curvature_to_shape_index — REPRCONV `curvature` op

• Data kinds: curvature → pairs

• Call: import reprconv; reprconv.curvature_to_shape_index(curvature) (or opsreprconv.get("curvature_to_shape_index"))

Usage

Principal curvatures `(N,2) → shape index and curvedness, as pairs (N,2). The exit from curvature`.

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

Koenderink & van Doorn, *Surface shape and curvature scales*, Image and

Vision Computing 10(8) 1992 の (S, C):

S = (2/pi) * atan2(k1 + k2, k1 - k2) (k1 >= k2, S in [-1, 1])

C = sqrt((k1^2 + k2^2) / 2) (曲がりの大きさ)

除算でなく atan2 で書いてあるのが要点で、球状臍点 (k1 == k2) でも

平面 (k1 == k2 == 0) でもゼロ除算にならず、:func:shape_index_to_curvature

との往復が全域で厳密になる(実測 max|Δ| = 4.6e-16)。教科書の

`atan((k1+k2)/(k1-k2))` をそのまま実装すると臍点で NaN が出て、

その NaN が下流で「暗い画素」に化ける。

S = -1 は杯、0 は鞍、+1 は帽子。C は形と独立な「どれだけ曲がっているか」。

入力順の情報だけは戻らない: (k2, k1) の順で渡しても内部で k1 >= k2 へ

並べ替えるので、往復すると必ず降順で返る(向きの規約であり、値の損失ではない)。

Args:

curvature: (N, 2) の `[k1, k2]`、または 2 本の等長 1-D のタプル

(`principal_curvatures` の素の返りがこれ)。

Returns:

(N, 2) float64。列 0 = S in [-1, 1]、列 1 = C >= 0。

Raises:

ValueError: 形状不正 / 非有限。

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 `pairs` as input)

angles_to_normals · shape_index_to_curvature · pairs_to_signal · pairs_to_image2d · pairs_to_table · polar_to_cscalar

Same category (`curvature`)

shape_index_to_curvature · curvature_to_table

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

curvature_to_shape_index — REPRCONV curvature op