One interior.
Several ways to transport its light.

Correctness repair · bounded medium shadows

A volume boundary is not a solid fog ball.

The old shadow-connection helper multiplied by exp(−σₜ × distance inside the bounding shape). It never evaluated the actual SDF, noise or reaction-diffusion density. Camera paths did evaluate that density, so naive tracing could show a hollow or patterned shadow while NEE and camera-completed LT/BDPT produced a filled-in silhouette.

Shadow connections now evaluate the same base density patterns, using ratio tracking through the bounded segment. Homogeneous media retain the exact Beer–Lambert shortcut. This applies to area-light and point-light connections; the defect was not a restriction of NEE to one light type.

T = exp(−∫ σₜρ(x) dx),   T̂ = ∏ⱼ [1 − ρ(xⱼ)]

Here the candidate positions form a Poisson process at rate σₜ, and the supported base density is bounded between zero and one. Empty holes contribute a factor of one. A finite number of candidates adds sampling noise, but does not turn the enclosing sphere or box into homogeneous extinction. The implementation does not impose a fixed marching-step count.

This repair covers the base procedural density models. Independently overridden scattering/absorption coefficients from advanced node graphs or decoupled slots still need their own matching extinction/majorant treatment; these are not certified by the base-density tests.

UPBP · inspect light transport

Bounded-medium photon beams, without adding global fog

Enable UPBP → Enable Medium, then Visualization → Record + Show Photon Beams. Changing the visualization requests a fresh light-path cache. The global-fog option is independent: it is not required for recording segments inside a passthrough volume box or a volume sphere behind a dielectric shell.

The old controls coupled segment storage to global fog and did not rebuild when beam visualization was enabled. A collision-only cache could therefore remain empty. Beam recording now explicitly requests light paths even when point merging is off, and the overlay searches beyond the first 500 emitted paths. The displayed beam count refers to stored segments; only a capped subset is drawn on screen.

These are diagnostic beam records. They show the sampled free-flight segments, clipped to medium boundaries, with incoming segment power before the terminal collision’s absorption/scattering weight. They do not introduce a beam-gathering or beam–beam MIS estimator. The implemented medium renderer remains collision VPT and volume-point gathering. A finite area or point emitter must illuminate the volume; the current UPBP light-path builder does not launch photons from an environment-only scene.

Coverage · complementary estimators

Fill missing transport, and show who supplied it

Under Render Settings → Light Strategy, enable Fill missing transport with backup estimator. For light tracing, choose Naive PT (BSDF only) or NEE camera PT. The display can keep original colors, show the backup contribution in red, or isolate the backup. The toggle defaults off so pure estimator limitations remain visible. Pyramid display filters are paused while completion is enabled; the completion views provide the attribution instead.

This is a partition of contributions, not a repair of black pixels. A dark pixel may be physically correct or merely unconverged. Instead, camera paths contribute only when the implemented light-side strategy has no support for that path class. On the supported partition, the native estimator retains sole ownership. If χ identifies the supported subset, the construction is L = ∫χF + ∫(1−χ)F. The two domains do not overlap; no averaging of two full renders is involved.

The red display is a diagnostic decomposition, not physical red illumination. Native contributions keep their color and only the backup is shown as red luminance, so mixed pixels can contain both. Splats, clamping and existing approximate BSDF implementations retain their previous limitations. The partition targets the renderer’s known camera/source support; it is not a proof of completeness for every advanced material, projector, temporal filter or medium configuration.

The theoretical foundation is complementary path sampling and support-aware weighting, as described in PBRT’s bidirectional path tracing chapter. The useful addition here is an explicit coverage control and a visible attribution of the filled transport, rather than a claim to have invented estimator combination.

Estimator identity · deliberate limitations

What is actually rendering this image?

Allow VPT completion fallback, under Light Tracer Parameters, makes the existing fallback explicit. It defaults on to preserve the usable preview. If the active medium cannot be handled by the selected LT/BDPT kernel, the enabled fallback runs camera-side MIS/VPT and labels that fact. Disable it to obtain intentionally black unsupported output. It does not enable an unimplemented heterogeneous BDPT algorithm.

With transport completion off, pure LT discards all camera-side radiance, including volume and environment contributions that could previously leak through while surface-emitter contributions were suppressed. The UI no longer describes pure LT as “Eye: MIS + Light”. The finite-pinhole warning applies only to naive LT.

A true zero-area point light also differs from a small emissive sphere named “Point Emitter”. Naive camera paths cannot randomly hit a mathematical point emitter, but can hit a finite sphere or the ceiling light. A shadow visible in naive mode therefore does not by itself identify which light produced it. Compare one enabled source at a time.

For the camera-connection distinction, see PBRT’s camera importance-sampling interface.

Read the active renderer before interpreting the tiles

VPT fallback means the current medium is outside the compact BDPT kernel’s support. It is not a collection of equivalent BDPT strategies. The strategy pyramid is paused in that state and the full VPT image is shown instead. A noisy or emissive medium can select this route even when the menu still requests BDPT.

For a supported medium, the pyramid groups paths by eye/light vertex counts. Each real volume scattering event adds a vertex; null tracking events are not extra physical scattering vertices. Several strategy images can resemble one another because they estimate the same path-length contribution with different sampling constructions. The Max displayed edges slider limits the visible length range without changing the transport budget or MIS weights.

PM: enable “VPM: cached volume photons” and inspect its cache-status line. The old “No Vol” badge was stale. The current VPM cache requires homogeneous bounded media; it does not render procedural or emissive interiors. Its active status reports actual cached collision photons. Scenes 115 and 116 are controlled examples.

UPBP: CPU execution is only one cost. Each pass traces paths, rebuilds photon neighborhoods and queries them along camera paths. The standalone route no longer builds a duplicate auxiliary map; collision-only mode skips light-map work unless diagnostic light paths are requested. Point reconstruction can still be expensive and noisy, and the CPU heterogeneous density model does not reproduce every GPU volume type. These are distinct from estimator coverage. Beam estimators may reduce variance for selected transport; simply adding beams does not establish correctness or guarantee speed.

Which renderer actually handles media?

These are implementation boundaries, not theoretical restrictions on the algorithms. Merely displaying a volume mesh or beam overlay does not mean that its scattering contributes to radiance.

A matched native experiment

Keep the interior. Change the shell.

The new Volume boundary scene presets contain one neutral scattering sphere, a concentric surface shell, two colored Lambertian area lights and diffuse calibration blocks outside the medium. Each renderer gets the same geometry, source power, camera and exposure. The two shell variants change only the boundary material and its IOR.

The fixtures reset display filters, photon selection and progressive-radius settings. PT, PM and UPBP use a 12-bounce budget; selecting compact BDPT imposes its smaller, shared eight-event maximum. Match that lower cap explicitly when comparing BDPT.

The homogeneous interior has radius 1.38, σ_s = 1.2, σ_a = 0.08 and HG g = 0.35. The smooth shell has radius 1.4. Its small separation from the medium boundary avoids coincident-hit ambiguity. It represents one dielectric interface enclosing a scattering interior; it is not a hollow glass bottle with an additional inner glass–liquid interface.

There is no world fog, environment illumination, hidden point source or volume emission. If the space around the spheres fills with mist, that is an accounting error. The medium remains active after a camera or photon ray refracts through the shell; “currently inside glass” must not suppress a separately declared overlapping volume.

Interactive schematic · unscattered transmission

Refraction changes the path through the same medium.

The rays below obey Snell’s law at the sphere. Their straight interior branch is attenuated by exp(−σ_tℓ); the transmitted dielectric branch also loses Fresnel-reflected energy. The schematic omits those reflected rays and every scattered branch. Their absence here is a drawing choice, not absorption.

σ_t = σ_s + σ_a   ·   T(ℓ) = e^−σ_tℓ

The bright medium disk indicates the scattering domain, not a calculated radiance image. The native presets above perform the actual transport calculation, including the paths omitted by this schematic.

Material model versus transport phenomenon

Is subsurface scattering different from glass with medium inside?

Subsurface scattering is the phenomenon: light enters an object, scatters internally and leaves, often at another position. An explicit dielectric boundary plus a participating interior can model it directly. Glass without internal scattering is a different case: it bends light and may absorb it, but does not generate volume scattering by itself.

The classic Jensen–Marschner–Levoy–Hanrahan model combines a single-scattering term with a dipole diffusion approximation for multiple scattering. Its approximation is a different estimator/model choice, not the definition of SSS.

Three estimators, three useful views of the same integral

Coverage comes before combination

A point emitter behind a specular boundary is a useful warning. Collision VPT with ordinary next-event connections cannot produce the required bent delta-source connection, while emitted photons can refract through the shell and then scatter. Averaging those estimates would halve that missing component. When true point sources and specular geometry coexist, this prototype therefore selects photon gathering for finite-source transport if it is enabled. Collision VPT alone remains incomplete for those paths. This conservative rule is not a replacement for a complete path-space MIS implementation.

UPBP combines complementary sampling constructions

The published Unifying Points, Beams, and Paths method combines volumetric density estimates and path sampling with a common weighting framework. The benefit comes from complementary sampling behavior: one representation can find transport that another estimates with high variance. Our current prototype’s implemented subset is stated separately; a name or a beam visualization is not evidence that the entire published algorithm is present.

Likewise, PP’s photon-point strategy and cached VPM are related density-estimation ideas with different execution contracts. The latter deliberately retains a light-side cache for reuse across camera queries. Sharing an underlying kernel idea does not make their cache lifetime, cost or sampling distribution identical.

Validation record

The scene catalogue regression passes 835,669 geometry, source, medium and paired-mode checks, including all six new fixtures. It checks identical geometry and illumination across estimators, a strictly enclosed homogeneous interior, matching CPU/GPU area-light records and the authored camera settings.

GPU BDPT · homogeneous HG regression

A small analytical scene contains one bounded homogeneous medium with σ_s = 0.35, σ_a = 0.07, g = 0.3 and radius 3, plus diffuse receivers and a finite emitter. The common depth cap is two. Production shaders link on the NVIDIA GPU that previously rejected the combined shader for too many instructions.

These are finite-sample mean-energy checks, not equal-time benchmarks or proofs for every material. Advanced material models, overlapping media and unsupported density fields remain separate validation questions. The new check also exposed and fixed a terminal medium-bounce accounting error in the VPT reference path.

GPU PT · medium inside glass

An axial pure-absorption test uses σ_a = 0.4 through a diameter-two interior. At IOR 1, GPU PT returns 0.451073 against Beer–Lambert’s 0.449329. With a smooth IOR 1.5 shell, it returns 0.415619 against the near-axis Fresnel/transmission reference 0.414235, including repeated internal reflections. The error is under 0.4% in both cases. This checks explicit volume occupancy and attenuation through a dielectric; it does not certify every BDPT refractive density.

UPBP’s audited CPU medium path

The production CPU routines are checked against independent Beer–Lambert and single-scattering references. Here “VPM” means the volume-point component inside UPBP; the main photon-mapper mode has its own cache and validation.

Doubling geometry, halving extinction and scaling point-source intensity by four changes the volume-point result from 0.00484135 to 0.00483382, consistent with the three-dimensional kernel normalization. A multiple-scattering glass test with a finite sphere emitter gives 0.0195114 for VPT and 0.0191523 for volume points at radius 0.16. The finite kernel retains smoothing and boundary bias; its single-scattering estimate is about 3.4% below the independent quadrature at the tested radius.

The single-scattering point maps use four batches of two million photons; the glass test uses four batches of 500,000. A separate point-source → glass → fog regression returns zero for collision VPT, 0.00551507 for point gathering, and exactly the same 0.00551507 with both enabled: the coverage safeguard avoids losing half the energy. These controlled CPU regressions validate the implemented subset. They do not validate beam–beam merging or establish that this prototype reproduces the complete published UPBP algorithm.

Cached PM-mode VPM

An independent homogeneous-slab single-scattering integral predicts total deposited flux 0.0826434; the baked photon map produces 0.0827497 (0.13% difference). A second bake verifies normalization across accumulated batches. Pure absorption leaves no scattering deposits, and unsupported heterogeneous inputs are rejected.

The production GPU gather shader links and renders both shell variants. A 140,000-path bake stores 81,679 scattering deposits with the direction-preserving shell and 146,643 with glass, including repeated interior events. Deposits stay within the declared medium and all inspected pixels are finite. These checks establish a working camera gather through the shell; they are not an equal-time image-quality benchmark against VPT.