construct op• 数据种类:无 → pairs(仅由参数决定的算子 —— 不接受图像或数据输入)
• 调用: import fullseye as fs; fs.ledger.space_filling_curve(kind='hilbert', order=4)(要直接调用实现,import mathops; mathops.space_filling_curve(kind='hilbert', order=4);从台账取用则 opsmath.get("space_filling_curve"))
`2**order` 方格上的希尔伯特/摩尔/扫描顺序 —— 并验证它确实是一个置换。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
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
pairs 作为输入)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 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.