construct op• 資料種類:無 → pairs(僅由參數決定的運算子 —— 不接受影像或資料輸入)
• 呼叫: import fullseye as fs; fs.ledger.space_filling_curve(kind='hilbert', order=4)(要直接呼叫實作,import mathops; mathops.space_filling_curve(kind='hilbert', order=4);從台帳取用則 opsmath.get("space_filling_curve"))
`2**order` 方格上的希爾伯特/摩爾/掃描順序 —— 並驗證它確實是一個置換。
> 以下的詳細說明為原文 —— 摘要與標題已翻譯。
Returns the visiting order as `pairs (4**order, 2)` of integer grid
coordinates. Two scan orders are included as control groups, not as
filler: `row_major` jumps a whole row at the end of each line and
`boustrophedon` (serpentine) does not, so "consecutive points are
adjacent" separates them, and the locality measurement separates all four.
★Why this earns its place — the defining properties are integers:
• The result visits `4**order` cells, each exactly once: a
permutation, verified by sorting, not by sampling.
• For Hilbert, Moore and boustrophedon, **consecutive points are always at
L1 distance exactly 1**. Row-major is not (it jumps at every line end),
which is the control.
• Moore's curve is closed: the last point is adjacent to the first.
Hilbert's is not.
• *Locality.* For a gap of `k` in index, the mean Euclidean distance
grows like `sqrt(k)` for Hilbert and much faster for row-major. That is
why Hilbert order is used for spatial indexes, and it is measurable here
rather than asserted.
Raises `ValueError: unknown kind; order < 1`; the grid would
exceed the cap; `moore with order < 2` (it is not defined below that).
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
pairs 作為輸入)neighbour_index_gaps · curve_locality
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · ifs_similarity_dimension · curve_locality
*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.