tb_inertia_tensor — 2D `typed` op

• Data kinds: points → matrix

• Call: fullseye.apply(img, "tb_inertia_tensor", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

*No figure: this op takes points as input. A Studio program starting from an image cannot reach that type — see the runnable examples below for how it is used.*

Usage

Inertia tensor of the point cloud (3,3) (from the central second moment, assuming equal mass and a total mass of 1).

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

I_xx = mean(y²+z²), I_yy = mean(x²+z²), I_zz = mean(x²+y²),

I_xy = -mean(xy), I_xz = -mean(xz), I_yz = -mean(yz)。

共分散 C を使うと I = tr(C)·E₃ − C(E₃ は単位行列)と等価。対称・半正定値。

重心中心化のため並進不変。

Returns

-------

np.ndarray, shape (3, 3)

対称な慣性テンソル。

2-D 進化レジストリへ橋渡しした 3d の op `inertia_tensor。実装は同じで、呼び出し規約だけ op(v, a, b) に合わせてある。この op に調整点は無く、a も b` も使われない。

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)

• (none yet)

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

identity · tb_mat_pinv · tb_mat_cond · tb_stat_covariance · tb_stat_correlation

Same category (`typed`)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tb_inertia_tensor — 2D typed op