construct oppairs → tableimport fullseye as fs; fs.ledger.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32)) (実装を直接呼ぶなら import mathops; mathops.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32))、台帳から引くなら opsmath.get("curve_locality"))Points k apart along the curve — how far apart are they on the plane?
The reason a space-filling curve is used for storage layout, texture tiling
or rendering order is locality: neighbours in the ordering should stay
neighbours in space. This op measures that directly — for each gap k it
returns the mean Euclidean distance between points i and i + k.
★Why this earns its place: the claim “Hilbert has better locality than
scanning row by row” is usually asserted and never measured. Here it is a
table you can read: a Hilbert curve grows roughly as sqrt(k) (measured
1.00 / 1.53 / 2.12 / 3.17 / 4.29 / 6.38 at k = 1 .. 32), while a boustrophedon
scan grows nearly linearly (1.00 / 1.96 / 3.79 / 7.07 / 12.12 / 16.07) —
an honest, reproducible gap rather than a slogan.
points : (N, 2) array
The curve’s points in visiting order.
gaps : ints
Index gaps to report. Gaps at or beyond N are dropped (not an error;
a short curve simply has nothing to say about a long gap).
Returns a table: gap (int), mean_distance, and ratio =
the first result when the first gap is 1, otherwise the minimum mean distance; a zero base yields NaN. Thus curves of different scales can
be compared directly.
Raises ValueError: not an (N, 2) array; fewer than 2 points;
non-finite coordinates; every requested gap out of range.
HALCON: no operator.
mathops の全 op は入力を検証してから計算する(黙って通さない):
ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。ValueError(件数を明示して拒否 — 結果全体に伝播するため)。ValueError。reshape を明示する)。stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。py -3.11 examples/poc_theorems_as_pictures.pytable を入力に取れる)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · ifs_similarity_dimension · space_filling_curve
Provenance: mathops.py — MATH 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.