shape_index_to_curvature — REPRCONV curvature op

• Data kinds: pairs → curvature

• Call: import fullseye as fs; fs.ledger.shape_index_to_curvature(pairs) (to call the implementation directly, import reprconv; reprconv.shape_index_to_curvature(pairs); from the registry, opsreprconv.get("shape_index_to_curvature"))

Usage

Shape index and curvedness (N,2) → principal curvatures (N,2). The inverse of curvature_to_shape_index.

With theta = pi*S/2, k1 = C(sin+cos), k2 = C(sin-cos). The closed form obtained by solving the defining equations of (S, C); no approximation or iteration is involved.

Args:

pairs: (N, 2) [S, C].

Returns:

(N, 2) float64 [k1, k2] (k1 >= k2).

Raises:

ValueError: |S| > 1 / C < 0 / invalid shape / non-finite.

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.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• representation_roundtrip — py -3.11 examples/representation_roundtrip.py

Ops the type connects to (they accept curvature as input)

curvature_to_shape_index · curvature_to_table

Same category (curvature)

curvature_to_shape_index · curvature_to_table

*Provenance: reprconv.py — REPRCONV 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.