RFC: Hybrid geometric acoustics (IS+UTD early, MC middle, diffusion late)

[rdmiller]

RFC: a hybrid geometric-acoustics solver (kind: "hybrid-ga"). Not a fifth tracer.

CRAM already has image source, Monte Carlo rays, beam trace (+ UTD), and ART. The missing product is what ODEON/CATT ship: deterministic early + stochastic middle + diffuse late, with one energy unit and a defined crossover. Today that is a splice inside the raytracer (#129) plus three other solvers the user must run by hand.

3D FDTD (#147) covers low-frequency wave physics. This solver covers high-frequency geometric physics. They share Surface / Source / Receiver; they do not share a grid.

Decision: orchestrate, don’t clone

Option	Verdict
Cone / frustum / pyramid tracing	No. Beam trace already does volumetric specular.
Phonon / sound-particle	No. That’s the raytracer with a different name.
Deterministic radiosity matrix	Later. ART is the MC version; a form-factor matrix is an ART upgrade, not a new solver.
Fix raytracer hybrid in place	Necessary (#129) but not a product. The flag still lives inside one MC solver, still first-receiver-only (#131), still peak-normalizes (#133).
Hybrid-GA: IS (+ UTD) early, MC rays optional middle, diffusion-equation late	v1. One tab, one IR, one LTP.

New tree src/compute/hybrid-ga/. It calls image-source / shared diffraction / ray energy histogram / a new ADE module. It does not copy arrivalPressure.

Three regimes

t = 0 ──────── t_early ──────── t_mix ──────── t_end
   [ IS + UTD ]    [ optional MC ]    [ ADE tail ]
         deterministic     stochastic      diffuse field

Early (order ≤ N, default N = 2). Image-source paths, 1/r² spreading (#122 / #99), energy R² from reflectionFunction, air on energy (10^(−α r / 10)), no Math.random sign (#124). Direct sound once. UTD from shared/diffraction with inbound arrivalDirection (#134). Skip IS across the same face twice; isInFrontOf must actually run (#127).

Middle (optional). Existing raytracer, but:

• Drop paths with chainLength−1 ≤ N (filter, do not splice this.paths).
• Each ray carries 1/N_rays of source energy (Raytracer IR: no 1/N, peak-normalize, 10 cm mesh detector — N-dependent shape #133).
• Detection along the segment vs a sphere about the receiver center, t = dist_center / c. Receiver mesh out of the BVH.
• Same initialSPL / spreading convention as IS so a first-order IS arrival and a lucky first-order ray would match — they must not both be deposited.

Late. Acoustic diffusion equation (Picaut / Valeau / Billon), not peak-normalized noise and not W-only HOA (#106 / #132).

∂w/∂t = D ∇²w − σ c w
D = λ c / 3,   λ = 4V / S,   σ = −ln(1 − ᾱ) / λ   (or ᾱ / λ)

w is energy density (J/m³) per octave band. Voxelize the room coarse (cell ~ 0.5–1 m, not FDTD Δx). Neumann at walls with loss σ; coupling through apertures = shared faces. CPU is enough (10³–10⁴ cells). Source for ADE is the residual energy at t_mix from the histogram, not a new 500-unit blast (ART #116).

Crossfade: energy envelopes, 20–50 ms. Pressure IR for the tail = band-filtered noise × √(w(t) at receiver cell), independent per HOA channel if ambisonic.

Energy units (non-negotiable)

One convention for the whole solver:

• Source: Lp @ 1 m → intensity I(1 m), then geometric spreading 1/r² on deterministic paths; MC uses hit rate × 1/N.
• Reflection: reflectionFunction is already energy R². Multiply intensity by it. Do not abs for the energy path; IR pressure uses sign(R_pressure)·√energy or keep random sign only in the ADE tail.
• Air: ISO 9613-1 dB/m → intensity m = α_dB · ln(10)/10 (RT60 Sabine/Eyring convert air dB/m with 20 log — 4mV is 2× too small #141 / ART applies pressure air absorption (20 log) to energy radiosity #118). Never 20 on energy.
• Export WAV unnormalized. Display copy may peak-normalize. Two receivers comparable in SPL.

If IS, rays, and ADE disagree on a 10 m cube, α = 0.2, the solver is wrong — don’t ship the tab.

Module layout

src/compute/hybrid-ga/
  index.ts                 # HybridGASolver extends Solver
  early.ts                 # wrap ImageSourceSolver + UTD, apply spreading
  middle.ts                # run/read RayTracer paths with order filter + 1/N
  diffusion/
    ade.ts                 # CPU ADE, per-band w[cell]
    voxelize-coarse.ts     # occupancy at ~1 m (can share ideas with #147, not the grid)
  assemble.ts              # IR / LTP / optional FOA
  __tests__/
    spreading.spec.ts      # 1 m vs 2 m vs 4 m direct
    crossover.spec.ts      # no double-count order ≤ N
    ade-decay.spec.ts      # cube T ≈ Eyring

Registry: registerSolverFactory("hybrid-ga", ...). Tab: N, t_mix (auto = mean free time 4V/(S c) or manual), enable MC middle, enable ADE, bands, assigned S/R/one room.

save() persists those IDs. No rooms[0], no findIDs() of the whole project (#123 / #135 / #143).

UI / results

One LTP chart with series: IS, UTD, MC (if on), ADE (if on), total. One IR play/download. Ambisonic: encode IS/UTD/MC by arrival direction; ADE tail all HOA channels, equal power, uncorrelated (#132).

Energy Decay (#139) should be able to take this IR from the store.

Validation

1. Free-field / empty-ish: direct SPL −6 dB per doubling of distance (air off).
2. Hard shoebox, N=1, MC off, ADE off: arrivals match analytic image sources in time and in 6 dB law; count = 1 + 6 first-order.
3. No double count: N=2, MC on → no stochastic path with order ≤ 2 in the IR; this.paths of the inner raytracer unchanged.
4. ADE cube: uniform α, T60 from w(t) at center within ~15 % of Eyring (air off).
5. Crossover energy: ∫ E_early + E_middle + E_late ≈ source energy × (1 − absorbed), order of magnitude, not 7× (ART direct sound is added to every octave band, then summed — 7× too loud #116).

Physics tests, not greps.

Phases

Phase	Ship
0	IS-only early with spreading + air-energy + one receiver IR/LTP. No MC, no ADE. Proves units. Unblocks #122.
1	UTD inject, inbound direction, LTP series.
2	MC middle, order filter without mutate, 1/N, sphere-along-segment. Inner raytracer can stay; this solver owns assembly.
3	ADE late, coarse voxels, Eyring test, energy crossfade.
4	FOA/HOA with diffuse tail on all channels; multi-receiver without mixing (#103).

Phase 0 is already more correct than today’s image-source tab. Phase 3 is the product.

Explicit non-goals (v1)

• New beam / cone / phonon tracer
• Touching 2D/3D FDTD grids
• Frequency-dependent ADE diffusion constant (use per-band ᾱ, constant D)
• Replacing ART (keep it; hybrid-GA does not shoot surface-to-surface form factors)
• Random polarity on specular paths

Relationship to open bugs

Hybrid-GA consumes fixes, it does not wait for every geometric issue to close. Phase 0 should implement spreading in a shared arrivalIntensity(path, r) used by IS and beam-trace (#99 / #122). Phase 2 must not copy raytracer splice. ADE is new code.

Acceptance (phase 3)

• kind: "hybrid-ga" in the registry
• Direct 1 m / 2 m / 4 m: −6 dB / −12 dB
• Hard box N=1: 7 arrivals, no extras, no missing
• MC on: stored ray paths unmodified; IR has each early path once
• ADE T60 on a uniform cube ≈ Eyring
• Exported WAV is not peak-normalized; two receivers differ