construct op• 数据种类:pairs → table
• 调用: import fullseye as fs; fs.ledger.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32))(要直接调用实现,import mathops; mathops.curve_locality(points, gaps=(1, 2, 4, 8, 16, 32));从台账取用则 opsmath.get("curve_locality"))
沿曲线编号相差 k 的两点, 在平面上相距多远?
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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 的每个算子都先校验输入再计算(不让任何东西无声通过):
• **complex 输入一律 ValueError** —— 强制转成 float64 会无声丢掉虚部(numpy 只发一个 ComplexWarning,然后返回一个「看着合理却是错的」实数)。请显式写出 .real/.imag/abs(),或改用支持复数的 complexops。
• **含被掩元素的 masked array 一律 ValueError** —— 拒绝「剥掉掩码直接使用下面原值」的隐式转换。请显式选择填充还是丢弃。
• **所有输入中的 NaN/Inf 一律 ValueError**(明确给出个数后拒绝 —— 它会污染整个结果)。
• 形状严格:不对 1-D 与 2-D 做隐式提升或广播(向量槽位收到矩阵、矩阵槽位收到向量都是 ValueError;请显式 reshape)。
• 尺寸上限:接受矩阵的算子与 stat_histogram 的 bins,超过 mathops.MAX_ELEMENTS(2^26 ≈ 6700 万个元素)即 ValueError。
• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。
• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。
• 算法的正典(作者・年份)与用途见上面的族使用指南。
• poc_theorems_as_pictures — py -3.11 examples/poc_theorems_as_pictures.py
table 作为输入)construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · neighbour_index_gaps · ifs_fractal · ifs_similarity_dimension · space_filling_curve
*Provenance: mathops.py — MATH 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.