ADR-0026: The liquid — a sea is a sheet, a valley is a strip, and a world is drawn in families

Status: accepted · 2 Sep 2026 · amended 3 Sep 2026: the bake's second pass carries relief, so a generated sphere shades its mountains

Context

ADR-0019 made the ground a geology and ADR-0021 took it below the canonical floor, and every generated world came out of both the same two colors: a rocky one in the class's brown and an icy one in the class's gray, with a sea — where the generator drew one — painted onto ground clamped flat at the datum. A shore seen from a landed ship was the seabed's own shape wearing blue. A world at 900 K had an ocean. Nothing ran downhill anywhere, and nothing grew.

The terrain plan deferred river networks to a drainage graph and flora to authored biomes, both correctly; what it did not say was how much of a world's look is the liquid rather than the rock. The brief for this phase named four things — a shoreline, river valleys, water that reflects and refracts, and color that is not brown and gray — and one constraint: the frame at the tail of the planet scale was 20–30 fps, and on a retina window 9.5.

Decision

A sea is a liquid the ground temperature admits. liquidKind names three — water between 238 and 395 K, hydrocarbons around a hundred kelvin, magma above the basalt solidus — and makeSurface reads the sea draw against it: the draw is still taken in its place in the stream, so SYSTEM_ALGORITHM does not move, and a datum on ground outside every window is dry. Thirty of the fifty-four seas within twenty light years sat on ground between 400 and 1,200 K, and fourteen remain. The grammar gains liquid, drainage and biota, each gated on air as well as temperature, because a puddle in a vacuum boils on the spot.

A valley is the zero-level strip of a warped noise. valleyField is 1 − |n| · sharpness over a three-octave fBm bent by a warp, and the strip where a noise crosses zero is a network of closed curves at every octave: it branches, it meanders where a finer octave bends the crossing, and it never ends in the middle of a plain. drainageCarve cuts a V inside a shallow floodplain into the landform the plates and the swell made, capped at 13% of the budget and — smoothly, through 1 − e^(−x) — at 85% of the ground's height above the drainage datum, so a valley shallows toward the shore and its floor meets the sea at the datum whichever way it ran to get there. Tributaries are the same construction at 3.1× the frequency on their own seed. Nothing here knows which way is downhill; a network that drains is the graph the plan still defers, and what this buys is the look at every scale the mesh reaches for the cost of a stateless field.

The coast is a remap. coastRemap pulls the landform toward the datum over a band either side of it — a shelf a fifth as steep under the water and a plain two fifths as steep behind the beach, C¹ where the band lets go, with a kink at the waterline itself, which is what a beach is. The band is a tenth of the hypsometry share, the scale the datum is set on: 267 m on Gliese 908 IV.

The cover grows to six channels in eight bytes. wet marks the floored riverbed; biota what grows — the biosphere's window read against the same latitude term the frost uses, a treeline, a rainfall, a province-scale patchiness. A vertex attribute is four lanes, so the record is one InterleavedBuffer with an attribute object per name at its own offset, through groundWear.ts for every geometry that wears the material, warm-up dummies included. The two spare bytes are where the canonical slope the deposits still want will go.

The heightfield is the seabed, and the sea is a sheet over it. drawnGroundElevation leaves the sea clamp off; drawnElevation keeps it for the readers that stand on the water rather than look through it, the stance and the detail-floor search, and for the heightfield of a body that gets no sheet — a mapped one, whose photograph is its sea — which the request says with a seabed flag. buildPatch emits a second grid for any patch the sea reaches — the datum sphere on the patch's own vertices, with the water depth over each and a morph target for both — and render/water.ts draws it: Fresnel between what comes up through the water and what reflects off it; the seabed read from the frame the opaque pass just drew, displaced by the wave slope and attenuated by e^(−absorption · path) along the refracted ray, so a shelf is turquoise and the deep is the liquid's own color; the sky and a two-lobe sun in the reflection; a swell and a chop; foam where the sea is shallower than a wave is high. Magma is the same graph with a glow. A river is painted on its bed rather than drawn as a sheet, because a sheet per valley is a mesh per valley.

A world is drawn in families off its own seed. appearance.ts replaces the class color with eleven rock families and five ice ones weighted by the ground temperature — the iron oxides, the basalts, the feldspars, olivine, sulfur, the tholins — with a little value and chroma of the world's own; seven haze compositions gated by temperature, from Rayleigh blue through dust, sulfuric glare, tholin orange and methane teal; six photosynthetic pigments, chlorophyll weighted as the common answer; and a LiquidAppearance with the deep color, the per-meter absorption and the glow. Forked from the surface seed so every other draw on the body stays where it was. The families are more saturated than the class means were on purpose: a generated world is drawn from this at every distance, and its deposits contrast against it.

Every per-pixel octave is a fetch of one baked texture, and the normal is the fetch's gradient. noiseTexture.ts evaluates a periodic gradient lattice once into a 128³ four-channel 3D texture — the value and its analytic gradient, four texels a cell over thirty-two cells — and fbmFetch samples it at each octave's scale. The macro, micro and grain bands of the ground and the swell and chop of the sea are five fetches where they were eight lattice evaluations of eight hashes and eight dot products each, and the field is periodic by construction, which is the property the sub-meter bands needed anyway. The gradient is what makes the shading: a normal differenced from a trilinear fetch in screen space is constant across each texel and the grid showed as a moiré on the sea, where the fetched gradient is smooth. The ground's bump left Mikkelsen's screen-space construction with it. The octaves also sit inside branches on their own fades and on the quality lever: a noise multiplied by a zero fade was a noise evaluated.

The aerial veil's view leg is the lesser of two paths. The flat-atmosphere 1/μ is a statement about looking down from space; from a standing camera it put the ground forty meters away behind eleven atmospheres. The distance over a scale height takes over exactly where the orbital term stops being true, and above the eight-pixel gate the distance is hundreds of scale heights, so the seam with the disk is untouched.

The sphere wears the ground's own picture. render/orbitalBake.ts asks the shared Heightfields module for a body's ninety-six level-2 regions, builds them with buildPatch, and draws them through the ground material in its bake mode from a CubeCamera at the body's center — the reflectance into one cube target and a relief record into another, because an opaque node material writes an alpha of one whatever its opacity node says. The record is the mesh normal's slopes along geographic east and north as x / 2 + 1/2 with the sea mask in the third lane, which is the layout and the encoding the sphere already reads the archive's normal map in, so one decode path serves a bake and a photograph. The sphere samples both by its unit position and keys its ocean color and sun-glint on the mask as it does on a photographed body's. One graph draws the ground and takes its picture, which is how the seam rule holds for a bake at all: there is no second deposit stack to keep in step. Asked the first time a mapless solid body's disk exceeds a hundredth of a radian, ready a few frames later, kept four deep.

The surface has four levers, and they are named costs. render/quality.ts carries the refinement threshold, the ground's octaves, the sea's refraction and waves, and the rocks, as one persisted record the frame loop reads and a driving script can set. Not a ladder: each is one measured term, so a frame rate can be reported against the setting it was taken at.

Alternatives considered

A drainage graph. The right answer and a phase of its own: a per-region graph of flow directions with the valleys carved along it, which is what makes a network drain. The strip field is what a stateless per-sample function can do, and at every scale the mesh reaches it reads as valleys; what it cannot do is join them. Deferred with its seam named, as before.

Painting the sea on the clamped ground, better. Depth-tinted, with a Fresnel term and a wave normal. It cannot make a shoreline: a shore is a flat surface meeting a slope, and a mesh clamped to the datum is the seabed's shape in blue. Rejected on the first plate from two meters.

Reading the scene depth for the water's path length. More exact than the vertex depth — it would see the ship's hull in the water — and a second texture the sheet would read every pixel. The vertex depth is the seabed's depth, which is what the absorption is about; the hull can wait for the water to matter to gameplay.

A screen-space reflection of the land. The one thing missing from the sheet. A march through the depth buffer per pixel of sea, on the frame this phase is trying to make cheaper. Named in the plan.

Drawing the seabed's detail under deep water. It is drawn: the sheet is transparent, so the seabed under it is shaded in full and then attenuated to nothing. A branch on the depth would skip it; measured, the sea's own terms were the larger cost and the levers cover the rest.

A color wheel. A hue drawn uniformly makes every world the same unlikely pastel; the families are the surfaces that exist.

Keeping the octaves as lattice evaluations and cutting their count. Fewer octaves is less detail; a fetch is the same detail for a tenth of the arithmetic, and the texture is the seam an authored material set will use.

Consequences

Terrain is algorithm version 3. Every wet world's ground moved and every hot world's sea went, and drawnDivergence is unchanged. The kernel ports all of it: terrainBands.gpu.test.ts isolates the drainage and the coast over the hypsometry alone, and the worst gap is 9.8 × 10⁻⁶ of the budget on Earth at level 0 — a warped fBm raised to the sixth power in float32 — against a bound of 2.5 × 10⁻⁵.

The frame at a retina size, measured at 1920×1200 over a device pixel ratio of 2, standing two meters over the sea on Gliese 908 IV with 1,227 patches at level 17:

At two kilometers over the same shore with 1,232 patches: 17.9 before, 19.1 branched, 15.3 at the end. A fetch of a four-channel texel costs about four times a fetch of a one-channel one at the texture unit whatever the texture's size — 96³ and 64³ measured within a frame of 128³ — so the gradient is paid for by fetching fewer octaves: the macro band's third, the micro's second and the grain's third, which was a fetch a pixel over the whole near ground for nine centimeters the chop under it already carried. The base cost with every octave off is what is left, and it is not in this record: the deposit stack, the aerial veil, the sky shell and MSAA at nine million pixels, which a timestamp query per pass is the instrument for. Run-to-run variance across this table is about two frames a second.

The fixture's plate world lost its plates. Proxima Centauri II drew a sea on ground at 491 K; read against its temperature the sea goes, and with it the ocean that weakens a lithosphere into plates. geology.test.ts finds the most-plated solid body in the fixture rather than naming one.

A generated world is itself from orbit. Measured against the streamed ground either side of the relief gate, at 650 and 1,100 km over Gliese 908 IV: the same lakes in the same places. A bake camera inside the shell sees the ground's winding backwards, so the bake's index is the patch's turned over rather than a second cull mode on the material. The relief the bake did not carry at this phase — the sphere's normal-map path was fed by the archive alone, so a generated disk shaded as a smooth sphere — is the second pass amending this record: the mesh normal's slopes east and north in the archive's own encoding, with the sea mask beside them.

The bake's twelve draws are one frame's stall. Ninety-six tiles of the producer, ninety-six patches built on the main thread, and twelve renders of them, in the frame the tiles arrive: a bake is a hitch of a few tens of milliseconds once per body. Spreading the build across frames is the plain next step if the hitch is felt.

The harness cannot draw the sea. viewportSharedTexture copies the framebuffer once a frame, ending the render pass and beginning it again, and the harness has neither a swap chain to copy nor a pass that survives being re-begun around its single draw. The frame read is a build option; materials.gpu.test.ts compiles the graph without it, and the copy is exercised where it runs.

The rocks are worth twelve milliseconds at a two-meter stance, drawn with frustumCulled off at the field's whole population. They have a lever; culling them is the next thing to measure.

Related

• ADR-0019 — the landform the valleys are cut into
• ADR-0020 — the cover this extends, and the seam rule the veil's second path had to respect
• ADR-0021 — the drawn field the seabed is
• ADR-0023 — the kernel that ports the new bands
• Content § biomes — the pigment's place in the biome table
• The terrain plan — what is still open