smallest_box3 — 3D `geometry` op

• Data kinds: points → primitive

• Call: import fullseye as fs; fs.ledger.smallest_box3(points) -> 'dict' (to call the implementation directly, import measure3d; measure3d.smallest_box3(points) -> 'dict'; from the registry, ops3d.get("smallest_box3"))

Usage

Near-minimum-volume oriented bounding box (the 3-D `smallest_rectangle2`).

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).

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)

• oriented_bounding_box — py -3.11 examples_3d/oriented_bounding_box.py

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

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

Same category (`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. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

smallest_box3 — 3D geometry op