Volumetric Clouds

Build a bounded volume whose broad mass comes from weather-scale causes, whose fine detail erodes that mass, and whose optical, shadow, and temporal errors are measurable.

Process

1. Select the claim and workload branches

State the claim first. Procedural weather, coverage, shape, and detail usually form an authored appearance model. Beer-Lambert attenuation is physical for the declared density and coefficients. Dual-lobe phase fits, octave multiple-scattering compensation, powder, and simple ground bounce remain approximations until validated against a transport reference.

Select each independent workload branch:

For causal precipitation, publish liquid and ice mass flux in kg m^-2 s^-1, or interval-integrated areal mass in kg m^-2, explicitly identified with its sample time, sample interval, physics frame/origin, physical support, area/Jacobian convention, fall delay or transport model, owner, contract version, generation, validity, conservation gate, and error. Publish each interval once to $threejs-rain-snow-and-wet-surfaces. The receiver converts flux to interval mass once, preserves the declared support/Jacobian, and applies the declared delay or transport before accumulation.

A density/emission recipe, incompatible physics frame/origin mapping, support/Jacobian convention, or delay model change starts a new generation. The receiver rejects stale or incompatible generations and never reinterprets prior interval mass. An appearance-only branch remains visual-only and publishes no receiver input.

Allocate no receiver-shadow product for the none branch.

Complete when: all five decisions name the selected representation and its observable; every admitted workload has a falsifiable cost or error gate; a none receiver-shadow branch records no receiver consumer and zero allocation; appearance-only precipitation publishes no receiver input; causal precipitation has one dimensioned generation accepted by one compatible consumer.

2. Define one optical and motion model

Choose dimensionless shape density with betas and betaa in length^-1, or physical mass density with mass-specific coefficients. Keep the convention end to end:

In the equations below, beta names the coefficient matched to rho: inverse length for shape density, or area per mass for physical mass density.

sigma_s = rho * beta_s
sigma_a = rho * beta_a
sigma_t = sigma_s + sigma_a
tau = integral sigma_t ds
T_step = exp(-sigma_t*ds)
DeltaL = T_acc * (j/sigma_t) * (1-T_step)

Use the zero-extinction limit DeltaL = T_accjds. Here j is source radiance per length. For direct light, distinguish finite-disc radiance, which needs a solid-angle integral, from a declared collimated irradiance convention.

Normalize phase so 2piintegral_-1^1 p(mu)dmu=1. Let rayDirection point camera-to-sample and toSun sample-to-sun; then mu=dot(toSun,rayDirection) makes mu=1 forward scattering. Keep dual-lobe weights nonnegative with unit sum.

Define one physics/render frame conversion, one metre scale, one cloud state clock, and one macro air velocity. Integrate velocity over elapsed simulation time; treat relative weather/shape/detail motion as bounded offsets from that macro advection.

Complete when: a homogeneous slab is invariant to step partition and reaches the zero-extinction limit, phase quadrature normalizes with the expected forward direction, and two update cadences integrate the same motion trace within tolerance.

3. Build bounded, conservative density

Keep active layers separate through altitude/profile, weather, shape, optical properties, and motion. Let a low-frequency weather field and compact vertical profile establish cloud mass. Apply shape at resolvable scales. Use detail as height-dependent erosion; it may roughen occupied boundaries but must preserve the weather/base-shape empty set used by the conservative bound.

Integrate one macro offset and add bounded relative offsets:

macroOffset += integral u_air(t) dt
weatherOffset = macroOffset + relativeWeatherOffset
shapeOffset   = macroOffset + relativeShapeOffset
detailOffset  = macroOffset + relativeDetailOffset

Intersect rays with the selected spherical shell, slab, OBB, or sparse-volume domain, then clamp the far end to the nearest opaque scene depth. Merge occupied altitude ranges and skip only their complementary gaps. For horizontal sparsity, build max-density macrocells that include weather, profiles, shape, warp reach, and every density-increasing operation. Average mips are appearance filters, not occupancy bounds.

Read [references/density-and-marching.md](references/density-and-marching.md) for density equations, domain intersections, conservative skipping bounds, and step selection.

Complete when: a debug view proves every skipped interval/cell is empty or inside the declared omitted-radiance bound, and brute-force versus accelerated marches agree on transmittance, HDR radiance, and first-contribution depth.

4. March and light the selected representation

Write current scene-linear cloud radiance, transmittance, and the depth data needed by the selected temporal branch. Bound steps by optical depth, resolved field bandwidth, cell/layer exits, opaque depth, and the remaining cloud interval. Terminate when the maximum remaining HDR contribution fits the output error gate.

On Three.js r185, run await renderer.init() and require renderer.backend.isWebGPUBackend === true before allocating or submitting compute/storage work. Then submit Fn().compute(count) through renderer.compute(). Use StorageTexture for 2D current/history/shadow products and Storage3DTexture only for writable volume fields. Treat computeAsync() as enqueueing rather than a completion fence. A PassNode.setResolutionScale() scales the whole pass, so keep the host scene at its required resolution and place reduced clouds in their own pass/resources.

Compute cloud self-shadowing from cloud optical depth only. A ground receiver can use the full sun-ray column. An in-cloud sample needs optical depth from its own position, supplied by a short sun march, deep-opacity slices, or another depth-aware representation.

Read [references/lighting-and-shadows.md](references/lighting-and-shadows.md) when the task includes scattering, atmosphere-derived light, phase fitting, cloud shadows, or shadow filtering.

Complete when: step-halving and higher-light-sample controls fit the linear HDR error gate, the cloud-off control returns unit transmittance and zero cloud radiance, and each admitted shadow query decodes optical depth from its actual receiver position.

5. Reconstruct broad clouds

For a reduced broad-coverage branch, store opacity-weighted representative depth and depth spread:

w_i = T_i * (1-T_step_i)
z_bar = sum(w_i*s_i)/sum(w_i)
variance_z = sum(w_i*(s_i-z_bar)^2)/sum(w_i)

Use one representative surface only for a unimodal contribution distribution. Use front depth plus moments or split histories for broad/multiple layers. Reproject an advected representative physical point into the previous camera. Record immutable current-render-to-physics and previous-physics-to-render transforms; map through them across an origin rebase. Host surface velocity is a different signal.

Blend with frame-rate-independent current response:

alpha_current = 1-exp(-dt/responseTime)
resolved = alpha_current*current + (1-alpha_current)*clippedHistory

Reject history outside the viewport or across depth/spread mismatch, camera cuts, projection changes, weather/topology discontinuities, encoding changes, resolution/tier changes, or a missing/incompatible previous origin mapping. Raise current response for disocclusion and low confidence. Variance-clip premultiplied linear HDR radiance and transmittance separately, then upsample with scene/cloud depth agreement.

Read [references/temporal-reconstruction.md](references/temporal-reconstruction.md) when history, sparse phases, depth encoding, reset policy, or upsampling is in scope.

Complete when: a translating-density control reprojects to the expected previous pixel, a mapped floating-origin rebase preserves that pixel, camera-cut/topology/incompatible-origin controls give history confidence zero, measured ghost decay matches the response model, and depth-edge upsampling does not cross the opaque surface.

6. Integrate the lighting and image handoffs

Choose one incident-light contract:

• an authored source that declares owner, revision, sample time and age, frame,

quantity, unit, basis, direction or angular support, filter, included attenuation, validity, and error; or

• atmosphere lighting that declares the same tuple.

For the atmosphere branch, choose either direct light already attenuated by the atmosphere or an unattenuated source plus atmosphere transmittance. Multiply each admitted cloud-only transmittance and opaque-visibility factor separately. Keep directional sky radiance distinct from hemispherical sky irradiance.

Composite clouds before the host tone map:

C_out = L_cloud + T_cloud * C_scene

Use one WebGPURenderer and one host RenderPipeline. Write data resources with explicit format/filter/mip policy and NoColorSpace. Let the host renderOutput() or outputColorTransform own the one display conversion; mark the pipeline dirty after replacing a diagnostic output node.

Complete when: the incident source has a complete contract, an attenuation trace accounts for every admitted atmosphere, cloud, and geometry factor once, cloud buffers remain linear HDR, and toggling clouds off returns the identical host image path.

7. Verify the system

Verify:

• homogeneous-slab transfer, zero-extinction limit, and phase normalization;
• bounds, opaque-depth clamp, conservative skipping, and early-exit error;
• fixed-seed weather mass, erosion, octave filtering, and advection continuity;
• each admitted ground or in-cloud shadow decoder, cadence, and stale-product

rejection;

• for causal precipitation, flux-to-interval integration, conserved mass under

cadence repartition and physical-support/Jacobian area repartition, declared delay-to-arrival mapping, and stale-generation rejection; the appearance-only control publishes no receiver input;

• for each admitted temporal branch, translating density, depth encoding,

history rejection, response time, and depth-aware upsample, including mapped and incompatible origin rebases;

• fixed-view HDR radiance, transmittance, silhouette, and halo against a

higher-quality reference;

• create, GPU completion, disposal, and each admitted resize/tier-switch or

history-reset lifecycle.

Complete when: every selected branch passes its numeric, temporal, visual, and lifecycle gates, and diagnostics identify each retained density, shadow, history, and causal-precipitation generation.

Failure signatures

Routing boundary

This skill owns weather-shaped cloud density, bounded cloud transport, cloud-only optical-depth shadows, and cloud-specific reconstruction. Use $threejs-sky-atmosphere-and-haze for molecular/aerosol transport and the shared sun/sky source, $threejs-image-pipeline for scene signals and final output, $threejs-rain-snow-and-wet-surfaces for causal precipitation transport and receiver accumulation, and $threejs-scalable-real-time-shadows for opaque-geometry shadow maps.