smallest_box3 — 3D geometry op

データ種: pointsprimitive

呼び出し: import fullseye as fs; fs.ledger.smallest_box3(points) -> 'dict' (実装を直接呼ぶなら import measure3d; measure3d.smallest_box3(points) -> 'dict'、台帳から引くなら ops3d.get("smallest_box3"))

使い方

ほぼ最小体積の有向外接直方体(3-D 版 `smallest_rectangle2`)。

> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。

Found by multi-start local refinement: seed the orientation from every convex-

hull face normal (the O'Rourke *case a* candidates — a box face flush with a

hull face), from the PCA axes, and from a fixed set of deterministic random

frames, then polish each by coordinate descent and keep the least-volume result.

This is exact for box-like objects (a rotated cuboid is recovered to machine

precision) and, unlike a PCA box (`fit_box3 / pcseg.obb`), reaches the true

minimum on shapes whose optimum has no face flush with a hull face — e.g. a

regular tetrahedron, where the PCA / hull-face box is ~2x too large.

Honest limit: this is not a *proof* of global minimality for every convex shape.

The exact guarantee needs O'Rourke's full *case b* (two box faces each flush with

a hull edge), which is not enumerated here; local refinement drives seeds into

that regime instead. Empirically the result is at or below a dense brute-force

rotation search, but a pathological shape could leave a small gap.

Returns `center (cd/cr/cc), axes` (3, 3 — unit ROW vectors), sorted

half-extents `l1 >= l2 >= l3, full size, volume, and corners`

(8, 3). Deterministic (fixed random seeds). Raises `ValueError` on < 4 points

or a coplanar/degenerate set (no 3-D hull).

参考(サンプルデータ・文献)

• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。

• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

oriented_bounding_boxpy -3.11 examples_3d/oriented_bounding_box.py

型が繋がる次の op(primitive を入力に取れる)

fuse_to_voxel · angle_between_lines · angle_between_planes · angle_line_plane · distance_point_plane · distance_point_line · distance_line_line · distance_segment_segment

同カテゴリ(geometry)

line_from_2points · plane_from_3points · angle_3points · angle_between_lines · angle_between_planes · angle_line_plane · distance_point_plane · distance_point_line


*Provenance: measure3d.py — 3D operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.