geometry op• Data kinds: image2d → table
• Call: import fullseye as fs; fs.ledger.geodesic_heat_grid(mask, source=None, *, spacing=1.0, t: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathgeometry; mathgeometry.geodesic_heat_grid(mask, source=None, *, spacing=1.0, t: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("geodesic_heat_grid"))
Computes obstacle-avoiding geodesic distance on the grid of a 2-D image or 3-D volume by the heat method (grid version of Crane et al. 2013).
mask is a bool array (2-D or 3-D) where passable pixels/voxels are True; source is the index of the start point (1 point (i, j[, k]) or a list of points; if omitted, the first passable pixel). spacing is the pixel size per axis (scalar or per axis).
1) (I − tΔ) u = δ (spreading heat; Δ is the 2d+1-point Laplacian linking only passable pixels = obstacles are insulating)
2) X = −∇u / |∇u| (with differences across faces) 3) Solve Δφ = ∇·X and shift to 0 at the start point.
Returns {"distance", "t"} (impassable pixels, and pixels not connected to the start point, are inf).
Gate: in obstacle-free space it converges to the Euclidean distance. Pixel Dijkstra (4/8-neighbourhood) has a grid-orientation error (up to 41% with 4-neighbourhood, up to 8% with 8-neighbourhood) that does not vanish with refinement, whereas the heat method's does.
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.
• geometry_tour — py -3.11 examples/geometry_tour.py
table as input)dynsys_poincare_section · dwt_inverse · chebyshev_eval_nd
geometry)mesh_euler_characteristic · angle_defect · delaunay_triangulate · geodesic_heat · mesh_torus · nurbs_curve · nurbs_circle · nurbs_surface
*Provenance: mathgeometry.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.