Curved-Ray Space Effects

Curved-Ray Space Effects

Treat every result as one of three claims: an artistic deformation, an Ellis null-geodesic solution, or a Schwarzschild null-geodesic solution. Numerical integration alone does not turn an artistic field into a metric solution.

1. Select the claim

Complete when: exactly one claim owns the ray path, and every visual claim is no stronger than that branch's evidence.

2. Declare the numerical domain

Define before authoring the march:

• the effect-to-world transform and a finite local integration bound;
• the camera event, ray origin, normalized direction, and exterior side;
• one length basis for positions, steps, horizons/cores, and medium coefficients;
• the state vector, its integration parameter, its owner, and its valid time;
• the environment orientation and the orthonormal frame used for escaped-ray lookup;
• horizon, core, disk, shell, proxy-exit, invalid-state, opacity, step-cap, and attempt-cap events that apply to the selected branch.

For metric rays, nondimensionalize with the Ellis throat radius a or the Schwarzschild mass length M = G M_SI / c^2, while retaining the conversion back to metres. Render delta never becomes a ray step. Preserve either spherical metric through a similarity transform: translation, rotation, and uniform scale. A nonuniform transform requires an explicitly derived transformed metric and frame plus renewed invariant, event, and convergence validation; otherwise reject it at setup.

Nonstationary metrics require an external solver that integrates or recovers coordinate time and samples or interpolates metric and emitter state, with validity and error, at every mapped integration evaluation. A frozen metric is a quasi-static approximation only when its declared evolution-error gate passes; otherwise report the model unsupported.

Complete when: every state component and event surface has a declared basis, owner, and finite validity domain, and world-to-solver-to-render round trips preserve the chosen scale and exterior. Each spherical metric uses a similarity transform or supplies validated transformed-metric evidence, and every nonstationary claim uses mapped coordinate-time sampling, is explicitly labeled quasi-static with a passing evolution-error gate, or is unsupported.

3. Build one bounded march

Use WebGPURenderer with TSL node functions. Initialize the renderer and confirm the WebGPU backend before selecting compute, storage, or MRT resources. The canonical march is:

1. Transform the camera ray into effect space and intersect the finite bound. A miss returns before numerical work.
2. Initialize position, tangent or canonical momentum, radiance, transmittance, event state, accepted-step count, and termination ID.
3. Propose one candidate segment. An error-controlled rejection changes only the next attempted step size.
4. Locate every applicable event continuously on the segment. Root-refine the earliest event; preserve ordered disk crossings when several contribute.
5. Accumulate the accepted segment's transfer, then commit exactly one state advance and increment the accepted-step count once.
6. Terminate as escaped, horizon, core, opaque, invalid, unresolved-critical, minimum-step, step-cap, or attempt-cap.

The attempt cap bounds divergent work independently of the accepted-step cap. step-cap bounds committed accepted steps; attempt-cap bounds accepted plus rejected attempts. A curvature or distance heuristic may propose a step; refinement against a tighter solution decides whether it is accurate.

Complete when: a trace proves one committed advance per accepted step, rejected attempts leave physical and event state unchanged, every ray receives an explicit termination ID, and event residuals meet their declared bounds.

4. Resolve transfer and the escaped direction

Sample an exterior environment only for escaped rays. Reconstruct its lookup direction from the integrated outgoing tangent in the declared orthonormal frame; orbital position angle alone is not a direction. Bound or integrate any far-field tail truncated by the proxy.

Keep transfer aligned with the claim:

• An artistic disk declares a scene-length basis and a linear-HDR source basis. Integrate extinction/emission front-to-back and label the result artistic.
• A physical disk uses ordered geodesic crossings, a named emitter four-velocity and observer tetrad, and invariant frequency transfer. Its geometry and orbital model must match the selected Schwarzschild claim.

Accumulate into linear HDR. One pipeline stage owns tone mapping and output conversion; diagnostics that replace the output mark the pipeline graph dirty.

Complete when: misses and non-escaped terminations cannot sample an exterior, the escaped tangent is finite and normalized, disk crossings retain their order, and transfer units reduce to radiance.

5. Select direct work or reuse

Use a direct bounded march for changing lenses, sparse probes, or artistic fields whose per-pixel work meets the target. Use a critical-split transfer map for a static spherical Ellis or Schwarzschild lens when coherent reuse beats direct integration. Use a local high-accuracy map near separatrices when GPU float32 direct rays miss the angular gate.

When a lens map, compute cache, or temporal reconstruction is selected, read lens-cache-and-history.md before allocating it. Keep the opaque scene and required depth at their required resolution; scale only the effect pass whose error was measured.

Complete when: each cache or history resource has a reuse reason, a stable identity, an invalidation rule, a completion/lifetime rule, and measured benefit over the direct path.

6. Verify the selected claim

Use a deterministic, seeded environment with high-frequency directional features so angular, critical-curve, and history errors remain visible. It is a validation input generated by the project, not a bundled visual preset.

For every branch:

• capture termination, accepted/rejected attempts, event count/location, remaining transmittance, final direction, and invalid-state diagnostics;
• compare h, h/2, and h/4 or an equivalent tolerance sequence at fixed rays and cameras;
• compare final angular error against the environment footprint and compare event residuals against the relevant geometric thickness;
• verify moved, uniformly scaled, camera-inside, miss, and far-from-origin bounds, plus nonuniform-scale rejection or the explicitly transformed metric;
• verify the required Three.js revision, backend, final-output owner, resize, reset, and disposal behavior.

Artistic rays pass when refinement preserves fixed-view silhouette, termination class, ordered disk events, and radiance within declared bounds. Ellis and Schwarzschild rays additionally require an independent CPU float64 reference, invariant drift, critical-regime classification, exterior/escape agreement, and convergence of the final tetrad direction. A capped, minimum-step, invalid, or unresolved-critical ray is diagnostic output rather than physical evidence.

Complete when: every requested observable has a passing branch-specific gate, every failure class is visible in diagnostics, and the final claim lists the numerical and domain limits that remain.