solvecraft/docs/render-glass-boundaries.md

Closed-glass ray boundaries

Closed dielectrics use the uploaded triangle boundary for medium transitions. A path that cannot classify its medium (an escape while inside glass, an exit with no matching entry, or an entry while already inside) ends there, keeping only the light it had already gathered; it is never converted into transparent background. Each job counts these paths. A handful at the limits of f32 geometry (a few per billion on the captured 69-body tumbler scene) are logged and tolerated; more than one in a million paths fails the job with the first failure's pixel, bounce, sample and code. Without explicit nested-media mode, a camera inside glass remains unsupported. Open meshes or overlapping solids are unsupported in either mode; the opt-in origin certificate is described below.

Surfaces may touch closed glass, as a tumbler resting on a table does. The offset launch from such a surface can start inside the glass, so its first crossing is an exit. A ray launched from an opaque or thin-sheet surface whose first crossing exits a closed body starts in that body's medium, with Beer absorption from the launch point; shadow connections do the same. Camera rays and closed-glass continuations that meet an unmatched exit are still errors.

A scene-wide normal offset and positive minimum distance are unsuitable for a closed volume: near a sharp rim they can jump across the next face or discard a valid short exit. Closed-glass continuation instead starts at an affine barycentric surface point, excludes its producing boundary, and considers every strictly positive intersection. Primary rays and opaque/thin-sheet launch policy remain separate. Finite emitters use the same minimum distance as the continued ray. Beer attenuation measures between physical surface points.

Triangle candidates first undergo an exact coordinate-bound test: when the ray is on or outside a stored coordinate bound and moves away, no positive hit is possible. This uses comparisons, without an epsilon or rounded division. It prevents cancellation in a projected intersection from turning a behind-origin intersection into a false forward hit. This check is narrower than the padded BVH broad phase.

The producing boundary is an exactly coplanar, edge-connected patch within one body, computed from the positions actually uploaded as f32. Adaptive exact predicates distinguish a plane from even an arbitrarily shallow bend; nearby parallel faces and disconnected surfaces retain separate identities. Excluding only this patch avoids a rounded surface point re-hitting its own plane at a grazing angle. Patch identities add four bytes per triangle and their preparation storage is included in admission. Nonmanifold or collapsed adjacency is not used to infer a patch.

Projected edge determinants retain the existing compensated expression for well-separated products, following Matt Pharr's discussion of Kahan's difference of products. When four or more leading bits cancel, normalized 12-bit high/low factors supply exactly representable partial products. Materialized scalar subtractions recover each product residual without requiring a fused fma. Compensated summation uses the existing integer-defined binary32 addition to establish round-to-nearest, ties-to-even boundaries, then rescales the result by a power of two. Choosing this arithmetic path leaves the geometric comparisons and distance bounds intact.

The scalar materialization barrier depends on the positive-zero bits of studio_weights.w. The host always writes that lane as positive zero; only xyz contain the three source weights. A retained shader-layout/host-serialization test checks the lane's actual offset and bits for implicit and explicit studio inputs. The numerical branch adds no owned host or storage buffer.

WGSL floating-point evaluation rules permit implementation variation, including expansion of fma. The split-product oracle checks exact product reconstruction and normal determinant bit patterns against an independent f64 reference. Hardware and software Vulkan runs also keep the original corner, medium-transition and transport-energy oracles. Floating subnormal consumers retain WGSL's permitted handling; backend qualification is still required, rather than claiming exact intersection on every WGSL device.

Hit depth also uses an affine base plus local vertex-edge increments. Summing three weighted distances can round a distant sharp-rim entry and exit to the same value and let traversal order choose the exit first. The captured coffee ray has real crossings separated by 0.00010076 mm at about 929.52 mm distance; its regression covers all axis permutations, coordinate reflections and both triangle orders. This improves distance ordering without treating an unmatched medium exit as transparent.

Candidates are ordered by that dominant-axis depth before it is scaled into a ray distance. Scaling can round two different depths to one distance: a captured 64-sample coffee camera ray crosses a bin rim at ray parameters 1124.0922606 and 1124.0923199, under one f32 ULP apart. The two depths still differed by one ULP, but both scaled distances were equal. Traversal order then picked the exit, and the path stopped at the medium gate. On an exact depth tie the hit that changes the current medium state wins: the entry face from outside, the exit face from inside. A ray through the shared rim edge itself exercises that rule. Traversal order never decides between them.

The regression fixtures distinguish short real exits, a normal offset crossing a sloped adjacent face, exact diagonal hits, and a captured impossible hit at a polygon edge. Original editable CAD renders exercise hollow walls and repeated reflection/refraction through the production command and job interfaces.

Actual-primary-origin certificate

This implementation and its regressions are part of published 00edaf6a/tree 38a7f0af; the GPU library passed 210 tests in CI7. Full CI7 remains red, and the opaque native fixture does not qualify a native Glass image. See the qualification record. In explicit nested-media mode, each actual primary/pupil origin performs one closed-boundary-only query before any opaque hit, visible analytic emitter, subsurface flight or escape can consume the segment. Opaque and thin geometry cannot hide that query. For a transverse nearest face-interior crossing in a valid certified containment hierarchy, an exit identifies the current medium, while an entry identifies its parent; immutable parent references then supply the complete outer-to-inner stack. Beer starts at the actual shader primary origin. Perspective pupils use the existing sampled eye disk. GPU orthographic primaries retain their existing target + back*(4*distance) + image-plane offset origin; generic Camera::eye() is not that orthographic origin, and no camera/projection policy changes here.

The query uses the existing uploaded-f32 intersection arithmetic, dominant-axis depth order and padded BVH. Its positive-depth search does not discard the ordinary primary's epsilon interval: an interface inside that existing launch interval refuses instead of being silently skipped. Detected boundary origins, nearest edge/vertex or transverse-sign ambiguity, tied nearest depths and stack overflow also use the existing medium diagnostics and unchanged failure fraction. No world position, minimum ray distance, tolerance, BRDF, PDF or random draw is changed. This is not a new exact world-space predicate or universal watertightness proof. Existing GPU certification checks welded closed/oriented homogeneous connected topology and strict convex-parent nesting; it does not independently prove a nonconvex leaf free from every self-intersection.

The additional query runs only with explicit nested-media mode. It has a fixed 32-entry node stack and 32-entry depth array (256 bytes of shader private array state), under the existing depth 30 host-built BVH. There is no new owned host allocation, uniform/storage buffer, retained plane or snapshot. One extra BVH query per sampled primary is bounded by the existing scene and sample caps. GPU work is scheduled by the existing measured dispatch controller, not a per-node debit ledger: the added cost participates in actual submission latency, with cancellation checked between the same bounded dispatches. No cap, diagnostic threshold or timeout is raised, and no hard wall-time guarantee is added.

The pre-fix analytic regression preserves exact source RGB, coverage and the existing Beer tolerance. A separate fixture correction establishes the actual packed orthographic world origin before qualification: the earlier generic-eye premise was wrong. The executed regression set retains first-opaque/emitter cases, parent order, no-hit air, exact/near-launch boundary refusal, silhouettes and f32 depth ties, physical per-pupil Beer with independent variates, copied subsurface parameters and strict outside-path identity. These tests executed in the published GPU suite. That execution does not establish every-backend watertightness, native Glass visual acceptance or convergence quality.

Candidate anchor and local-offset continuation

A rounded world-space hit point can lie outside a sharp rib even when all three barycentric weights are valid. The candidate continuation representation keeps the dominant stored vertex as an anchor and keeps the two weighted edge increments as a separate local offset. It is an anchor plus displacement, not an error-free two-float expansion. All three barycentric weights are retained directly; recovering a small weight as 1-u-v can erase corner clearance.

Ordinary floating expressions do not establish an evaluation barrier under WGSL. In the captured rib case, the compiler transformed a relative expression equivalent to (vertex-anchor)-offset into subtraction from a rounded world point. A float TwoSum/FMA residual formulation also lost its residual on that backend. The candidate therefore evaluates nonzero-offset point deltas using integer-defined binary32 addition and subtraction: align significands with a sticky bit, normalize, and round to nearest with ties to even. The sequence is RTE(RTE(a-b)+RTE(a_offset-b_offset)). No floating reassociation can change those integer rounding boundaries. Zero-offset rays retain the existing floating path. Integer bit results include subnormals; later floating consumers remain subject to WGSL's allowed subnormal handling.

The candidate routes triangle coordinate bounds, relative vertices and hit depth of triangles near the origin, analytic emitter intersections, and physical-point Beer distances through this representation. Traversal itself does not: BVH boxes are tested in ordinary arithmetic from the rounded origin anchor+offset, grown by the scene broad-phase pad plus 2^-20 of the origin's largest coordinate magnitude (several ULPs, covering the rounding of that origin). Every point the true ray reaches at depth t lies in the grown box along the rounded ray at the same t, so box rejection stays conservative. A triangle whose stored bounds are separated from the rounded origin by more than 2^-8 of that magnitude on some axis (about 4 mm at 1 m) uses the ordinary intersection from the rounded origin: an origin error of a few ULPs cannot reorder a hit that far away. It can still move the ray across an edge. In a concave rib, a ray leaving through one face can re-enter the next face within micrometres of their shared edge. The far face, tested from the rounded origin, then reported a miss just outside that edge, while the nearby face across it, tested exactly from the true origin, correctly missed too, so the re-entry was lost (captured at 256 spp: bounce 5, code 2). Far candidates whose bound or edge decision lies within 2^-20 of the origin magnitude, scaled by the projected edge length, therefore also take the exact path. Only those and the nearby triangles, which include every sharp-rib exit, use the integer-defined deltas. On the exploded coffee machine at 1080p and 8 samples per pixel this cuts closed-glass time on an NVIDIA GB10 from 43.5 s to 5.7 s (opaque: 5.2 s); 3 of 2,073,600 pixels differ from the all-exact result, by at most 6/255. For a finite emitter, it first subtracts the previous physical point from the ray origin and then adds the ray segment d*t. It does not add a short segment into a large local offset and subtract that offset again. Area-light density uses the same resulting physical segment.

This is a specified sequence of rounded operations, not an exact four-term sum or a universal watertightness proof. In particular, a large anchor difference followed by cancellation against the offset may still lose small information; edge projection, barycentric evaluation, and local-offset construction also retain ordinary floating arithmetic. Acceptance requires the integer bit oracle, captured rib/corner regressions, and production renders on each supported backend. These candidate notes do not claim those checks have passed.

A closed-glass continuation within 1e-6 of tangent to its producing face ends the path. It skims that face, and the rounding of its reconstructed start point (a few 1e-8 mm on the captured 69-body tumbler scene) then decides which side of the neighbouring faces it is on. The captured ray left a face at a cosine of 4e-8 while inside a glass, and then entered the adjacent face of the same glass from outside at a shared edge. Those directions carry about a millionth of the hemisphere's projected solid angle; ending them removes negligible energy, not a classified medium error.

The bounded opt-in glass shadow connection uses the same unshifted, zero-minimum continuation and exact producing-plane exclusion at closed interfaces. Thin-sheet shadow traversal retains its existing offset policy. A corner oracle checks a real exit shorter than the old global minimum while retaining both Fresnel interface factors and Beer attenuation.

Closed shadow continuation also retains the stored anchor and local offset. It uses the same integer-defined point deltas for bounds, interfaces and Beer segments. For a finite endpoint inside a medium, attenuation uses the current ray-origin-to-entry difference plus the remaining ray segment; it does not form a rounded world endpoint. Geometry crossings are tested up to the true endpoint, without applying the separate analytic-emitter self-intersection allowance. The scatter history used by area-light MIS carries its associated local offset.