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"))
> This operator's description has not been translated yet. The original text follows as it is.
2-D 画像・3-D ボリュームの格子の上で、障害物を避けた測地距離を熱法で求める(Crane et al. 2013 の格子版)。
`mask は通れる画素/ボクセルが True の bool 配列(2-D か 3-D)、source は始点の添字(1 点 (i, j[, k])`
か点の列。省略すると最初の通れる画素)。`spacing` は軸ごとの画素の大きさ(スカラーか軸ごと)。
1) (I − tΔ) u = δ(熱を広げる、Δ は通れる画素の間だけを結ぶ 2d+1 点の Laplacian = 障害物は断熱)
2) X = −∇u / |∇u|(面の間の差分で) 3) Δφ = ∇·X を解いて始点で 0 にずらす。
返り値 `{"distance", "t"}`(通れない画素と、始点と繋がらない画素は inf)。
門: 障害物の無い空間ではユークリッド距離へ収束する。画素の Dijkstra(4/8 近傍)は格子の向きの誤差
(4 近傍で最大 41%、8 近傍で最大 8%)が細かくしても消えないが、熱法は消えていく。
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.