A full far ground without drawing it

Question: In Day Hike, a first-person hiking game in Babylon.js, a still taken on a trail under a closed conifer canopy shows a full foreground, ferns, grass blades, tufts and leaf litter, out to about 25 m. Past that, between the trunks, the ground is a flat, even grey-green with nothing standing on it. The trunks meet it in clean lines, the trail crosses it as a pale ribbon, and the whole band reads as a game floor rather than a forest floor. What cheap GPU tricks make that far ground read as full of grass and ground cover, at a cost far below drawing real blades there?

Short answer: the far ground is bare because every layer that makes the foreground full ends between 18 and 40 m, and what the terrain shader does past that was tuned for open meadow, not for ground under trees. The ground can carry most of the impression on its own: a cover colour fitted to what the near grass actually renders at, a clump pattern that shades with the sun, and less of the grazing sky reflection that a smooth floor gets and a grass canopy does not. That is a few dozen arithmetic instructions in a shader the game already runs, an estimated 0.1 to 0.3 ms at 4K. Paint cannot stand up off the ground. For the fuzzy line where cover meets trunks and the trail, the documented answer is sparse vertical cards that widen as they thin, which the game's card and culling code can already draw. Shells fail at the 1 to 3 degree angles a walker sees this ground at.

This is the complement of the September note on near-field fullness [1], which recommended that the terrain carry the far sward. The game is public at game-dayhike.

From a 1.6 m eye, ground 30 m away is seen 3 degrees above edge-on, and ground 100 m away under 1 degree. At those angles "full" is whatever stands up: a tuft 0.3 m tall at 40 m hides several metres of ground behind it, while a 2 m texture tile is on its coarsest mips and its normal map averages to flat. So a bare far ground is first a geometry problem and second a shading one: the ground that shows must have the colour, value and break-up of the cover that would hide it.

The fields that make the foreground, on the high tier:

Under a closed canopy the grass cover sits at its floor of 0.75 of open ground, and each card's albedo is multiplied by 1 − 0.5ρ, ρ being the forest density. The meadow cards there come at about 1.1 to 1.9 per m² and the grass-class tufts at about 0.07 to 0.11 per m², so across 28 to 40 m the number of things standing on the ground drops more than tenfold. That is the edge in the still. The low tier draws every class at 0.6 of its radius, so there the edge comes at 24 m.

What the terrain does with that ground:

• Colour. Baked per vertex: a 34 m mottle between forest floor (0.11, 0.09, 0.06) and grass (0.09, 0.15, 0.06), pulled toward a dark crown green (0.045, 0.085, 0.05) by up to 0.85ρ, and toward a tan needle bed by 0.75 of the litter weight. Five tiled textures are multiplied over it, each divided by its own mean so it adds variation and not hue.
• Detail. The textured relief fades out over 80 to 140 m, the finer grass detail over 8 to 20 m, and a lush-to-dry macro tint (18 and 6 m wavelengths) with the relief.
• The sward pull. Inside the blade reach the floor is pulled toward a dark thatch colour, keyed on the per-vertex ground cover. It is gone by 18 m.
• The horizon tint. From 35 to 90 m the floor is pulled up to halfway toward a tuft colour (0.18, 0.22, 0.11), weighted by the grass texture's share. Under trees that share is small, because litter turns the ground toward the forest-floor layer, so in the forest this tint moves the colour by a few percent.
• Reflectance. Grass and forest floor have roughness 1 and half the usual dielectric F0. But the compiled terrain stages use Babylon 9.18's legacy energy-conservation path, in which the grazing reflectance F90 is the material's specular weight, 1, whatever F0 is. At 1 to 3 degrees the Fresnel term is near its grazing end, so the far floor reflects a share of the grey sky that a real grass canopy, whose blades shade each other, would not. How much of the grey in the still this is has not been measured.

The per-vertex data the far ground would need is already there: ground cover, litter and canopy density ride on every clipmap vertex, at 1 m spacing out to 64 m and 2 m to 128 m.

For scale on cost: at native 1080p on the high tier the blades in view cost 0.88 to 0.94 ms for an 18 m disc. Carrying blades to 60 m covers eleven times that area. The grass-class tufts cost 0.43 ms unculled and 0.11 ms culled; the far meadow cards 0.44 ms for 8,700 cards. On the fragment side, the grass floor's hex tiling, six to twelve extra texture fetches and nine to eighteen sine hashes per grass fragment, measured about +3 ms at four times the pixels.

Every published grass level-of-detail chain ends with the terrain carrying the sward. Ghost of Tsushima's last tier replaces "entire grass field with a single texture on terrain" [2], and its blades widen as they thin [3]. Horizon Zero Dawn's grass has three LODs, scales its animation down over distance and "vertically push[es] the vertices of the mesh down" [4], which is what Day Hike's far sink already does. Horizon colourises most vegetation from a 512 by 512 world-data texture of erosion, flow and closeness to water [4]; Day Hike's macro tint is the same idea. Forbidden West's foliage work concerns cost, a visibility buffer and compute shading for alpha-tested geometry, not the far look [5].

Frostbite's 2007 terrain draws undergrowth only near the player, in 16 m cells, and its grass "blends in with the terrain by compositing its color map with the diffuse color from the actual terrain grass shader. Lighting uses the normal of the heightfield to look the same as the terrain" [6]. That is the hand-off rule: the card and the ground under it share colour and lighting, so the card's disappearance changes little. Unreal places grass from the same painted landscape layer the ground material samples [7] and can feed the landscape's colour to the grass through a runtime virtual texture [8]. Unity culls detail meshes at a "Detail Distance" [9] and past a "basemap distance" draws terrain from "a precomputed low res basemap" [10]. Rockstar has not published Red Dead Redemption 2's ground cover; its rendering talk covers the atmosphere [11].

Smaller renderers say the same. A Godot series ends in an impostor plane with no geometry that replicates the blades' world-space colour noise and wind, about 2 ms for the whole field on the author's machine [12]. Helio goes to "terrain material only" past 120 m with 2 m blend bands [13]. Boulanger, Pattanaik and Bouatouch divided a field into three regions: instanced geometry near, vertical volume slices in the middle, horizontal slices far, with a density map deciding blade by blade [14], [15].

4.1 A cover colour fitted to the rendered near field

How it works: where the cards are already half gone, the terrain pulls its albedo toward the colour the near cover renders at, keyed on the per-vertex cover. The target is neither the dirt's colour nor the card texture's mean but the near crop as rendered: cards, the ground between them, the canopy shade and the root tint. That is a number to fit from stills, as the game's horizon tint was fitted ("the mean albedo a lit tuft card reads at, measured against the far field in the running game").

For this game: the designed but unbuilt far-sward pull (cover-keyed, 24 to 30 m) is the start. It needs two things for the forest. A litter colour mixed in by the per-vertex litter weight, because under trees the near field is ferns and tan leaves as much as grass. And the cards' own canopy shade, 1 − 0.5ρ, on the target, or under a closed canopy the far paint is twice as bright as the cards it replaces.

Cost: two smoothsteps and a few mixes per terrain fragment, no texture fetch. The far band takes the near field's hue and value, so the 30 m line weakens; texture is 4.2's job.

4.2 Clumps that shade with the sun

How it works: real cover at 40 m is a field of light and dark clumps, tussocks lit on the sun side and pools of shade between them. A value noise at two wavelengths, about 0.8 m for tussocks and 3 m for patches, perturbs the normal through its analytic gradient [16] and darkens the troughs as micro-occlusion. The clumps then catch low sun on one side and lose it on the other, and move with the time of day where a painted mottle would not. Ghost of Tsushima drives clump height, colour and facing from Voronoi cells [2]; a smooth noise does the same job at this distance for less.

Two cautions from the code. The far-sward design's mottle is constant per 1.5 m cell, which on the ground would show as a grid of squares at 40 m. It needs an interpolated noise. And any procedural pattern must fade where its cells shrink below two pixels, by the band-limiting rule noise × smoothstep(1.0, 0.5, w) with w from fwidth [17], or it shimmers at 100 m.

Cost: about 8 lattice hashes and 20 to 30 further instructions per far fragment, branch-gated to the band. Under a closed canopy, where light is mostly ambient, the occlusion mottle carries most of the effect; in sun the normal does.

4.3 Grazing sky reflection and a canopy-like response

A flat microfacet floor reflects more as the view turns edge-on. A grass canopy seen grazing shows blade sides and self-shadowed depth instead, and its reflectance peaks with the sun behind the viewer, where blades hide their own shadows: the "hot spot" [18]. Cloth renderers model fibre fuzz with a sheen lobe that dominates at grazing angles [19]; Babylon's is material-wide and cannot follow distance or cover without plugin code.

For this game: scale the specular weight, which in the compiled path sets F90 as well as F0, down by the far-cover weight through the same regex rewrite the terrain already uses for roughness and F0. Then add a small brightening toward the backscatter direction and a darkening toward a grazing, front-lit view. Cost: a few instructions. The first half can be tested before any code: setting the terrain material's metallicF0Factor to zero at run time is a uniform change, and a crop of the far band with and without it says how much of the grey is sky.

4.4 Macro variation

The macro tint fades with the 80 to 140 m relief and is weighted by the grass texture's share, so it is missing exactly past 80 m and under trees. Keying it on cover and running it to the fog costs nothing new: the noise is already evaluated. Roughness break-up is moot at roughness 1.

Paint cannot occlude a trunk's base. What makes ground look covered at a grazing angle is the irregular line where cover meets anything standing on or crossing it.

Shells. Copies of the ground offset upward, each hashing and discarding fragments, read as fur from above [20], [21]. At grazing angles NVIDIA's reference says "the shells become too transparent and their gaps become visible", which is why fur adds fins [22]. Here, a 1 m noise cell at 50 m seen at 1.8 degrees, through the game's 80-degree lens, projects to about 25 pixels wide and under 1 pixel tall at 4K, so a shell reads as horizontal dashes. Shells suit the 0 to 4 m ring the September note named, not this one.

Ray-marched slices in the ground shader. Habel, Wimmer and Jeschke trace a grid of implicit vertical grass slices inside the terrain's fragment shader, with front-to-back compositing, four iterations sufficing, at 140 fps at 1024 by 768 on a 2006 GPU, against 90 fps for real billboards [23]. It gives true parallax for flat cover with no geometry. It draws nothing above the carrier surface, though, so trunks keep their clean bases, and it costs several texture reads per pixel. The game also declined parallax on grass near the eye because it drags the texture sideways as the player walks; at 40 m that drag is under a pixel, but the cost is not.

Screen-space fuzz and horizon cards. A post pass cannot find the ground-to-trunk contact, both being at one depth; a card ring at a fixed distance breaks on relief.

Trunk-base grounding. The cheapest silhouette is on the trunks. Past 25 m, darken and tint the lowest 0.3 to 0.5 m of bark toward the far cover colour with a noisy upper edge, so the trunk seems to stand in something. It is fragment arithmetic on trunk pixels only. Without discarding pixels the bark stays opaque and keeps early depth rejection.

Sparse vertical cards, wider as they thin. Vertical slices are the right primitive at a grazing angle; that is Boulanger's middle region [14], [15]. Ghost of Tsushima's policy is a constant count per tile as tiles double in size, "3 out of 4 blades are dropped" per step [2], with the survivors widened [3]. For Day Hike, a renderer-only fill across 28 to 80 m, keyed by a per-instance hash so the survivors of each thinning are fixed and nothing pops, using the meadow card's 20-vertex LOD, widened continuously in the vertex stage rather than rescaled at each rebuild, and run through the existing frustum filter, which keeps 19 to 26 % of grass instances at the measured poses. Starting at 0.5 per m² at 28 m and thinning fourfold per doubling of distance, about 2,600 instances cover the band and 500 to 700 survive the view: under 0.1 ms of vertex work by the far meadow cards' measured cost, plus alpha-tested fill in a thin screen band. These cards give what paint cannot: a broken line against trunks and the trail.

Baked billboards. The forest's far trees are one alpha-tested quad per species, baked at run time to 256 by 256 under the sky's light, thin-instanced to 2 km. The same bake could make a grass atlas, but a lit bake keeps the light it was baked under, which grass at 50 m cannot hide as a crown at 500 m can, and a 20-vertex card is nearly as cheap as a quad. An albedo-only bake, lit at run time, is the fallback if the card texture reads wrong at this distance.

Dither-free fades. Dither bands cost more the wider they are. Sinking cards into the ground, as Horizon does [4] and the meadow's far band already does, is the dither-free fade at a grazing angle.

One lighting model across the hand-off. The cards are lit with a wrapped diffuse (wrap 0.35) and a normal forced toward the viewer; the terrain is lit Lambertian. In shade or low sun the cards read brighter on their dark side than the ground beside them. Frostbite's rule [6] applies: weight the terrain's per-light diffuse toward the same wrap by the far-cover weight, through the per-light regex the foliage already uses. Cost: a few instructions per light.

Translucency. Horizon's grass glows when backlit, from the light behind it, the view-light angle, albedo, thickness and occlusion [4]. Far cover seen toward a low sun should do the same.

Shade between clumps. At 30 to 100 m the shadow cascades are coarse and the ground has no self-shadowing below its vertex spacing; 4.2's trough occlusion stands in, matched to the near crop's luminance within the 0.8 to 1.25 ratio the September measure set.

No source gives a frame time for a terrain-only far-cover shader, nor for the reflectance cut. The estimates here scale the game's own measurements, the hex tiling's +3 ms at four times the pixels and the far cards' 0.44 ms, and need the game's paired method at the canopy and meadow poses. How much of the far grey is sky reflection, rather than fog and palette, is open; it is a one-uniform test. And whether paint holds up on a walk toward it, where it must turn into cards, can only be judged walking.

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