wave_nodal_lines — MATH wave op

• Data kinds: matrix → mask

• Call: import fullseye as fs; fs.ledger.wave_nodal_lines(field, tol=0.0) (to call the implementation directly, import mathops; mathops.wave_nodal_lines(field, tol=0.0); from the registry, opsmath.get("wave_nodal_lines"))

Usage

Where a signed field changes sign — the nodal set, as a mask.

A pixel is marked when it differs in sign from its right or lower neighbour

(or is within *tol* of zero). That is the discrete version of "the sand

collects where the plate does not move".

★Why this earns its place: the count is predictable. A plain `(m, n)`

rectangular mode has `m-1 interior nodal lines in one direction and n-1`

in the other, so the mask can be graded against integers rather than by eye.

Returns a `mask`.

Raises `ValueError`: not a 2-D array; non-finite values; negative *tol*.

Family-wide input contract (fail-closed)

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).

Detailed usage guide

• math_metrology family guide

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)

• poc_beats_fringes_and_screens — py -3.11 examples/poc_beats_fringes_and_screens.py

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

—

Same category (wave)

wave_membrane_mode · wave_mode_frequencies · wave_two_slit · wave_fringe_period · wave_grating_orders


*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.