complex op• Data kinds: none → cpoints (an op determined by its arguments alone — it takes no image or data input)
• Call: import fullseye as fs; fs.ledger.cplx_contour_circle(center=0.0, radius=1.0, n=256, orientation='ccw') (to call the implementation directly, import mathops; mathops.cplx_contour_circle(center=0.0, radius=1.0, n=256, orientation='ccw'); from the registry, 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) (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).
Every mathops op validates its input before computing (nothing slips through silently):
• complex input raises ValueError — coercing to float64 silently discards the imaginary part (numpy only emits a ComplexWarning and returns a plausible-looking wrong real number). State .real/.imag/abs() explicitly, or use complexops, which handles complex data.
• masked arrays with masked elements raise ValueError — the implicit conversion that peels off the mask and uses the raw values underneath is refused. Say explicitly whether to fill or to drop.
• NaN/Inf raises ValueError on every input (refused with the count stated — it propagates through the whole result).
• Shapes are strict: 1-D and 2-D are never implicitly promoted or broadcast (a matrix in a vector slot, or a vector in a matrix slot, raises ValueError; reshape explicitly).
• Size cap: ops that take a matrix, and the stat_histogram bins, raise ValueError beyond mathops.MAX_ELEMENTS (2^26 ≈ 67 million elements).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• math_complex — py -3.11 examples/math_complex.py
cpoints as input)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. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.