geometry op• Data kinds: mesh → table
• Call: import fullseye as fs; fs.ledger.geodesic_heat(vertices, faces=None, source=0, *, t: 'float | None' = None) -> 'dict' (to call the implementation directly, import mathgeometry; mathgeometry.geodesic_heat(vertices, faces=None, source=0, *, t: 'float | None' = None) -> 'dict'; from the registry, opsmath.get("geodesic_heat"))
> This operator's description has not been translated yet. The original text follows as it is.
熱法による曲面上の測地距離(Crane et al. 2013)。`source` は頂点番号(または番号の列、既定は頂点 0)。
メッシュは `(vertices, faces)` でも mesh の組 1 つでもよい。
1) (M − tL) u = δ を 1 ステップ解く(熱を時間 t だけ広げる、t の既定 = 平均辺長²)
2) 各三角形で X = −∇u / |∇u|(熱が来た向きと逆 = 距離が増える向き)
3) L φ = ∇·X を解き、source で 0 になるようずらす
門: 平面メッシュでユークリッド距離、球面で大円距離 Rθ に、細かくするほど近づく。
返り値 `{"distance", "t"}`。
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_grid · 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.