complex opなし → cpoints(引数だけで決まる op —— 画像やデータの入力を取らない)import fullseye as fs; fs.ledger.cplx_contour_circle(center=0.0, radius=1.0, n=256, orientation='ccw') (実装を直接呼ぶなら import mathops; mathops.cplx_contour_circle(center=0.0, radius=1.0, n=256, orientation='ccw')、台帳から引くなら opsmath.get("cplx_contour_circle"))Sample a circle as a closed contour — the standard integration path.
Returns n complex points center + radius * exp(±i * 2*pi*k/n),
k = 0..n-1. The closing segment z[-1] -> z[0] is implicit: the
first point is not repeated (every contour op in this family closes the
polygon itself; repeating it would only add a zero-length segment).
orientation is explicit because in complex analysis the sign of every
result depends on it: 'ccw' (default) is the positive/mathematical
direction — the one for which the residue theorem, the Cauchy formula and
the argument principle carry a + sign — and 'cw' negates all three.
Honest limitation: this is a polygon through samples of the circle, not
the circle. Its enclosed area is short by a factor sinc-like in
2*pi/n, and every quadrature on it converges as O(n^-2)
(:func:cplx_contour_integral documents the measured rate).
Raises ValueError: non-finite center/radius, radius <= 0,
n not an integer in [3, MAX_CONTOUR_POINTS] (a fail-closed size cap
— n=10**9 would allocate 16 GB), unknown orientation.
HALCON: no complex-plane operator (gen_circle_contour_xld draws the
same geometry as an XLD contour for image space).
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.pycpoints を入力に取れる)cplx_poly_eval · cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski · cplx_mobius
complex)cplx_poly_eval · cplx_contour_integral · cplx_winding_number · 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.