pegsym op• Data kinds: scalar × scalar × scalar → table
• Call: import fullseye as fs; fs.ledger.rotation_window(n: 'int', apothem: 'float', clearance: 'float', chamfer: 'float' = 0.0, peg_vertices=None, hole_vertices=None, tol: 'float' = 1e-10, mu: 'float | None' = None) -> 'dict' (to call the implementation directly, import pegsym; pegsym.rotation_window(n: 'int', apothem: 'float', clearance: 'float', chamfer: 'float' = 0.0, peg_vertices=None, hole_vertices=None, tol: 'float' = 1e-10, mu: 'float | None' = None) -> 'dict'; from the registry, opsdrive.get("rotation_window"))
Rotation window within which the peg enters the hole (or its mouth, if chamfered). Closed form for a regular n-gon (derived): with centers aligned, the vertices lie at directions π/n ∓ φ from the face normal, and the peg enters if the normal-direction extent of the outermost vertex, a cos(π/n − |φ|), is at most A + δ (+ W): φ = π/n − arccos(x), x = (A + δ + W) cos(π/n)/A (if x ≥ 1 the window fills the half period π/n). Since arccos has a rounding floor near 1, it is written as atan2(√(1 − x²), x). If peg_vertices and hole_vertices are given, the windows in the positive and negative directions are also measured by bisection on the linear program (polygon_fit_check, translation also free) (second (independent) implementation; the only option for keyed shapes). Returns phi_fit (the narrowest part, not the mouth), phi_cap (chamfer mouth), period = 2π/n, M = ⌈period/(2 phi_cap)⌉ and lp (plus/minus: when vertices are given, both ends of the window entering the mouth = the connected interval containing 0; the scan divides the half period into 360 steps, the ends by bisection).
> The detailed description below is the original text — the summary and the headings are translated.
mu を渡すと摩擦で止まる限界も返す(導出、45° の面取り): 口に載った頂点(面の法線から β = π/n − φ の向き)が面取りを滑り下りるには、ペグが回らなければならない(偶数の n では向かい合う頂点の横向きの力が打ち消し合い、並進しない)。軸まわりのばねが弱いと接触力の軸まわりのモーメントが 0 で釣り合う: 面取りの法線の接線成分 sin β/√2 と、滑りの向き(面の上で下り + 回転)に逆らう摩擦 μ/√(1 + sin²β) が等しい所が境で、回るのは s√(1 + s²) > √2 μ(s = sin β)、すなわち s² > (√(1 + 8μ²) − 1)/2 の時。phi_friction = π/n − β*、phi_eff = max(phi_fit, min(phi_cap, phi_friction))(面取りに頼らず入る分は摩擦に依らない)。六角形(頂点が面の法線に近い)は摩擦で窓が狭まり、三角形・四角形は幾何で決まる —— MuJoCo の試作で確かめた(PoC の --full)。Raises ValueError: n < 1、apothem ≤ 0、clearance < 0、chamfer < 0、mu < 0、頂点を片方だけ渡した。
• 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.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• poc_peg_symmetry_search — py -3.11 examples/poc_peg_symmetry_search.py
table as input)course_layout · course_occupancy · course_contains · world_build · world_camera · world_move · lidar_scan · rss_longitudinal_same
pegsym)polygon_peg · polygon_offset · polygon_fit_check · polygon_two_point_depth · polygon_coverage_image · plane_topview · polygon_yaw_read · relative_yaw_from_images
*Provenance: pegsym.py — DRIVE operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.