. 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_grasp — py -3.11 examples_3d/curvature_grasp.py
• curvature_shape_index — py -3.11 examples_3d/curvature_shape_index.py
signal as input)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).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.