geometry op• 資料種類:points → primitive
• 呼叫: import fullseye as fs; fs.ledger.smallest_box3(points) -> 'dict'(要直接呼叫實作,import measure3d; measure3d.smallest_box3(points) -> 'dict';從台帳取用則 ops3d.get("smallest_box3"))
近似最小體積的有向包圍盒(3-D 版 `smallest_rectangle2`)。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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).
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
• oriented_bounding_box — py -3.11 examples_3d/oriented_bounding_box.py
primitive 作為輸入)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 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.