construct op• 資料種類:pairs → table
• 呼叫: import fullseye as fs; fs.ledger.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32))(要直接呼叫實作,import mathops; mathops.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32));從台帳取用則 opsmath.get("curve_locality"))
沿曲線編號相差 k 的兩點, 在平面上相距多遠?
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
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.
Parameters
----------
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` =
`mean_distance / mean_distance[gap == 1]` so 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 的每個運算子都先檢驗輸入再計算(不讓任何東西無聲通過):
• **complex 輸入一律 ValueError** —— 強制轉成 float64 會無聲丟掉虛部(numpy 只發一個 ComplexWarning,然後回傳一個「看似合理卻是錯的」實數)。請明確寫出 .real/.imag/abs(),或改用支援複數的 complexops。
• **含被遮罩元素的 masked array 一律 ValueError** —— 拒絕「剝掉遮罩直接使用下面原值」的隱式轉換。請明確選擇填補還是丟棄。
• **所有輸入中的 NaN/Inf 一律 ValueError**(明確給出個數後拒絕 —— 它會汙染整個結果)。
• 形狀嚴格:不對 1-D 與 2-D 做隱式提升或廣播(向量槽位收到矩陣、矩陣槽位收到向量都是 ValueError;請明確 reshape)。
• 尺寸上限:接受矩陣的運算子與 stat_histogram 的 bins,超過 mathops.MAX_ELEMENTS(2^26 ≈ 6700 萬個元素)即 ValueError。
• 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。
• 演算法的正典(作者・年份)與用途見上面的族使用指南。
• poc_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
table 作為輸入)construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · ifs_similarity_dimension · space_filling_curve
*Provenance: mathops.py — MATH 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.