smallest_box3 — 3D geometry op

데이터 종류: pointsprimitive

호출: import fullseye as fs; fs.ledger.smallest_box3(points) -> 'dict'(구현을 직접 호출하려면 import measure3d; measure3d.smallest_box3(points) -> 'dict', 원장에서 가져오려면 ops3d.get("smallest_box3"))

사용법

거의 최소 부피의 유향 경계 상자(3-D 판 `smallest_rectangle2`).

> 아래 상세 설명은 원문입니다 —— 요약과 제목은 번역되어 있습니다.

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).

참고(샘플 데이터·문헌)

• 샘플 데이터 카탈로그(DL URL / 라이선스) —— 2-D 는 skimage.data(BSD/public)+ 합성, 3-D 는 실데이터 소스(Stanford/PDS 등)의 DL URL.

• 연산자의 내력·참고문헌 —— 이 연산자 족의 바탕이 된 연구/기법의 출처.

실행 가능한 예제(이 연산자를 실제로 호출하는 검증된 샘플)

oriented_bounding_boxpy -3.11 examples_3d/oriented_bounding_box.py

타입이 이어지는 다음 연산자(primitive 를 입력으로 받는 것)

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

같은 카테고리(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 연산자 레지스트리. 이 op 노트는 tools/opdocs.py md 가 자동 생성합니다(직접 편집하지 마세요).*

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