fresnel_integrals — DRIVE lateral op

• Data kinds: any → any

• Call: import fullseye as fs; fs.ledger.fresnel_integrals(x) (to call the implementation directly, import drivelateral; drivelateral.fresnel_integrals(x); from the registry, opsdrive.get("fresnel_integrals"))

Usage

Fresnel integrals C(x) = ∫₀ˣ cos(π t²/2) dt, S(x) = ∫₀ˣ sin(π t²/2) dt (odd functions).

For |x| ≤ 3.5 a power series, above that an asymptotic expansion (auxiliary functions f, g). Error is 1e-8 or less (gate: numerical integration).

Returns: (C, S) (same shape as x).

Raises ValueError: non-finite.

Empty input (x with 0 elements) raises ValueError.

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• gallery_drive_lateral_env — py -3.11 examples/gallery_drive_lateral_env.py

Ops the type connects to (they accept any as input)

course_crank · course_s_curve · course_turnaround · course_slope · course_intersection · course_parallel_parking · course_crossing · course_road

Same category (lateral)

friction_circle_usage · curve_speed_limit · design_min_radius · understeer_gradient · steady_cornering · bicycle_model_step · ackermann_steer_angles · offtracking_circle

*Provenance: drivelateral.py — DRIVE 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.