transform op• Data kinds: image2d → voxel
• Call: import fullseye as fs; fs.ledger.abel_revolve(slice_rows, dr: 'float' = 1.0) -> 'np.ndarray' (to call the implementation directly, import mathtransforms; mathtransforms.abel_revolve(slice_rows, dr: 'float' = 1.0) -> 'np.ndarray'; from the registry, opsmath.get("abel_revolve"))
Revolves a cross-section f(z, r) ((H, R), r = 0, dr, …) around the symmetry axis into a 3-D volume (H, 2R−1, 2R−1).
Combined with abel_inverse_image, the 3-D distribution of an axisymmetric object is recovered from 1 photo.
Gate: summing the resulting volume sideways (projecting it) gives back the original projection image (round trip).
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.
• transforms_tour — py -3.11 examples/transforms_tour.py
voxel as input)—
transform)abel_transform · abel_inverse · abel_inverse_image · hankel_transform · tf_poles_zeros · tf_freq_response · tf_impulse_response · tf_step_response
*Provenance: mathtransforms.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.