complex opcpoints → measurementimport fullseye as fs; fs.ledger.cplx_winding_number(z, w=0.0) (実装を直接呼ぶなら import mathops; mathops.cplx_winding_number(z, w=0.0)、台帳から引くなら opsmath.get("cplx_winding_number"))Winding number of a closed contour around a point (turning number).
How many times the polygon z (closing segment implicit) travels
counter-clockwise around w: +1 for a simple positively-oriented loop
containing it, -1 clockwise, 0 outside, ±k for a k-fold
loop. Computed as the sum of the principal-value argument increments of
z_k - w divided by 2*pi and rounded — for a polygon that sum is an
exact multiple of 2*pi, so the result is an exact integer, not an
estimate (the rounding merely removes ~1e-14 of accumulated float error).
Honest limitation — the count can alias low, and no local check can stop
it: this is the winding number of the polygon through the samples,
which equals that of the underlying curve only if the sampling resolves it.
A segment that turns the ray to w by >= pi is ambiguous (which side
did it pass?) and raises. Below that there is no contradiction to detect:
z**5 sampled on a 4-point circle turns exactly pi/2 per step and
counts 1 instead of 5 (measured). From pi/2 up, a
RuntimeWarning says so (WIND_ALIAS_WARN); the only real remedy is
the classical one — refine until the count stops changing.
Raises ValueError: w coincides with a vertex or lies on a segment
(the winding number is undefined on the contour), a segment subtends
>= pi as seen from w (undersampled — refine the contour), fewer than
3 points, degenerate contour, non-finite/masked input.
HALCON: no operator (test_region_point answers the related but weaker
inside/outside question for regions).
mathops の全 op は入力を検証してから計算する(黙って通さない):
ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。ValueError(件数を明示して拒否 — 結果全体に伝播するため)。ValueError。reshape を明示する)。stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。py -3.11 examples/math_complex.pymeasurement を入力に取れる)—
complex)cplx_contour_circle · cplx_poly_eval · cplx_contour_integral · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski · cplx_mobius
Provenance: mathops.py — MATH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.