principal_moments — 3D `moment_invariant` op

• Data kinds: points → descriptor

• Call: import fullseye as fs; fs.ledger.principal_moments(points) -> 'np.ndarray' (to call the implementation directly, import moments3d; moments3d.principal_moments(points) -> 'np.ndarray'; from the registry, ops3d.get("principal_moments"))

Usage

The eigenvalues of the inertia tensor (the principal moments, sorted descending, rotation invariant).

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

慣性テンソルは対称なので固有値は実。点群を回転 R で回すと I → R I Rᵀ と

相似変換され、固有値は不変(厳密)。返り値は降順にそろえるので座標系や

回転に依らず一致する。

Returns

-------

np.ndarray, shape (3,)

降順の主慣性モーメント λ1 >= λ2 >= λ3 >= 0。

補足:

• `inertia_tensor の固有値で、共分散の固有値 c_i とは λ_i = (c_1 + c_2 + c_3) - c_i` の関係。細長い棒では最小固有値(棒の軸まわり)が 0 に近づき、球では 3 つが等しい。

• 単位は長さ²。並進と回転には不変だが スケールには不変でない(s 倍で s² 倍)。スケール不変が要るなら `moment_invariants`。

• 入力は (N,3)、N >= 1(1 点なら全て 0)。形状不正・非有限は `ValueError`。

• 主軸ベクトル(固有ベクトル)が要るなら `moment_axes`。決定論的。

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)

• shape_desc_pose — py -3.11 examples_3d/shape_desc_pose.py

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

fuse_to_voxel · shape_distance

Same category (`moment_invariant`)

moment_invariants · central_moments · inertia_tensor

*Provenance: moments3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

principal_moments — 3D moment_invariant op