RadianceLab

The breadth pays off in the connections between capabilities: a difficult caustic can be composed visually, investigated through several sample constructions, and rendered with the same scene and camera context.

Ten is the number of top-level selectable modes, not ten independent, complete reproductions of established papers. MLT and PSSMLT currently both use primary-space mutation; UPBP (Unifying Points, Beams, and Paths) and manifold exploration have narrower implementations, described in their chapters. The source therefore supports a broad academic-methods laboratory with explicit experimental branches.

Real-time describes the intended interaction loop. The GPU material preview, a progressive CPU estimator and a converged high-resolution photograph have different costs. Work and resolution controls let those routes remain usable; no universal frame-rate or instantaneous-convergence claim is implied.

Photon primitives are listed as part of the transport dimension but get their own row, because they are a large system in themselves. The photon-primitive chapter (Mode 10) explains how a hand-picked set of swept dimensions becomes a technique, how techniques combine under MIS, and how stacked techniques cover every transport exactly once.

The difficult integration problem is not placing ten names in a selector. Each backend must agree with the application about scene edits, camera state, film ownership and when accumulated samples become invalid. A camera move must not blend old and new viewpoints. A material change must reach the actual transport implementation, rather than changing only the raster preview. A switch from GPU compute to a progressive CPU film also changes the producer of the displayed image.

RadianceLab makes these producers explicit. The GPU tracer contains the path tracer, light tracer and bidirectional path tracer in one compute shader. Conventional photon mapping builds photon data on the CPU and gathers it on the GPU. The other progressive modes maintain their own CPU films and diagnostic state. Consequently, equal pass counts do not establish equal work: a pass may launch camera paths, build a photon population, run a mutation batch or evaluate many swept primitives.

This separation is useful experimentally. A comparison can first match a supported diffuse or homogeneous-medium scene, then vary the estimator. More elaborate GPU materials and heterogeneous media remain valuable demonstrations, but they cannot serve as a reference for a CPU lane that does not implement the same model. The correct comparison is between matching image-formation contracts, not merely matching scene-file names.

The GPU tracer specializes around transport features such as bidirectionality, spectral behavior, participating media and explicit path-density MIS. A single maximal shader is not automatically the best implementation: its instruction footprint can exceed the practical limits of the target OpenGL driver. The application therefore starts with a smaller configuration and selects specialized variants as features change.

One consequential boundary is instruction size. If a requested feature mask exceeds the driver budget, the explicit BDPT MIS variant is dropped and the failure is logged, rather than silently rendering a different estimator. Since the BDPT audit, a compact BDPT kernel keeps explicit MIS with one homogeneous medium; other media use a labeled volumetric path-tracing fallback, and finite-aperture camera BDPT still uses flat weights. These are visible feature boundaries, not evidence that surface MIS and medium transport separately fail.

The studio’s system contribution is the inspectable path from control to implementation: which backend runs, which variant was compiled, which film is accumulating, and which diagnostic buffers belong to it. Keeping those distinctions explicit prevents a visually plausible image from silently becoming evidence for a feature that was never enabled.

A photon beam contributes only to camera rays that pass within its kernel radius, and a photon point only to rays that pass near the point. A refracted sheet is a surface in the fog, so a camera ray collects a contribution wherever it crosses it. In the numerical variance study, 74% of hourglass samples contribute to a fixed camera ray at the waist, against 11% for a beam of radius 0.01. At the waist that thin beam is as good per sample (relative variance 9.3 against 11.3), but below the waist, where the light bundle is wide, its relative variance grows to 92 against 14.5 for the hourglass. Fog density does not change those hit rates.

The equal-time figures come from the linear film, not the displayed image. On the collinear two-ball chain (preset 68), relative variance per pass times milliseconds per pass is 6.8 for the hourglass chain against 241 and 329 for beams of radius 0.12 and 0.06, and the total energy on the caustic agrees with the beam within about 0.6%. On the unfolded mirror leg (preset 71) the equal-time gain is 17.4 and 20.6 times.

Speed has a limit. Two four-ball chains under two lights (preset 77) carry a relative variance of 34 per pass on the caustic: 29% relative error at 400 passes, 15% at 1,600 and 7% at 6,400, which at 50 passes a second is about half a minute and two minutes of holding still. The recording of that scene, in the chains chapter, is still grainy after a few hundred passes, as measured.

A collinear sequence of rotationally symmetric interfaces can preserve the original azimuth sweep: rotate the seed and the complete chain rotates with it. This permits a relatively compact continuation of the hourglass construction. The challenge is then to carry the correct branch, transmission and domain restrictions through every interface.

An off-axis follower sphere breaks that invariance. A rotated ray does not encounter an equivalent cross-section of the next object. The later T3 route therefore traces a numerically varying family and searches ruled-strip crossings under explicit restrictions. Its evaluation cost and failure cases differ from the analytic quadratic. Calling both examples “two spheres” would conceal the key algorithmic distinction.

The chain study consequently records both successful configurations and refusal conditions. Those restrictions are useful information: they identify which transformations preserve a solvable geometric family, which require numerical continuation, and which are outside the current implementation. They also provide concrete future work—broader chain support requires a new parameterization and corresponding density evaluation, not only a more elaborate scene.

Reflection-cone, exit-cone and glossy studies also vary the seed and path class. A glossy vertex adds real directional freedom, so treating it as an ideal mirror changes the problem. Camera-side reflection or refraction introduces additional viewing legs that current chain and correlated configurations do not all support.

On a common point-source axis, tracing one meridian gives the complete azimuth family by rigid rotation. Additional collinear spheres change the seed path and transmission product, while the final outgoing line still sweeps the same quadric class. A source displaced relative to one sphere alone does not destroy this symmetry: its source-to-center line simply becomes the axis.

A follower away from that axis is different. Its entry point, chord, exit point and outgoing direction vary nontrivially with azimuth; some azimuths miss it. The native off-axis solver samples rulings, brackets sign changes of the camera-crossing residual, refines on the true Snell chain, and evaluates a changing Jacobian with finite differences. Grazing root pairs can need an adaptive rescan. Repeated chain evaluation per queried camera ray accounts for much of the extra work.

The native off-axis implementation currently supports one displaced follower, with an uncorrelated query path; it does not have the same reusable correlated/raster bound as the axial chain. The schematic permits a third sphere to make the geometric consequences visible, but does not claim the renderer supports that extra general-chain case. More interfaces in the picture are specular transmissions before a volume query, not a demonstration of arbitrary multiple volume scattering.

Paths sampled from the light and from the camera have to meet, and a single meeting point has zero measure. Connecting the two endpoints fails at specular vertices; blurring them together adds bias. Photon primitives take a third route: sweep, that is integrate analytically, some of the random choices made while building a path. The endpoint then becomes a curve, sheet or volume that the other subpath crosses with nonzero probability. Any choice made during path construction can be swept: the direction angles θ and φ and the flight distance t at any vertex, the emitter’s surface coordinates, or the aperture sample on the camera side.

Once the swept dimensions are picked, the framework builds the technique. A primitive is a list of swept terms, each naming a dimension, the vertex it belongs to and whether it is integrated analytically or sampled. A classifier names the shape: θ and φ at one vertex give a sphere, φ and t a cone, θ and t a disk, all three a ball, two distances a plane, φ at one vertex with t at the next a cylinder, and three distances a parallelepiped. The matching intersector and Jacobian then evaluate it, always through one template: swept dimensions, manifold, crossing roots, Jacobian, contribution. Three free coordinates in total, split between the two subpaths in any way, give an unbiased connection; with fewer, a blur kernel is needed, which is where photon points and beams sit.

Established techniques belong to the same family. The UI names each technique by what it sweeps: L[θφT]=C, with all three coordinates swept on the light side, is NEE (equivalent to the photon ball), and naive path tracing sweeps the light’s own surface and meets the camera ray there. The Photon Primitive Editor draws the idea: toggle θ, φ and distance at any vertex of a camera or light subpath, and it names the shape, shades its Jacobian-weighted density and shows two chosen sweeps combined with the balance heuristic.

Every primitive is a sampling strategy, and techniques combine under MIS by re-evaluation: a primitive pretends to be another one, asks how that technique would have generated the same contributing path, and the balance heuristic weights the densities on a shared measure. Primitives of the same type combine too, such as three planes that sweep different pairs of distances, and so does a continuum of them: arbitrarily oriented planes are MIS-weighted analytically. The best partners behave most differently as the view changes; a photon sphere always has a bright rim, while a plane’s brightness depends on how it faces the camera ray. In the renderer the shared measures group emitter planes on the light-area measure; sphere, disk and cone conditional on the light point; beam, point and hourglass along the camera ray; and beam, ring and arc at one shared radius. Strategy 31 lets you pick your own pair or trio from ten members.

Every non-temporal dimension is supported. Time is the one dimension left out, because a temporal dimension makes the primitive too hard for the algorithm to reason about and adds much more complexity. A time gate removes one more support dimension, so isolated crossings would need three swept coordinates instead of two, and once the camera leg counts, the level set changes from a sphere around the light to an ellipsoid, with an extra coarea factor, degenerate gradients and several branches.

Earlier photon-primitive implementations, including ours from the photon-primitive research project, supported only a handful of these strategies; stock Tungsten, for one, implements photon points, beams and two plane variants.

A technique created this way rarely covers a whole scene on its own, so the next layer stacks techniques into complete transport.

The rule is about radiance contributions, not the number of sampling strategies. Several strategies may estimate the same path class if MIS combines them with the appropriate weights. What must be avoided is adding two independent, fully weighted estimates of the same transport—for example, a photon beam and a photon plane both counting double scattering. RadianceLab’s Comp mode uses a hard partition between its primary estimator and backup camera walk; the primary may itself contain MIS strategies.

Comp mode renders each pixel with two estimators in the same sample: a primary photon-primitive strategy and a backup camera walk, summed into one radiance, one film and one tone map. Each strategy declares the path classes it owns as a box of counts: non-medium vertices before the first fog scatter (q), fog scatters (nV) and specular vertices between the first scatter and the light (k). The backup multiplies every deposit inside the primary’s box by 0 and every other deposit by 1. Primary and backup estimate disjoint sets of paths, so they add without double counting whatever their correlation, and the declared supported classes have one combined owner. Correct ownership declarations and coverage by the backup remain requirements; the partition alone does not prove complete scene coverage. The hourglass MIS primary (21) weights its beam and point kernel members against the hourglass sheet, so it is consistent rather than unbiased, and the stack keeps its finite-radius bias.

Class counters check the declaration. They print an alarm for any class that receives energy from both layers, the one test that catches a declaration that is too narrow, because a mean image averages that error away. Two more layers follow the same rule: a surface caustic photon map deposits only photons that have passed at least one specular vertex, so surface NEE keeps the direct case, and specular NEE through planar mirrors takes one class over from the walk as a hard hand-over.

Measured with the hourglass MIS strategy (21) as primary and the MIS walk (2) as backup, no class was non-zero on both layers on the test presets, and the primary occupied exactly its declared classes. Seam 0 and seam 1 are two complete partitions and must agree; their ratio was 1.0028 and 1.0060 on presets 48 and 47, against 1.329 and 1.105 with the ownership predicate removed, and 0.9995 on the full hero frame with the specular continuation on. The surface caustic map raised a floor disc’s mean from 0.175 to 21.94 and agreed with an independent first-principles trace to within 2.1%, depending on kernel radius.

The comparison is about bringing point, beam, surface and volume constructions, their compatible MIS combinations, and the additional refracted and reflected families into one working environment. It does not imply that every proposed variant is equally robust, or that all scene configurations are supported.

The 2022 reference implementation demonstrates several temporally sliced primitives. DARTS is a later extension of that code for time-of-flight sampling and camera-warped measurements; its supplement explicitly leaves photon balls, volumes and hyper-volumes outside that adaptation. It is a real follow-up, but not evidence of a broader implementation of the whole primitive family.

I have not found a published implementation covering a broader set of this framework. “The most complete implementation I am aware of” preserves that distinction: it is a literature-informed assessment, not a proof that no other implementation exists.

The ring and arc share a stationary-distance solver. Its squared equation is quartic; the real roots of the cubic derivative split a guaranteed bracket into monotone intervals. Each sign change is refined with 50 bisections, followed by restoration of the sign condition lost during squaring. More than one admissible stationary point can contribute. The beam’s small linear solve and the directional trio’s quadratic/planar queries do much less work per candidate.

On the recorded unobstructed single-scatter rig at radius 0.15, the ring/arc/beam mixture reduced median relative variance per pass from the beam’s 108.0 to 39.0. Its mean pass cost was 7.447 ± 0.357 ms versus 1.073 ± 0.062 ms for the beam. Multiplying variance by pass cost gives 290 ± 14 versus 116 ± 7: a smoother pass still lost on equal time. The quoted timing uncertainty is the recorded run-to-run spread; the combined uncertainty does not include an error bar on median variance. These are historical measurements of one native rig, not browser benchmarks.

The constant-power light-size series used a 217 × 140 film and emitter edge lengths from 0.2 to 8.0. Median relative variance per pass for three-plane MIS fell from 135.67 to 3.22. The directional trio rose only from 1.10 to 1.49. Expanding the light helped the planes strongly, but the directional mixture’s complementary densities suppressed the moving singularities better than the initial prediction expected.

At the largest light the reported equal-time products were 4.7 ± 1.4 for planes and 3.6 ± 0.35 for the directional trio. That separation is too small relative to timing uncertainty to claim a decisive speed advantage. The six-member cross-family mixture had the lowest measured per-pass variance, 0.92, but also paid for more queries. In this easy directly connectable single-scatter setup, conventional NEE was a stronger baseline than either family. Visibility, phase anisotropy, kernel width, source size and the chosen error statistic can all change the ordering.

The older footprint laboratory deliberately smoothed emitter edges; its “thin sheet” retained a finite band. A central difference also produces a finite displacement band even when the source is sharp. PP33’s optional screen Gaussian is a third, separate choice. None of those is required by the mathematical sharp boundary.

The new derivative integrates the sharp boundary through a pixel footprint. Translation along one edge direction activates two opposite quad edges; a general in-plane vector can activate all four. Their extruded planes meet the receiver in curves. A finite pixel receives a finite contribution even though the geometric curve has no width.

The source remains collimated, with fixed receiver response and transport. Curved surfaces use a local affine pixel model. The comparison to displaced images tests the derivative of that declared model; moving occluders, attenuation, refraction and indirect transport still need additional terms.

Select PP33 → Sheet family → Cone + plane: balance MIS, or launch Surface-Curve-MIS.bat for the paired caustic scene. The AIO launcher selects the updated build. An older already-running executable can still have only the earlier two choices.

The existing 54-render comparison found no efficiency win in its fixtures. Both charts have the same marginal emitted-path PDF; the difference is within-sheet correlation and orientation. Balance weights are allocation fractions here. A line and a ring looking different does not by itself mean their common-measure densities complement each other.

A strategy can only return energy for paths it generates with non-zero probability; everything else stays absent however long it runs, and each case below fails exactly as that predicts.

Light tracer with camera connections. The last light vertex is joined to the camera by a shadow ray. At an ideal mirror or glass vertex the outgoing direction is fixed by the surface, so a connection toward an arbitrary camera point has zero BSDF value. Directly visible glass and mirror spheres therefore render black, while a glossy sphere stays with the light tracer and is only noisy.

Naive light tracer. Without a connection, a light path contributes only when it physically passes through the lens. For a perfect pinhole that probability is zero and the image stays black. With a 500 mm aperture the room fills in slowly and heavily defocused; a larger splat radius or more paths per pixel smooths the image by blurring it. A normalization fix for this finite-aperture case has been applied.

Naive path tracer and a point light. A BSDF-sampled ray cannot hit a zero-area source. NEE samples the point light directly, as does BDPT’s NEE branch; the light tracer does not currently emit from true point lights. A small emissive sphere is a different source and remains reachable by chance.

Light Sample Only, the pure NEE. Only shadow-ray connections from scattering vertices are kept, so emitters reached directly or after specular bounces (LE, LS+E and the caustic class LS+DE) are lost: visible lights render black, and in the spectral recording the caustic under a glass sphere disappears. The option labelled NEE is NEE plus naive emitter hits, so a path that reaches the light through the glass still counts and the caustic stays; MIS of naive sampling and NEE keeps it too.

The MIS menu offers legacy flat 1/N weights, the balance heuristic and the power heuristic, and a status line confirms which is active. The audit found that balance and power had been returning flat 1/N weights, and fixed that together with related faults: light-tracer splats raced between threads and now accumulate into a frame-local atomic sum; the camera density used one pixel’s footprint instead of the whole film; the weights assumed that NEE and emitted light paths sample lights the same way, which they do not; density ratios overflowed and are now computed as log-space products; the GGX density did not account for both preimages; and depth budgets differed between strategies, so explicit BDPT now stops at eight surface scatters without unmodeled Russian roulette. A follow-up gave NEE contributions from a true point light weight one after a brightness deficit was found.

Regression renders at 96 × 64 with 256 eye samples and one light path per pixel show the effect. On the diffuse scene, ordinary path tracing with MIS was cheaper and slightly more accurate than BDPT: RMSE 0.00539, against 0.00554 for power, 0.00586 for balance and 0.00998 for the old flat weights. On a mirror scene with a small light, flat weights gave 0.1486 and path tracing with MIS 0.0861, while balance and power gave 0.0190 and 0.0188. Balance took about 245 ms against 176 ms for flat weights and about 74 ms for the noisier path tracer. The audit calls these small regression scenes, not a general performance ranking.

Cost grows quickly with depth. Up to four edges there are already 14 candidate strategies; connections grow quadratically with depth and each explicit MIS evaluation is linear, so the weighting can approach cubic scaling. The stated objective is lower error per second, not more strategies.

The compact BDPT kernel supports one non-emissive homogeneous Henyey–Greenstein medium, with MIS over free-flight survival, collision density and phase densities. In a homogeneous-medium check against an 8,192-sample volumetric path-tracing reference, balance and power BDPT were within 1.75% and 1.81%; these are finite-sample mean-energy checks, not equal-time benchmarks. Several medium regions, heterogeneous coefficients, volume emission and other phase functions use an explicit, labeled volumetric path-tracing fallback. Finite-aperture or tilted-camera BDPT remains a flat-weight preview, and advanced materials such as rough dielectrics, subsurface scattering, anisotropy, spectral and textured inputs are not yet certified.

The transport pyramid is an estimator inspection tool. First pick one path-length antidiagonal and isolate its cells one at a time. Then compare raw contributions with the corresponding weighted image. If a strategy produces rare enormous values before weighting but contributes steadily after weighting, its alternatives may be covering the problematic region. If an entire supported feature is absent from every raw cell, weighting is not the first suspect.

A staircase of different roughnesses under emitters of different extent is a useful controlled scene. An eye-sampled reflection can match a narrow glossy lobe while a light-sampled connection can match a small source. Their raw and weighted views turn the mixture’s density preference into a visible spatial explanation.

The weight-only image is conditional on events actually sampled and displayed. A black region does not, by itself, mean a zero probability or a mathematically invalid technique. It can also mean that the chosen finite sample population never generated the event. A small test scene, stable camera and repeated sample batches make those interpretations easier to separate.

The tiled display partitions image space among techniques rather than rendering a full independent high-resolution scene for each cell; the shrunken display instead shows a small version of the whole scene per technique. Both change the effective film area and evidence per cell. Use them to understand path families; use matched linear-film exports for quantitative estimator comparisons.

A connection asks whether two sampled vertices can be joined into a valid path. A merge asks whether a sampled light vertex lies close enough to a camera-side vertex to contribute through a kernel. The first is geometrically precise but can miss concentrated transport; the second trades finite-radius smoothing for a much larger acceptance region. Combining them is useful only when their contributions, effective densities and support are accounted for coherently.

The VCM-labelled implementation supplies both surface connections and progressive merges, combined with density-based heuristic weights and a fixed factor. This is a substantive working experiment, but those weights should not be described as a verified implementation of every density conversion in the reference VCM derivation. The UPBP lane adds a subset of unified surface and medium transport: collision tracing and volume-point gathering are available in media, while stored beam records are diagnostic rather than gathered estimates.

The distinction matters visually. Drawing beams in an inspection viewport proves that the light walk produced beam data; it does not prove that those beams contributed to the rendered film. The brochure therefore treats connection, point merging, beam storage and beam gathering as separate capabilities. This also provides a concrete extension path: add the missing estimate and cross-density evaluation, then test it against a shared supported scene.

The old modes reuse a tracer picture; the enhanced route computes linear surface appearance, extinction and photon scattering separately, and disables the old guided branch while active. Camera, scene and transport changes invalidate its accumulation, while display blend, exposure and screen blur can change without restarting the transport film.

A medium-method MIS choice in the enhanced panel combines the supported strategies of one photon-primitive family. It does not mean that the surface guide and the raster image are MIS-weighted, and more samples reduce noise without removing the compositing and filtering bias.

In the current CPU estimator, the correlated switch first asks whether the chosen family has a record builder. Only the UV plane, tracer beam and axis-revolution hourglass have one. Sphere, disk, cone and direction-trio MIS use the reconstruction fallback: every pixel regenerates each pool member from the same seed. Enabling raster gathering on those families logs that no record builder exists and keeps the fallback.

The default pool has 16 draws. All-N mode loops over all 16 in every pixel and divides by 16, including misses. For direction-trio MIS, each draw includes the active member samples. Stippled mode chooses one pool draw per pixel instead. For a fixed camera ray and equal numbers of independent light-side draws, correlation alone preserves the marginal estimator; it changes how errors line up across pixels. A frozen pool is an inspection mode and does not average away its light-side realization.

The presentation loop normally targets about 8 ms of sampling before updating the display, but it checks that budget between complete passes. One large all-N pass can therefore make interaction feel much slower even when its cost per evaluated draw is comparable. The cached route also reuses camera-side facts that the reconstruction route can calculate repeatedly.

The September 2026 implementation record separates the original seed-replay path from later record caching and bounded gathering. Early comparisons were also distorted by display overhead: one independent pass paid for a whole presentation, while an all-N pass performed many evaluations before presenting. Batching corrected that comparison.

The strongest native timing evidence concerns converted families. At equal evaluated terms, cached hourglass records made the correlated route faster than independent sampling. Adding bounds helped thin planes and beams much more than the broad hourglass. That is evidence against a universal claim that correlation itself is slow.

A separate geometric experiment on a preset-44-like fog room estimated sphere bound coverage at 47.74% of the film and true crossings at 28.41%; the cone figures were 30.66% and 27.81%. Those are Monte Carlo geometry measurements, not render times or universal footprint ratios. No matched current sphere-versus-trio timing series is claimed here.

These are recorded startup-adjusted sampling measurements, not whole-application frame rates. The cached-versus-independent ladder uses the best of four runs after subtracting a measured startup floor; its 700×440 application window produced a 217×140 film. The bounded-gather table uses the best of three and differences two pass counts to remove the startup floor. Those historical timings have not been rerun for this page.

In PP quick settings or PP Estimator, select strategy 31, Custom combination. Presets are UV + sphere, sphere + disk, arbitrary + sphere + cone, and beam + ring + arc. Keep one member as a diagnostic control, or choose any pair or trio. Each render draw evaluates the selected members within each group; adding a third is additional work, not a free extra density.

The mode covers first-segment single scattering in one homogeneous convex medium with the emitter inside. Plane selections support one or more emissive quads; source identity and source-selection probability are included in the common MIS measure. Mixed quad/non-quad emitter rosters are refused when a plane is selected. The selected beam is this first-segment construction, not standalone strategy 18’s multi-bounce traced beam. Unsupported source/medium configurations and unsupported mask bits produce a visible refusal.

Strategy 26 and the existing standalone families remain available for comparison. Fixed arbitrary planes now join the exact-family common (s,u,v) density ledger, including the offset-sampling range and orientation-dependent determinant.

The isolated probes share a camera at (0, 3, −12), looking toward (0, 6, 0), and a downward-facing source. In the native quad convention, UT sweeps the z edge, approximately along the viewing direction; VT sweeps the x edge, across that view. Their projected Jacobians therefore have very different weak directions. VT avoids the particular near-parallel configuration that hurts UT here. Rotating the camera or the source can change which member is favorable.

A large UV sheet crosses more of this camera’s rays, but it still samples a flight distance and can be viewed obliquely. The observed improvement is strong without making UV universally efficient. The three-plane mixture can use a different member when UV’s coverage is poor, which helps explain why its large-source result improves much more than a single UV-versus-sphere comparison suggests.

For the huge laser-like source, the observed variance–cost proxies were 24,355.7 for sphere alone, 595.4 for UV + sphere, 236.1 for the directional trio, 61.5 for the plane trio, 55.5 for VT, and 44.7 for all six. The pair reduces the sphere’s severe spikes, but it does not supply enough useful coverage to compete with the best alternatives in this configuration. These are finite-run measurements; they do not establish an asymptotic tail exponent.

The density formulas suggest why this particular pair struggles: UV has a projected factor |nL · d|, while the sphere has |ω · d|. Laser-like emission concentrates useful paths around ω ≈ nL. Their weak directions then nearly coincide, despite their different shapes. VT supplies a transverse direction in this camera. This is a geometric interpretation consistent with the measurements, not a uniquely established causal explanation.

For the huge cone source, VT reached 3.019, the plane trio 3.270, and all six 4.572. The additional density in the six-member combination lowered per-pass dispersion, but the extra evaluations cost enough to lose on the observed time-weighted proxy. This is exactly why the charts show dispersion and cost separately.

The physical emission profile changes the contribution at a connection. The current plane proposal remains cosine-hemisphere even for a laser-like source, and the directional constructions sweep different angular coordinates. Narrowing the radiance lobe can concentrate useful energy into a small part of those supports. Complementarity must therefore be assessed against radiance, visibility and the camera—not just against the names or dimensions of the shapes.

The native Diffuse profile has radiance proportional to cos θ. Laser-like uses cos⁵⁰⁰ θ, a narrow finite lobe, and Cone is constant inside a 25° half-angle. The geometric emitter cosine is additional: the UI’s Diffuse profile is narrower than constant-radiance Lambertian emission.

For the plane families, direction sampling remains cosine-hemisphere sampling. Tightening the physical emission lobe does not focus that proposal, so many candidate connections can carry negligible light. This changes the integrand and its overlap with the sampling density; it does not change a geometric Jacobian by itself.

Each lamp has integrated luminance-weighted RGB power 120. The normalization is area × peak radiance × angular integral, with integrals 2π/3, 2π/502 and π sin²25° respectively. Equal power avoids making the huge lamp win merely by emitting more energy. It is a renderer-space control, not a spectral-watt calibration.

The current light-selection distribution uses area × peak luminance, without integrating the angular profile. At equal total power, a laser-like source therefore receives about 167 times the selection mass of a native Diffuse source. Correct reciprocal source probabilities preserve normalization, but the allocation can still waste effort or starve other lamps. The isolated probes remove this effect; the combined rooms deliberately retain it.

The nine centered probes keep source position and camera fixed. Each of the eight selections uses the same six deterministic seed keys, with independent random streams between replicates. Every completed film contains 1,024 passes at 160 × 100. The complete scenes repeat four selections—UV, directional trio, UV + sphere and all six—under the same protocol. Jobs run serially in a deterministic shuffled order.

The medium is the box [−13,13] × [0,12] × [−13,13], with σs = 0.08, σa = 0.004 and isotropic scattering. Emitters point down from y = 10.8. Centered probes share a 22 mm camera at (0,3,−12), looking at (0,6,0). Full matrix framing is oblique; its camera and every other launch setting are retained in the downloadable record.

For each condition, sample variance is computed across the six linear RGB films at every pixel/channel, then summed. All strategies share a normalization from the equal-weight pooled mean image for that condition. This gives a repeatable finite-budget noise statistic without pretending that one strategy is exact ground truth.

The cost proxy multiplies this normalized variance by 1,024 × median measured milliseconds/pass. Timing excludes eight initial warm-up passes, but the estimated cost includes all 1,024 film passes; those warm-up samples are not treated as free. Timing ranges show variation across runs. CPU scheduling, clock speed and background work can still affect absolute cost.

Six seeds cannot certify a finite second moment or reliably capture arbitrarily rare contribution tails. Nearby scores are not a universal ranking. The result is a controlled baseline for this implementation, camera, resolution, power normalization and path class. It does not measure bias, equal-time image error or high-resolution GPU throughput.

All six had the lowest observed variance–cost proxy among the four tested combinations in each complete room: 4.407 for three diffuse source sizes, 151.044 for three emission profiles, and 244.244 for the nine-source matrix. Its native pass cost was approximately 2.00, 1.97 and 2.85 ms respectively; the additional work was offset by substantially lower measured seed dispersion.

The UV + sphere pair tells a useful contrasting story. In the all-diffuse size room it improved on the directional trio, reaching 53.483 versus 144.577. In the profile room and nine-source matrix, the directional trio was stronger. A combination’s value depends on the actual mixture of useful connections, not just on choosing two visually different primitives.

These room results include source selection, overlapping light footprints and different spatial positions. Equal integrated power does not imply equal sampling frequency: the existing source CDF uses area times peak luminance. The authored profiles therefore predict approximately 97.25% of source selections for laser-like emission, 2.17% for cone and 0.58% for diffuse—per profile group in the nine-light matrix. These are derived probabilities, not sampled-count measurements. The isolated probes remove that source-roster effect; the full rooms deliberately retain it. Neither set of measurements proves absence of bias.

Observed variance–cost proxy [ms], lower within each room. Six seed-key runs per method, 1,024 passes per film, 160 × 100 linear RGB. Each room has its own shared signal normalization; the composite chart uses separate logarithmic vertical scales. These are noisy finite-run comparisons, not ground-truth errors.

The 640 × 400, 4,096-pass nine-light showcase contains one pixel responsible for 99.77% of its total linear luminance. It lies over the medium laser-like emitter. The raw film remains unchanged. This separate display capture is outside the 504 timed measurement films; its mean must not be treated as a converged brightness reference.

The averaged film does not preserve the responsible primitive, pass or sampled path. A near-source floating-point inconsistency is one concrete hypothesis: the sphere branch obtains a direction by dividing a computed hit offset by its sampled radius, while cross-evaluated densities reconstruct direction from actual distance. A slightly non-unit direction can be amplified by a cos⁵⁰⁰ emission profile. This is a source-level lead, not a confirmed explanation.

A rare valid contribution and a numerical defect require different remedies. This observation is not evidence by itself of infinite variance, and the tone-mapped image cannot diagnose it. The complete float film, extreme-pixel counts and source-footprint analysis are available below. The controlled low-resolution rankings remain finite-budget observations, not a guarantee against outliers at other resolutions.

A renderer can hide a compensating error: an incorrect source factor may be offset by an incorrect PDF, or a missing root may be obscured by a bright surviving branch. Small operator-level experiments make those coincidences harder. Check finite-difference derivatives against the geometric Jacobian, solve the same crossing in different coordinate frames, and compare oriented parameterizations of the same emitter.

Limiting cases supply independent expectations. Refraction approaching index one should reduce the hourglass to its corresponding unbent construction. A shared-pool gather should agree with direct evaluation of the same frozen primitives and camera rays. A disabled optional component should reproduce its baseline, and a supported mixture should preserve paths for which only one member has support.

Statistical comparisons then need both a model contract and a work contract. Match the actual source, material, phase function, camera and supported path population before comparing energy. Report resolution, sample allocation and elapsed work separately. Equal passes answer a different question from equal time; a method that does more work per pass should not receive an unexplained advantage.

Regression manifests preserve selected films across source changes. Byte identity is strong evidence that those pinned configurations did not change, not a proof of mathematical correctness or complete strategy coverage. The verification ledger identifies unpinned modes, flags and GPU paths. Recorded comparisons also include scenes where conventional NEE is better matched than a swept construction, particularly uncomplicated area-light single scattering.

The native comparison path can export linear floating-point RGB rather than relying on an exposed or tone-mapped screenshot. The documented PGR1 payload records dimensions and pass metadata before the linear pixels. This preserves the values needed for regional means, energy checks and error images without conflating transport with the display transform.

Film normalization still depends on the producer. Metropolis splats require mutation-based normalization; a photon estimate accounts for emitted draws and kernel support; a progressive camera film averages camera samples. Those conventions must be checked before subtracting two exports. A shared pass field is metadata, not proof that the normalizers or computational budgets are the same.

The evidence should also retain failure context. Report unsupported features, rejected constructions, masks and the fraction of pixels used by an error metric. For heavy-tailed estimators, repeated batches and tail diagnostics are more revealing than a single favorable crop. The result is a reproducible experiment: scene, supported transport, sampling settings, linear output and a stated interpretation.

At the start of every camera path the tracer draws one wavelength uniformly from 380 to 780 nm; the light tracer draws its own for each light path. Surface reflectance, glass transmission and emission are read from each material's Gaussian-lobe curve at that wavelength and multiplied into the path as a gray factor.

At the end, the path's value is weighted by the color matching functions, converted from XYZ to linear sRGB and divided by the wavelength density. The code normalizes by the integral of the luminance function so a flat, equal-energy spectrum matches RGB-mode luminance. There is one wavelength per path and no companion wavelengths, so spectral noise shows as colored speckle that averages out over passes.

An unedited material gets one lobe for each RGB channel above 0.01, at 630, 532 and 467 nm with a standard deviation of 15 nm, scaled by that channel. A pure black color gets a broad gray lobe instead. Three narrow lobes carry far less energy than a flat spectrum, so a scene usually renders darker after the switch. They also explain the separated bars behind a prism. A light source's emission spectrum is its lobe curve times its strength; its RGB emission color is not used. Smoothing widens every lobe for a broader spectrum.

Some effects are still computed as RGB factors: albedo from baked node-graph textures, procedural patterns or the projector; the thin-film tint, fixed at 650, 550 and 450 nm; the Mie color lobes; Rayleigh's sky-mimic tint; and the volume color. In spectral mode only the red component of the path's value is converted, so these effects act as a gray weight equal to their red channel. The procedural sky is achromatic. Bidirectional connections in BDPT are not converted, so spectral claims here apply to the path and light tracers.

The CPU photon-primitive estimators copy the GPU's Cauchy convention and evaluate it at the three RGB channel wavelengths; they have no spectral mode of their own. The hourglass sheet depends on the index only at its two refractions, so drawing a channel for each sample and using that channel's index leaves the swept construction and its Jacobian unchanged. The caustic splits into red, green and blue sheets, not into a continuous spectrum.

Strategy 20 chooses a channel per hourglass sample. When the hourglass is paired with the beam estimator (strategy 21), one channel is chosen per sample and shared by both, so the balance weights compare the same transport. Only light that passed through a dispersive dielectric carries the three-channel weight; the rest of the frame keeps its full-RGB estimate and does not become three times noisier.

A floor pattern does more than decorate the room. It anchors perspective, makes a glass object’s distortion legible and gives reflected light a recognizable source. Fine grain and larger mineral features provide different scales of detail; roughness variation changes the reflected highlight as well as the local color.

These scenes use the existing material-node bake at 512 × 512 per textured entity. Direct-light evaluation and sampled path continuation must use the same local albedo and roughness. The new checks caught and corrected a mismatch in direct lighting that previously washed out node-authored patterns.

The paired route is the GPU path tracer. These are procedural appearance studies with no medium, normal mapping or geometric displacement; other integrators have separate texture-support limits. Reloading a preset restores its authored graph, and leaving these presets restores the previously active graph.

A medium node graph does not always become a general spatial shader. A constant-folded route evaluates to entity-level coefficients. A recognized live 3D generator can supply a procedural payload interpreted by the GPU. An explicit volume bake instead evaluates a grid and stores spatial absorption, scattering, tint and emission fields in 3D textures.

Those routes differ in both cost and fidelity. Evaluating an unrecognized expression at an entity’s center produces a scalar parameter, not a heterogeneous field. A single supported procedural payload is not equivalent to arbitrary composition of every node. A finite grid can represent more general fields, but introduces sampling resolution, memory traffic and interpolation.

The medium preview is useful precisely because it makes spatial behavior inspectable before committing a scene. It still belongs to its own preview path. The photon-primitive CPU implementation uses a narrower homogeneous coefficient contract, so a GPU volume-graph effect is not automatically available to a PP experiment.

The GPU tracer offers RGB transport and a hero-wavelength route that samples the visible range from 380 to 780 nm. Supported material spectra and wavelength-dependent refraction connect that sample to the final color response; the spectral chapter identifies effects that still use RGB approximations. Spectrum controls define transport inputs; they are separate from a post-process hue change.

Emission has several dimensions: where a source occupies space, how radiance varies with direction, and how it varies with wavelength. A broad area emitter, a sharply directed source and an emissive volume expose different sampling problems even in the same room. The light-selection PDF and source radiance profile remain separate quantities.

Participating media add absorption, scattering, phase response and emission along a path. Supported GPU procedural and baked-volume routes represent spatial variation; the photon-primitive CPU experiments instead isolate the homogeneous cases for which their measures and crossings are derived. The source and backend determine which combinations are available.

The ReSTIR direct-lighting route operates on the tracer’s geometric buffers. Candidate selection and temporal reuse populate ping-ponged reservoir textures, followed by a spatial resampling pass. Candidate count, neighboring samples, spatial radius and temporal reuse are visible controls. Diagnostic views expose reservoir weight, selected samples, visibility and candidate quality.

The separate ReSTIR-GI-style route reuses screen-space indirect information with geometry gates, radiance clamps and damping controls. It is not a full sub-path-reservoir implementation. This distinction matters because a stable indirect image can result from a different approximation than the direct-light reservoir algorithm.

These reuse mechanisms complement progressive accumulation and path guiding. Accumulation refines a fixed view over time; guiding learns a directional proposal; reservoir reuse redistributes candidate information across frames and nearby pixels. Their inputs and intermediate buffers explain how each spends rendering work.

The physical tilt/shift mode uses an ideal paraxial thin lens. Sensor, lens and focused object plane satisfy the thin-lens conjugate relation, and for planar geometry their extensions meet along the Scheimpflug line. Controls cover lens tilt and shift, sensor tilt and shift, focus distance, pupil rotation and anamorphic ratio. A real tilt lens has separate principal planes and pupil magnification, so this is a useful optical model rather than a complete lens prescription; multi-element surfaces, vignetting, aberrations and diffraction are not modeled.

CPU and GPU share the equations, sensor inversion and pupil distribution. A GPU parity test compiles the actual camera shader and compares 2,560 rays across five aperture families with the CPU camera: the largest origin difference was 4.8 × 10⁻⁷ m and the largest direction difference 1.91 × 10⁻⁷. The photo-camera test suite, which also checks the three-plane Scheimpflug intersection, inverse pixel projection and pupil moments, passes 203,189 checks. These are model and parity tests, not a calibration of a manufactured lens.

The depth-reprojected photograph is one RGB-D capture rebuilt as geometry behind a plate fixed in the world, so parallax appears as you move. The record-and-replay tool propagates three transparent test masks with the scalar angular-spectrum method, records them against an off-axis reference and recovers the complex wave from intensity, with a relative L2 error of 1.15 × 10⁻¹⁴ on its default recording.

An authored material passes through several representations. Typed links define a graph; CPU evaluation resolves parameter expressions and supported procedural descriptions; selected outputs are baked into texture-array layers; the renderer reads those layers alongside entity-level parameters. This is not an arbitrary shader compiler. A pin drawn in the editor is only useful if its value has a defined route into the selected backend.

The editor supports compatible-node creation from typed links, image drag-and-drop into a Texture node, inline thumbnails and detached previews. GPU, CPU Fast and CPU Full previews expose different evaluation costs; a dedicated orbitable medium preview makes spatial behavior inspectable. The layout diagnostic also reports the rectangles and placement decision used to position the editor around a selected object.

For surface outputs, the documented bake packs channels into three RGBA8 layers at a selectable resolution. That finite payload introduces real precision and coverage decisions. Not every rich material input is a per-texel baked channel: some remain uniform parameters, and supported 3D procedural paths can be evaluated directly rather than flattened into a 2D mask. A preview of a graph and a rendered surface therefore need to be checked against the same delivery route.

Detached editing supplies another practical separation. The user edits a shadow graph while the committed graph continues to render. Commit replaces the live graph and invalidates the appropriate accumulated result. This allows material experiments to remain interactive without treating each unfinished connection as a valid new scene, while the path through evaluation, baked channels and supported live fields to the active renderer stays inspectable.

A camera move invalidates the relevant view-dependent film and requests a refreshed image; a stationary view allows progressive accumulation. View-independent photon or light-path data can be reused when the selected backend permits it. Scene edits, transport switches and diagnostic display remain inside the same application loop.

The backend work is heterogeneous. A compute path-tracing pass, a CPU photon-map rebuild and a CPU image pass have different costs. Most standalone CPU modes render at half the scaled viewport dimensions. Photon Primitives has an additional full-resolution option and parallel image work; Metropolis loops check a work budget during mutation batches. These are concrete latency controls rather than evidence of equal work per displayed pass.

FPS in the window title measures application updates. Film samples, passes, mutation counts and emitted photons measure different populations. A moving camera can respond promptly while each refreshed image remains noisy; a stationary camera can spend many updates refining one film. Resolution and work-budget controls keep those costs visible without claiming equal latency across all modes. Record both update behavior and estimator work when describing performance.

A first visit can start with a material or lighting showcase, object selection and a camera move. A transport study benefits from a simpler scene where path classes are recognizable. The one-ball hourglass setup isolates the refracted construction before a larger caustic room introduces additional visibility and support questions.

A repeatable session retains camera pose, exposure, source power, medium coefficients, material support and integrator settings. The displayed image must be attributed to the active producer rather than the name last selected in a menu.

Take a shot is the dedicated shutter. While it renders, the resolution scale is forced to one, the photon-primitive film switches to full resolution, node and volume animation are frozen and temporal blur is off; the preview settings return when it finishes or is cancelled. A native validation run recorded a still, a long exposure and a three-frame sequence, plus raster and VCM captures, with finite HDR radiance where the film is linear. Comparison-report exports and photon-primitive linear films remain the routes for numerical studies.

Unsupported combinations are refused rather than silently changed: tilt-shift needs a naive, NEE or MIS eye-ray strategy, the CPU estimators need a pinhole, and camera motion needs a linear film. Changing the scene, camera type or renderer during a capture cancels it and restores the preview.

A photon cloud and its KD-tree explain spatial sample coverage and gather work. A light–eye connection display shows which vertices were joined and which path lengths were represented. Mutation traces and acceptance statistics expose whether a Metropolis chain is exploring or repeatedly revisiting a narrow region. Guiding histograms reveal a learned proposal before its consequences are folded into a noisy film.

The Primitive Explorer adds a different level of inspection: it displays the sampled construction, camera crossings and Jacobian-related quantities. That makes it possible to connect a bright pixel to a specific sheet tangency or branch decision. Geometry views are especially useful when an image error could arise from either a bad weight or a bad hit test.

The in-process validator probes selected quantities, schematics identify sampled and swept coordinates, and the ray tree follows transport through the scene. Split A/B runs independently configurable PP passes and can freeze one side; PP-versus-GPU compares separate producers with camera and bounce controls. Neither display replaces the exported linear-film arithmetic used for quantitative ratios. Overlay availability and recorded visual verification also vary by strategy.

The important discipline is to name what a view proves. A stored beam is evidence of beam generation, not necessarily beam gathering. A weight visualization shows evaluated contributions, not every point in the mathematical density. A screenshot after tone mapping is evidence of appearance, not a linear energy measurement. These limits make the diagnostics more useful because they suggest the next experiment rather than inviting an unsupported conclusion.

Seeing is where checking starts, not where it ends. The project’s own rule is that these views decide where to look, while reference films and ratios decide whether a number is right. In a deliberate wrong-divisor experiment, an image that looked correct at every sample count converged to about 4.45 times the reference brightness; only a reference film and a median ratio exposed it.

The Photon Primitive Editor takes one traced light or camera subpath and sweeps chosen degrees of freedom at chosen vertices: the polar angle, the azimuth and the segment length. The swept endpoints form a curve, a surface or a volume, which the editor marches on the GPU and draws as splats, oriented quads, a smooth surface, a ray-marched volume or an exactly ray-traced analytic shape.

A header-only classifier names the resulting shape, such as a sphere, cone, disk, arc, planar sector, ball sector or parallelepiped, and is covered by a unit test. The transport-estimate view colors each cell by its physical weight including the sweep Jacobian, and a double-primitive view shades two chosen sweeps by their balance-heuristic density to show how two strategies share the same paths. The analytic tracer and the double-primitive view are working but still being refined.

The camera node supplies a projection pose and the texture node supplies image values. A screen-space use places those values in the image; a live surface projection evaluates them through the chosen camera; Bake to UV transfers the result into the mesh’s texture coordinates. After the bake, the material is attached to the surface rather than to the viewing camera.

That is an authoring operation, not inverse reflectance recovery. A photograph can already contain shadows, highlights and exposure decisions. Baking it into albedo preserves those image features, and subsequent lighting can illuminate them again. The useful demonstration is the transformation between coordinate systems and stages, with that assumption stated.

The optical experiment’s projector is different: it enters the transport estimator as sampled illumination and therefore participates in light visibility, scattering and path-length modulation. Comparing the two workflows helps separate “an image that looks projected” from an image whose values were actually transported through the scene.

The image-processing bank includes operators driven by scene depth or normals, mathematical and field-inspired effects, and emulations of print, stipple or tape. A geometry-aware effect needs inputs a photograph may not contain. A history-dependent effect reads previous frames. A procedural field can animate without solving a dynamical system. These distinctions describe the mechanism more clearly than the number of menu entries.

Particle or grid states can be converted into renderer inputs, and a Gray–Scott field exists in the source. The documented simulation audit also records source-selection and dispatch problems that keep several advertised routes from displaying their intended state. A named solver or node is therefore not sufficient evidence of a working coupled simulation.

These experiments broaden the studio, but are kept separate from transport validation. Quantization, bloom, tone mapping and output-media effects deliberately alter the displayed signal. The original articles retain implementation ledgers, dead-control findings and capture recipes so that those exploratory modules can be assessed on their own terms.

The preserved collection contains one standalone hourglass manuscript and twelve assembled portfolio articles. The standalone manuscript develops the symmetry, crossing solver and cost argument. The long photon-hourglass article extends the discussion with the ring / arc lattice, vertex variants, proposed surface constructions, variance studies and correlated-sampling experiments.

The other articles cover rendering architecture, bidirectional decomposition, authoring, cameras, imaging, simulations and image operators. Twelve authoring page bodies, five topic fragments and shared header / footer files are indexed separately; some retain assembly tokens and are not additional independent articles.

Original figures, equations, interactive views and correction records remain available. Some early derivations and status statements were superseded by later notes or measured solver fixes; the library links both the original notes and the correction records.