geometry op• データ種: points → primitive
• 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"))
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).
• 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。
• oriented_bounding_box — py -3.11 examples_3d/oriented_bounding_box.py
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
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.