construct op• 数据种类:pairs → signal
• 调用: import fullseye as fs; fs.ledger.neighbour_index_gaps(points, k=6)(要直接调用实现,import mathops; mathops.neighbour_index_gaps(points, k=6);从台账取用则 opsmath.get("neighbour_index_gaps"))
最近邻之间在编号上相距多远 —— 把斜列(parastichy)变成数。
> 以下的详细说明为原文 —— 摘要与标题已翻译。
In a phyllotactic pattern the visible spirals (parastichies) are not drawn
by anything; they are an illusion of which florets happen to sit next to each
other. This op replaces the illusion with a count: for every point, take its
*k* nearest neighbours in space and record the difference of their
ordering indices. The histogram of those differences is returned, index
`g holding how many neighbour pairs were g` apart.
★Why this earns its place: with the golden angle the peaks land on
Fibonacci numbers (8, 13, 21, 34, 55 ...), and with any other angle they
do not. That is a statement about the arrangement which can be checked
without looking at the picture — which is the whole point, because the
spirals look convincing at every angle.
Parameters
----------
points : (N, 2) array
Ordered points — the order is the data here, not a convenience.
k : int >= 1
Neighbours per point (6 is the natural choice: a well-packed planar
arrangement is locally hexagonal).
Returns a `signal: counts[g]` = number of neighbour pairs whose index
difference is `g (counts[0]` is always 0 — a point is not its own
neighbour).
Raises `ValueError: not an (N, 2) array; fewer than k + 1` points;
`k` below 1; non-finite coordinates.
Limits: the first points of a spiral sit near the centre where the packing
is degenerate, so the histogram has a low-index tail that carries no
parastichy information. Compare *peaks*, not the raw tail.
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
signal 作为输入)mat_solve · mat_lstsq · stat_describe · stat_histogram · stat_zscore · interp_linear · interp_cubic · interp_scattered
construct)circle_packing_apollonian · ford_circles · phyllotaxis_pattern · ifs_fractal · ifs_similarity_dimension · space_filling_curve · 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.