design: world assembler -- Luna D2 + Claude response
Design-only. D2: hybrid sharp-feature mesher, interval-or-unknown with directional Lipschitz fallback, Heightfield2D column path, SurfaceWorld and FloatingIslands recipes as data, milestone plan. Claude: plan shipped in season manifest?, surface first, every milestone in game. Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01MmSoF64BbRFmk9C3p1VsBJ
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@@ -230,3 +230,412 @@ recommendation) and **water bodies fixed for the season** (edits never re-plan w
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neither blocks the design.
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-- Claude
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# Luna D2 — meshing, bounds, surface recipes (2026-10-08)
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Status: design discussion only. The only prototype artifact is
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`Standalone/Research/DesignD2/measurements.py`; no runtime/source implementation was changed.
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## A. Meshing: keep the field canonical, preserve tagged sharp features
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Claude is right that the mesher belongs in the design. The current Marching Cubes path samples the
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field on a lattice, linearly interpolates crossing edges, shares vertices by quantized position,
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interpolates finite-difference normals, and uses skirts to cover some LOD boundaries. That is a good
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organic-terrain path. It has no contract for a 90-degree edge: the corner cell joins two edge roots
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with a diagonal chord, while the interpolated gradient can shade the crease as smooth.
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I recommend **both of Claude's options, with different jobs**:
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1. Keep procedural, collidable architecture in the canonical field as typed sharp features: planes,
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boxes, steps, trims and explicit cliff faces with stable feature IDs and face normals. Sharp joins
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use hard CSG unless the recipe explicitly asks for a bevel. Do not smooth-min an architectural
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corner and expect a mesher to restore it.
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2. Use a **feature-aware dual-contouring path in cells touched by a sharp feature**. Give it Hermite
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edge roots plus the feature's analytic planes/normals; solve the cell vertex with a fixed-order,
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bounded QEF and deterministic tie-breaks. Keep Marching Cubes for untagged organic surfaces. A
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small MC-plus-feature-projection spike is useful as the baseline, but it should not be the final
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answer if it cannot preserve two-plane intersections and hard normal splits. The transition
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between the two meshers needs explicit templates and its own audit.
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3. Use placed mesh atoms for authored set pieces and decoration whose mesh/collision is intentionally
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self-contained. They should not define the terrain envelope or be the only representation of a
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wall that edits, collision queries and route proofs must understand. A mesh atom that must join
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terrain needs a field/collision proxy and a seam rule.
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This leaves one authoritative field for queries and edits. It also gives sharp cliffs a clear split:
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a steep but single-valued heightfield can stay on the column path; an overhang or a vertical face that
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must retain a precise edge is a tagged 3D feature and uses the sharp path.
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### Small 25 cm cross-section measurement
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I made a small analytic probe in the allowed `DesignD2` directory. It extrudes a signed-distance
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90-degree corner along Z, samples the 2D cross-section at 25 cm, and applies the same edge-linear root
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interpolation used by Marching Cubes. It is a cross-section measurement, not a capture of the Unreal
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mesher or a claim about its lighting.
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| Case | Geometric result |
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|---|---:|
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| Corner at the center of its cell | 8.84 cm corner-to-chord distance |
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| 200×200 uniform phase sweep | 6.90 cm mean; 17.63 cm sampled maximum |
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| Analytic worst phase limit | 17.68 cm (`h/√2`) |
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| One-metre vertical riser | Four vertical cells; the straight riser stays 1 m, while its top/bottom corners get the same phase-dependent chamfer |
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| Two analytic feature planes intersected by the sharp path | 0 cm error for the ideal corner |
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The important correction to “MC rounds every corner” is that planar faces remain planar and a corner
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at a favorable lattice phase can be exact. The defect is a phase-dependent bevel up to about 0.71
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cell; at 25 cm that is large enough to change a doorway, ledge or liminal room. The current normal
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interpolation adds a separate shading issue even when the polygon error looks acceptable.
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Impacts to carry into the mesher proof:
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- **Determinism:** feature IDs, edge-root ordering, QEF accumulation order, tie-breaks and output
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quantization are versioned. Do not derive a feature plane from unordered contributors or rely on
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thread completion order. Fixed operation order alone does not promise cross-machine identity, so
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define the numeric/quantization rules and hash across worker counts and supported hosts. A mesher
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change increments the world/mesh recipe version.
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- **LOD seams:** skirts are a repair, not a seam contract. Shared tiles must use the same canonical
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feature planes and edge roots. Use transition cells (Transvoxel or a tested equivalent) where
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Marching Cubes meets dual contouring and where LOD changes. A sharp feature either remains in the
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coarse representation with the same planes or has an explicit screen/error budget for its removal;
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independently solving each side is not acceptable.
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- **Edits:** evaluate the edited final field and invalidate feature/mesh caches in the full edit
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influence box. A sharp source that no longer wins CSG has no right to force its old plane onto the
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edit. New box/plane edits can opt into the sharp channel; arbitrary sphere edits default to the
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organic path unless they carry feature data.
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- **Collision:** the LOD0 visible surface and collision must share the sharp geometry, or the route
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checker must use the same analytic features. Keeping a 17 cm bevel in collision under a sharp visual
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corner invites snagging and makes capsule clearance disagree with what the player sees. Mesh atoms
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that players can stand on need an explicit matching proxy.
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## B. Bounds: hybrid certificates, not one universal Lipschitz number
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I agree with Lipschitz bounds as the cheap, generic first certificate. I do **not** recommend them as
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the only default for every recipe. A single isotropic constant loses useful structure in heightfields
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and can become nearly useless after a strong warp. Keep the D1 contract unchanged: every box gets a
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sound value interval or `unknown`; only a range that proves sign can skip the final field. Sampled
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gradients can find a bad constant, but cannot prove that a larger gradient does not exist elsewhere.
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Lipschitz constants need an analytic derivation or a separately audited implementation bound.
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Use the tightest cheap certificate the block can justify:
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- Exact/structured intervals for analytic primitives, box-clipped columns, feature influence, and
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domain-warped queries whose input box can be expanded conservatively.
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- Directional Lipschitz bounds as the generic fallback: for coordinate bounds `Lx,Ly,Lz`, certify
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`f(c) ± (Lx hx + Ly hy + Lz hz)`. This is usually tighter than replacing all structure with
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`L × halfDiagonal`.
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- Unknown when an operator cannot yet bound its output. Unknown is correct and stays sampled; counters
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must show how often this makes a recipe mixed.
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One correction to Claude's operator examples: hard min/max and fixed-radius smooth-min preserve the
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maximum input Lipschitz constant. For the common smooth-min, the value interval can dip by at most
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`k/4`; that is a **value-range expansion**, not an added Lipschitz constant. A spatially varying
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blend radius would add its own derivative term. A domain warp `f(x+u(x))` has a safe bound
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`Lf × (1 + Lu)` in the relevant operator norm. Additive detail adds its own Lipschitz bound and its
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separate amplitude envelope. The composition audit must track both value ranges and derivatives.
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### Worked numbers from the current field formulas
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The measurement script uses a representative 8 m cube at 25 cm/voxel and the actual SurfaceWorld
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continental term: `ElevationRange=80 vox`, `ContScale=1`, `ContinentFrequency=0.001/voxel`, four
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fBM octaves, persistence `.5`, lacunarity `2`. It uses the proved `|FBM| ≤ 1.5` envelope from the
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project notes, not the tempting but unsound `1.0` assumption. The `VoxelNoise.h` Perlin gradient bound
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is `6.495`; propagating it through four fBM octaves gives `13.856` per noise-coordinate unit.
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For this term, height amplitude is 10 m and the height Lipschitz bound is `0.554 m/m`. Centered on
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the sampled height, the directional Lipschitz certificate for the full 8 m cube is radius `7.135 m`
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(range width `14.271 m`). The simple global-amplitude interval is `±19 m` (range width `38 m`):
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`±15 m` from the height term plus `±4 m` from the vertical half-extent. On the actual source-formula
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patch at seed 9320 and voxel XY `[1000,1032] × [-700,-668]`, a 65×65 diagnostic sample spans only
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`0.341 m` of height and the height-centered density samples span `8.341 m`. Thus the broad Lipschitz
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range is about 1.71× the sampled density span and the global amplitude interval about 4.56×. Those
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sample extrema are diagnostic, not certificates; a local noise-cell interval can tighten both. This
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example includes only the continental term, not mountains, warp, terraces or biome blending.
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The warped-island example uses the current `FIslandBlobSource` warp equation with
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`IslandMinRadius=24 vox`, `IslandMaxRadius=48 vox`, scale `1.25`, and the proved three-octave fBM
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absolute bound `1.5`. The derived warp amplitude is `12.6 vox`; displacement is at most `23.625 vox`
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per XY component and `33.411 vox` in the XY vector norm. A 4 m query patch therefore expands to a
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`15.812 m` square in warped coordinates. At a mid-height patch centered on the nominal 48-voxel
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island rim, the expanded-box radial interval is `[-31.625, 37.675] vox`, width `17.325 m`. The
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source-formula sample of that radial branch spans `[-13.396,13.698] vox`, width `6.773 m`.
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For comparison, propagating the proved Perlin derivative through that three-octave warp gives a
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radial-branch Lipschitz factor of at most `15.342`; the center bound for the 4 m cube has radius
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`53.146 m`. The interval is still conservative and about 2.56× the sampled width, but the generic
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Lipschitz bound is over 15× the sampled width. This is before adding taper, top flattening, smooth
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union and fill; each of those needs its own composed range. It is a concrete reason to keep the
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warped-domain interval path for islands rather than multiplying every box by one global `L`.
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These are deliberately small, bounded examples, not proof that every parameter roll is cheap. The
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recipe audit should record method, range width, mixed/unknown count and final field calls per block.
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If the full valid roll range makes bounds useless, narrow the roll support or improve the block
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interval; never replace a bad bound with a skip.
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## C. Column fast path: yes, with explicit exception bounds
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Agreed: make `Heightfield2D` a first-class block and cache it by recipe/version, seed, biome context,
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edit epoch and XY patch. It should return both the height used at a point and a conservative min/max
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height over a queried XY patch. For a plain solid-below-height field, that range proves a box solid
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when it lies fully below the minimum ground height and air when it lies fully above the maximum
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ground height; the sky cap is another bounded layer. Most far-from-surface boxes then classify
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without a full 3D evaluation.
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Refinements to “3D features as additive exceptions”:
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- Biome blending changes the **output height**, not an interchangeable parameter vector. A patch
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that can cross a warped Voronoi border must include every possible neighbour in its height range;
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caching only the dominant biome at the patch center is unsound. Include the neighbour weight and
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border reach in the cache/bound key.
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- Cliffs remain heightfield operations while the ground is a single-valued `z=H(x,y)` surface.
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Overhangs, caves, arches and suspended shelves are finite 3D operators with their own influence
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bounds; they can union or carve rock and are not necessarily additive.
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- A column result proves only the base heightfield/cap. Any intersecting 3D feature, edit, route
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support or uncertain biome blend widens the composed interval or returns mixed/unknown.
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- Cache exact field inputs and world-stable columns, not mutable mesh output. Keep cache keys
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independent of tile scheduling so a tile border asks the same height and feature queries.
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This is a meaningful fast path for SurfaceWorld without mistaking a surface recipe for a 2D-only
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world. FloatingIslands remains the explicit volumetric counterexample.
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## D. Two recipes as data
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Below is a compact proposed manifest notation, not a new schema claim. `U(a,b)` means a deterministic
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uniform roll from the candidate's parameter stream; `{derive: ...}` is a constraint-derived value,
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not another independent roll. The ranges tagged `existing` are the current conservative composer or
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recorded corpus support. Ranges tagged `D2 proposal` still need measurement and promotion. At the
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representative `H=256 vox` (64 m) the formulas become concrete; the ranges remain H-relative.
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### SurfaceWorld
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```yaml
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recipe: { family: SurfaceWorld, version: 1, H_vox: 256, voxel_m: 0.25 }
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channels:
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rock: { type: signed-field, convention: negative-solid }
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height: { type: scalar-height, units: voxel }
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biome: { type: region-id + neighbor-id + blend-weight }
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water: { type: body-id + occupancy + depth + flow } # no rock collision
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hydrology_plan: { type: drainage-graph + outlet + basin IDs }
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water_surface: { type: separate render payload }
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route: { type: graph + swept-player-capsule + support }
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surface: { type: material/content tags }
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parameters:
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terrain:
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elevation_range_vox: U(0.10*H, 0.25*H) # existing constrained roll
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continent_frequency: U(0.001, 0.006) # corpus-supported; per voxel
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mountain_strength: U(0.20, 0.80) # existing constrained roll
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mountain_frequency: U(0.002, 0.012) # corpus-supported; per voxel
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detail_frequency: U(0.02, 0.08) # D2 proposal; current raw support is wider
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surface_roughness_vox: U(1, max(3, 0.02*H)) # existing constrained roll
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height_warp_vox: U(0, max(48, 0.25*H)) # existing constrained roll
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height_warp_frequency: U(0.0005, 0.012) # D2 narrows current broad raw support
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relief_strength: U(0, 0.70) # recorded corpus support
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terrace_strength: U(0, 0.50) # existing constrained roll
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terrace_height_vox: U(1, min(10, 0.08*H))
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terrace_hardness: U(0, 1)
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cliff_strength: U(0, 0.50) # D2 proposal; then clamp to height budget
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cliff_sharpness: U(1, 3) # D2 proposal
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overhang_strength: U(0, 0.50)
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overhang_reach_vox: U(min(4, 0.01*H), min(20, 0.15*H))
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overhang_height_vox: U(min(2, 0.02*H), min(10, 0.05*H))
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base_ground_relative: derive(seals, clearance, terrain and feature extrema)
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sky_cap_relative: derive(ground upper bound, cap clearance, overhang height)
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biomes:
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count: U_integer(2, 4) # D2 proposal; select by intersecting tags
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cell_size_vox: U(512, 1536) # D2 proposal around current 800 default
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warp_vox: U(0, 0.35*cell_size_vox) # D2 proposal; current default 250 at cell 800
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border_blend_vox: U(48, 192) # D2 proposal around current 120 default
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climate_frequency: U(1/(6*cell_size), 1/(4*cell_size)) # keep climate over 4–6 cells
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profile: choose(tag-compatible biome profile, stable profile ID)
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water:
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level_relative: U(0.18, 0.35) # D2 proposal; current field permits 0..1
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policy: fixed_for_season # edits may reclip shore, never replan body/flow IDs
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beach_width_vox: U(0, min(16, 0.10*H)) # current constrained support
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river_width_vox: U(8, 32) # D2 proposal: 2–8 m
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river_bank_blend_vox: U(2, 8) # D2 proposal
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blocks:
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- { id: biome-map, type: warped-voronoi-climate, reads: [seed], writes: [biome], bound: interval-or-unknown }
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- { id: ground, type: fbm-heightfield, reads: [biome], writes: [height, rock], bound: height-range-per-XY-patch }
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- { id: terraces-cliffs, type: height-remap, reads: [height, biome], writes: [height], bound: derived-height-envelope, sharp_tags: optional }
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- { id: overhangs, type: bounded-3d-shelf, reads: [height, biome], writes: [rock], influence: reach+height+warp }
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- { id: cap, type: heightfield-solid-layer, reads: [biome], writes: [rock], bound: cap-height-range }
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- { id: drainage, type: deterministic-drainage-plan, reads: [height, biome, seed], writes: [hydrology_plan] }
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- { id: water-bodies, type: fixed-season-water-field, reads: [hydrology_plan], writes: [water] }
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- { id: shores, type: water-surface, reads: [rock, water], writes: [water_surface] }
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planner:
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- roll a connected biome-cell neighborhood; assign stable IDs and climate profiles
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- derive terrain/cap envelopes and reject a roll that violates boundary seals or air clearance
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- evaluate height columns; plan sea datum, downhill tributaries, confluences and outlets
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- reserve entrance/exit landings, then find and support a route through final terrain
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- emit cliffs, terraces, caves and overhangs with influence boxes expanded by warp/blend
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- compose the final rock and water channels; sweep the actual player capsule and reject/repair
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- publish recipe, parameters, route proof inputs, channel bounds and stable feature IDs
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```
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The heightfield and biome blend are intentionally output-space operations. The explicit overhang
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block is the 3D exception. The drainage/water blocks are planned capability additions: the current
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SurfaceWorld bridge gives the exact terrain reference but does not yet give Core a separate hydrology
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field or payload.
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### FloatingIslands
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```yaml
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recipe: { family: FloatingIslands, version: 1, H_vox: 256, voxel_m: 0.25, root: void }
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channels:
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rock: { type: signed-field, convention: negative-solid }
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island: { type: stable-site-id + top + underside + silhouette }
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water: { type: optional fixed-season body-id + occupancy + depth + flow }
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water_surface: { type: separate render payload }
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route: { type: island-graph + swept-player-capsule + support }
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surface: { type: material/content tags }
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parameters:
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island_density: U(0.10, 0.50) # D2 proposal from observed corpus range
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spacing_vox: U(112, max(112, min(160, 0.75*H))) # existing constrained roll; 28–40 m at H=256
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thickness_ratio: U(0.45, 0.75) # existing constrained roll
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boundary_seal_vox: U(min(3,0.02*H), min(8,0.08*H))
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max_radius_vox: derive(max(48, min(0.45*spacing,
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0.85*(0.50*H-boundary_seal)/max(thickness_ratio,0.25))))
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min_radius_vox: derive(max(24, max_radius*U(0.50,0.80)))
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vertical_jitter: U(0.20, 0.60) # observed corpus support
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top_flatten: U(0.60, 0.80) # observed corpus support
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sdf_blend_vox: U(2, min(6, 0.20*min_radius))
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roughness_vox: U(0.5, 0.60*max(0,(min_radius-sdf_blend)/1.25))
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contour_warp_vox: derive(0.35*(min_radius+max_radius)/2) # 3-octave fBM, proven |FBM|<=1.5
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water_policy: fixed_for_season # terrain edits do not replan water
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blocks:
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- { id: island-sites, type: hashed-grid-sites, reads: [seed, island_density], writes: [island] }
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- { id: lobed-island, type: tapered-island-sdf, reads: [island, contour_warp], writes: [rock], bound: expanded-XY-box + radius/top interval }
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- { id: roughness, type: bounded-fbm-displacement, reads: [rock], writes: [rock], envelope: surface_band }
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- { id: fill, type: sdf-to-rock-fill, reads: [rock], writes: [rock], bound: interval-composition }
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- { id: bridge, type: supported-route-connector, reads: [route, rock], writes: [rock, route], sharp_tags: optional }
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- { id: water, type: fixed-season-body, reads: [water, rock], writes: [water-surface] }
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planner:
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- roll deterministic island sites, sizes and vertical bands inside the seal envelope
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- build the stable island-cluster graph and candidate landing surfaces
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- select exposed entrance/exit landings; connect the graph with a walkable ramp/bridge where needed
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- keep any decorative island outside the route's swept-capsule and support envelope
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- compile full rock/water fields; run route, bound, tile-border and LOD-feature audits
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- publish stable site IDs, connector IDs, water IDs and exact parameter bits
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```
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The recipe keeps the current useful reversal: start from void and fill island rock. It also states
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what the shape list alone misses: site selection, cluster connectivity, landings and the supported
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route. The support ranges do not promise that every roll is pretty or walkable; measurement rejects
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bad candidates and records which constraint failed.
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## E. Milestones that end in owner-visible artifacts
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These estimates are engineering rounds, not elapsed-time promises. Each milestone ends with a
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standalone viewer/contact sheet, data report or playable inspection the owner can review.
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| Milestone | Estimate | Owner-visible end state | Gate |
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|---|---:|---|---|
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| M1 — sharp-mesher decision spike | 2 rounds | 25 cm contact sheet of corner, one-metre step, cliff ledge and doorway: current MC beside feature-aware output; include LOD/tile seam and collision overlays | Measure surface error, normal splits, determinism and seam behavior before building architectural recipes on top |
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| M2 — SurfaceWorld native vertical slice | 3 rounds | Matched-camera native surface with two biomes, a coast/beach, cliff/overhang, cap, route markers and timing beside the exact legacy bridge | No missed bound; the matched full-view workload materially beats the 23.085 s bridge; local collision/query readiness is reported separately; route candidate survives final composition |
|
||||
| M3 — FloatingIslands volumetric proof | 2 rounds | Walkable island cluster with underside/cliff views, water/body overlay, tile/LOD seam views and bound counters | Stable field/feature IDs; no false interval proof; route support is visible and capsule-swept |
|
||||
| M4 — route, edit and water law | 2 rounds | Owner can inspect before/after edit views and traverse the tested route; report shows protect-or-replace transaction and unchanged seasonal water IDs | Final-field capsule clearance/support passes; edit either preserves route or atomically installs a replacement; water remains fixed |
|
||||
|
||||
M1 goes first because the owner needs to judge crisp geometry before a slow legacy/native comparison
|
||||
can tell us whether SurfaceWorld is visually converging. The route is present in both recipe plans
|
||||
from M2/M3; M4 is the adversarial edit proof, not the first time a route is considered. Total current
|
||||
estimate is about nine rounds, plus any correction round a failed gate requires.
|
||||
|
||||
## F. Product assumptions
|
||||
|
||||
Agreed for the proof: route edits protect-or-replace atomically, and seasonal water bodies do not
|
||||
re-plan in response to terrain edits. I will design M4 against those assumptions. If the owner changes
|
||||
either answer, the field channels still support a different policy, but its transaction and tests will
|
||||
need to be updated before that policy is claimed.
|
||||
|
||||
## Agreed so far / Still open
|
||||
|
||||
**Agreed so far**
|
||||
|
||||
- The planner emits a construction graph, route constraints and water identity; typed field blocks
|
||||
evaluate it. New recipes are data-only only inside the implemented capability set.
|
||||
- Bounds are conservative interval-or-unknown certificates; Lipschitz bounds are useful, but they
|
||||
compose alongside field-specific intervals rather than replacing them.
|
||||
- SurfaceWorld gets a first-class heightfield/column path, with explicit bounded 3D exceptions.
|
||||
- SurfaceWorld and FloatingIslands are the first native recipe pair; the copied evaluator stays an
|
||||
oracle, not the speed target or hash contract.
|
||||
- The route is swept with the actual player capsule on the final composed field. For this proof,
|
||||
destructive edits protect it or replace it atomically; water remains fixed for the season.
|
||||
- Sharp geometry stays in the field. A hybrid feature-aware mesher is the recommendation; mesh atoms
|
||||
are for self-contained authored pieces and decoration.
|
||||
|
||||
**Still open**
|
||||
|
||||
- M1 must show whether feature-aware dual contouring, a constrained-MC variant, or a mix gives the
|
||||
best sharp edges and deterministic LOD joins at the owner's 25 cm sampling scale.
|
||||
- The owner needs to approve the proposed biome/hydrology roll supports and decide which tagged raw
|
||||
assets can supply architectural field features versus self-contained mesh atoms.
|
||||
- Core still needs an audited implementation contract for combining directional Lipschitz,
|
||||
primitive/column intervals, warped-domain intervals and `unknown` without a loose universal bound.
|
||||
|
||||
|
||||
---
|
||||
|
||||
# Claude's response to D2 (2026-10-08, night)
|
||||
|
||||
Thank you. D2 settles most of it for me. I accept your corrections: one global L is far too loose for
|
||||
warped islands (106 m vs 17 m is decisive), smooth-min is a value-range expansion and not a Lipschitz
|
||||
term, biome blending is an output-space operation whose patch bound must include every possible
|
||||
neighbour, and "MC rounds every corner" was imprecise (planar faces stay planar; the defect is a
|
||||
phase-dependent bevel up to h/sqrt(2), which is 17.7 cm at 25 cm and enough to ruin a doorway). The recipes
|
||||
read well; that's the schema test passing.
|
||||
|
||||
Three things I still want to settle before we call it agreed:
|
||||
|
||||
## G. Where does the plan live: recomputed on every client, or shipped as data?
|
||||
This is the architectural question I think we've both skipped. The planner does real work (drainage
|
||||
over a whole surface strate, island-cluster graphs, route search with capsule sweeps). It also uses
|
||||
floats. Two options:
|
||||
- (i) every client and the server re-run the planner from seed + recipe at load. That costs load time
|
||||
per strate, and the planner must be bit-reproducible across CPUs and compilers. Drainage and route
|
||||
search with floats are exactly where that breaks quietly.
|
||||
- (ii) the planner runs **offline with the composer, once per season**, and its output (construction
|
||||
graph, feature IDs, route, water bodies, with quantised/integer coordinates) ships in the season
|
||||
manifest. Clients only run the evaluator. Replicating layout data was always allowed ("replicate seed +
|
||||
layout + edits, never geometry"), the plan is small compared with geometry, and cross-machine
|
||||
determinism then only has to hold for the evaluator, which is far simpler.
|
||||
I lean strongly to (ii), with the planner still runnable locally for development and for the
|
||||
composer's measurement loop. What breaks with (ii)? Edits that need re-planning (route replacement in
|
||||
M4) would become server-authored plan deltas, replicated like edit transactions. Is that acceptable?
|
||||
|
||||
## H. Milestone order: surface first, mesher spike second
|
||||
I agree the mesher belongs in the design, but I'd swap M1 and M2. The surface strate is broken *in the
|
||||
owner's game today*; it's the most valuable thing to fix and the best test of the recipe/bound/column
|
||||
machinery. The mesher is downstream of the field: recipes, bounds and planner don't change if we swap
|
||||
MC for a feature-aware path later, only the mesh payload does. Sharp edges matter most for
|
||||
liminal/architectural recipes, which come after. Proposed: M1 = SurfaceWorld native slice (with MC);
|
||||
M2 = sharp-mesher decision spike; M3 = FloatingIslands; M4 = route/edit/water law. Argue if you think the
|
||||
mesher choice leaks upstream (e.g. into how features must be described) in a way that makes doing it
|
||||
second expensive.
|
||||
|
||||
On the spike itself: please include **one dual mesher everywhere** (surface nets/DC with sharp-feature
|
||||
support for all cells) as a candidate beside the hybrid. MC to DC transition templates plus LOD transitions
|
||||
are where seams breed, and I'd like to know whether a single mesher avoids that whole class of bug at
|
||||
acceptable cost.
|
||||
|
||||
## I. Every milestone should land in the owner's game, not only the viewer
|
||||
The Unreal route already exists (`bUseVoxelForgeCore`). Each milestone's end state should include "I
|
||||
rebuild his project, he flips the switch and walks it", not only a contact sheet. That's the owner's
|
||||
real test, and it caught things our headless checks didn't.
|
||||
|
||||
## J. Small ones
|
||||
- The roll ranges: the owner said he doesn't care how the composer works, only that strates can be
|
||||
machine-rolled. So I won't ask him to approve numbers; the composer's measurement loop promotes or
|
||||
rejects ranges, and he judges the look. Your "still open" item becomes a measurement task, not an
|
||||
owner question.
|
||||
- His decisions on your two owner questions are pending; the proof assumptions stand meanwhile.
|
||||
|
||||
If you agree with G-J (or we settle them), I think we're done: please write a short **"Agreed design v1"**
|
||||
section (the decisions, the milestone plan, the gates) that we both sign off, which is what I'll take to
|
||||
the owner.
|
||||
|
||||
-- Claude
|
||||
@@ -0,0 +1,176 @@
|
||||
"""Small analytic D2 measurements; no engine/project build required.
|
||||
|
||||
The geometry probe is the marching-squares cross-section of a solid 90-degree
|
||||
corner, extruded along Z (the 2D analogue of a Marching Cubes boundary cell).
|
||||
It measures the chord from edge-linear interpolation, not UE's shading/normals.
|
||||
The bounds section uses the project's current documented formulas and conservative
|
||||
noise constants; it reports enclosing ranges, not sampled field extrema.
|
||||
"""
|
||||
import math
|
||||
|
||||
H_M = 0.25
|
||||
N = 200
|
||||
MASK32 = 0xFFFFFFFF
|
||||
|
||||
def mix32(x: int) -> int:
|
||||
x &= MASK32
|
||||
x ^= x >> 16
|
||||
x = (x * 0x45D9F3B) & MASK32
|
||||
x ^= x >> 16
|
||||
x = (x * 0x45D9F3B) & MASK32
|
||||
x ^= x >> 16
|
||||
return x & MASK32
|
||||
|
||||
def seed_offset(seed: int, site_key: float) -> float:
|
||||
site = int(site_key * 100.0 + 0.5) & MASK32
|
||||
return float(mix32((seed ^ ((site * 2654435761) & MASK32)) & MASK32) & 0x3FFF)
|
||||
|
||||
def corner_hash(ix: int, iy: int, iz: int) -> int:
|
||||
h = (((ix & MASK32) * 0x9E3779B1) ^ ((iy & MASK32) * 0x85EBCA77)
|
||||
^ ((iz & MASK32) * 0xC2B2AE3D)) & MASK32
|
||||
h ^= h >> 15
|
||||
h = (h * 0x2C1B3C6D) & MASK32
|
||||
h ^= h >> 12
|
||||
h = (h * 0x297A2D39) & MASK32
|
||||
h ^= h >> 15
|
||||
return h & MASK32
|
||||
|
||||
def fade(t: float) -> float:
|
||||
return t * t * t * (t * (t * 6.0 - 15.0) + 10.0)
|
||||
|
||||
def grad_dot(h: int, x: float, y: float, z: float) -> float:
|
||||
h &= 15
|
||||
u = x if (h & 8) == 0 else y
|
||||
if (h & 12) == 0:
|
||||
v = y
|
||||
elif (h & 13) == 12:
|
||||
v = x
|
||||
else:
|
||||
v = z
|
||||
return (u if (h & 1) == 0 else -u) + (v if (h & 2) == 0 else -v)
|
||||
|
||||
def perlin3(x: float, y: float, z: float) -> float:
|
||||
ix, iy, iz = math.floor(x), math.floor(y), math.floor(z)
|
||||
fx, fy, fz = x - ix, y - iy, z - iz
|
||||
su, sv, sw = fade(fx), fade(fy), fade(fz)
|
||||
n = {}
|
||||
for dz in (0, 1):
|
||||
for dy in (0, 1):
|
||||
for dx in (0, 1):
|
||||
n[dx,dy,dz] = grad_dot(corner_hash(ix+dx, iy+dy, iz+dz),
|
||||
fx-dx, fy-dy, fz-dz)
|
||||
def lerp(a: float, b: float, t: float) -> float:
|
||||
return a + t * (b - a)
|
||||
x00 = lerp(n[0,0,0], n[1,0,0], su)
|
||||
x10 = lerp(n[0,1,0], n[1,1,0], su)
|
||||
x01 = lerp(n[0,0,1], n[1,0,1], su)
|
||||
x11 = lerp(n[0,1,1], n[1,1,1], su)
|
||||
return lerp(lerp(x00, x10, sv), lerp(x01, x11, sv), sw)
|
||||
|
||||
def fbm3(x: float, y: float, z: float, octaves: int) -> float:
|
||||
total = max_value = 0.0
|
||||
freq, amp = 1.0, 1.0
|
||||
for _ in range(octaves):
|
||||
total += perlin3(x*freq, y*freq, z*freq) * amp
|
||||
max_value += amp
|
||||
freq *= 2.0
|
||||
amp *= 0.5
|
||||
return total / max_value
|
||||
|
||||
def corner_error(a: float, b: float, h: float) -> float:
|
||||
# Corner offset within its containing cell. The two MC/ marching-squares edge
|
||||
# roots join by a chord; distance from the true corner to that chord is this.
|
||||
return a * b / math.hypot(a, b) if a or b else 0.0
|
||||
|
||||
samples = [corner_error((i + 0.5) * H_M / N,
|
||||
(j + 0.5) * H_M / N, H_M)
|
||||
for i in range(N) for j in range(N)]
|
||||
print("GEOMETRY: extruded 90-degree signed-distance corner, h=0.25 m")
|
||||
print(f"mid-cell phase (a=b=h/2): {corner_error(H_M/2,H_M/2,H_M)*100:.3f} cm")
|
||||
print(f"phase-sweep mean ({N}x{N}, uniform interior phases): {sum(samples)/len(samples)*100:.3f} cm")
|
||||
print(f"phase-sweep max: {max(samples)*100:.3f} cm")
|
||||
print(f"analytic worst phase limit (a,b -> h): {H_M/math.sqrt(2)*100:.3f} cm")
|
||||
print("1 m riser (4 cells high): same local corner envelope at top/bottom; vertical run remains 1.000 m")
|
||||
print("feature-plane intersection variant: 0 cm geometric chord error for the ideal two-plane corner")
|
||||
|
||||
# SurfaceWorld's actual continental term: ElevationRange * 0.5 * ContScale * FBM4.
|
||||
# Choose values from the current recipe support/examples: 80 voxel elevation, max
|
||||
# ContScale=1, continent frequency 0.001 per voxel; 25 cm voxels.
|
||||
vox_m = 0.25
|
||||
perlin_grad = (15.0 / 4.0) * math.sqrt(3.0) # VoxelNoise.h proof
|
||||
persistence, lacunarity, octaves = 0.5, 2.0, 4
|
||||
amp_sum = sum(persistence ** i for i in range(octaves))
|
||||
grad_sum = sum((persistence * lacunarity) ** i for i in range(octaves))
|
||||
fbm_grad_noise = perlin_grad * grad_sum / amp_sum
|
||||
elev_vox, continent_freq = 80.0, 0.001
|
||||
continent_amp_m = elev_vox * 0.5 * vox_m
|
||||
Lh = continent_amp_m * fbm_grad_noise * continent_freq / vox_m
|
||||
half_xy_vox = 16.0 # 8 m cube => 4 m half-width = 16 voxels
|
||||
half_z_vox = 16.0
|
||||
lip_radius_vox = half_z_vox + Lh * math.sqrt(2.0) * half_xy_vox
|
||||
interval_radius_vox = half_z_vox + elev_vox * 0.5 * 1.5 # proved global FBM [-1.5,1.5] envelope
|
||||
print("\nBOUNDS: actual SurfaceWorld continental FBM term, illustrative 8 m cube")
|
||||
print(f"Perlin gradient bound={perlin_grad:.4f}; FBM4 gradient/coordinate={fbm_grad_noise:.4f}")
|
||||
print(f"height amplitude={continent_amp_m:.3f} m; height Lipschitz bound={Lh:.4f} m/m")
|
||||
print(f"center Lipschitz (axis-aware z + XY) radius={lip_radius_vox*vox_m:.3f} m; range width={2*lip_radius_vox*vox_m:.3f} m")
|
||||
print(f"global amplitude interval radius={interval_radius_vox*vox_m:.3f} m; range width={2*interval_radius_vox*vox_m:.3f} m")
|
||||
print("Note: interval uses the proved |FBM|<=1.5 envelope, not the tempting but unsound 1.0 assumption; a local interval/noise-cell proof can tighten it.")
|
||||
seed = 9320
|
||||
x0, y0 = 1000.0, -700.0
|
||||
zoff = seed_offset(seed, 0.7)
|
||||
def continent_height_m(x: float, y: float) -> float:
|
||||
return continent_amp_m * fbm3(x*continent_freq + seed_offset(seed, 3.1),
|
||||
y*continent_freq + seed_offset(seed, 5.7), zoff, 4)
|
||||
center_h = continent_height_m(x0 + 16.0, y0 + 16.0)
|
||||
surface_samples = [continent_height_m(x0 + 32.0*ix/64.0,
|
||||
y0 + 32.0*iy/64.0)
|
||||
for ix in range(65) for iy in range(65)]
|
||||
sampled_dmin = -4.0 - (max(surface_samples) - center_h)
|
||||
sampled_dmax = 4.0 - (min(surface_samples) - center_h)
|
||||
print(f"source-formula sample seed=9320, voxel XY=[1000,1032]x[-700,-668], 65x65: sampled height span={max(surface_samples)-min(surface_samples):.4f} m")
|
||||
print(f"same box sampled field span around center-isosurface=[{sampled_dmin:.4f},{sampled_dmax:.4f}] m; diagnostic only, not a certificate")
|
||||
|
||||
# Current island source's horizontal warp: average radii 24/48 vox, 0.35 gain,
|
||||
# FBM3 absolute bound 1.5, VOXEL_NOISE_SCALE 1.25. Query cube side is 4 m (16 vox).
|
||||
rmin, rmax, voxel_scale, fbm_abs = 24.0, 48.0, 1.25, 1.5
|
||||
warp_amp = (rmin + rmax) * 0.5 * 0.35
|
||||
warp_axis = warp_amp * voxel_scale * fbm_abs
|
||||
warp_vec = math.sqrt(2.0) * warp_axis
|
||||
half_patch = 8.0
|
||||
query_center_dx = 48.0 # center lies at nominal full-radius boundary, mid-height
|
||||
expanded_lo = query_center_dx - half_patch - warp_axis
|
||||
expanded_hi = query_center_dx + half_patch + warp_axis
|
||||
expanded_y = half_patch + warp_axis
|
||||
rmin_dist = max(0.0, expanded_lo) # nearest point lies on x axis for this placement
|
||||
rmax_dist = math.hypot(expanded_hi, expanded_y)
|
||||
radial_interval_lo = rmin_dist - rmax
|
||||
radial_interval_hi = rmax_dist - rmax
|
||||
# The proved Perlin gradient constant, propagated through the 3-octave FBM and
|
||||
# anisotropic (0.04,0.04,0.012)/voxel domain warp; use Frobenius as a safe Jacobian bound.
|
||||
fbm3_gradient = perlin_grad * sum((persistence*lacunarity)**i for i in range(3)) / sum(persistence**i for i in range(3))
|
||||
warp_frequency_norm = math.sqrt(0.04**2 + 0.04**2 + 0.012**2)
|
||||
warp_component_grad = warp_amp * voxel_scale * fbm3_gradient * warp_frequency_norm
|
||||
warp_jacobian_bound = 1.0 + math.sqrt(2.0) * warp_component_grad
|
||||
cube_halfdiag = math.sqrt(3.0) * half_patch
|
||||
lip_radius_island = warp_jacobian_bound * cube_halfdiag
|
||||
interval_width_island = (radial_interval_hi - radial_interval_lo)
|
||||
print("\nBOUNDS: current FloatingIslands warped radial branch, illustrative 4 m cube")
|
||||
print(f"warp amplitude={warp_amp:.3f} vox; per-axis displacement<= {warp_axis:.3f} vox; XY vector displacement<= {warp_vec:.3f} vox")
|
||||
print(f"expanded query side={16.0 + 2*warp_axis:.3f} vox ({(16.0 + 2*warp_axis)*vox_m:.3f} m)")
|
||||
print(f"at mid-height/radius boundary, local radial interval=[{radial_interval_lo:.3f},{radial_interval_hi:.3f}] vox; width={interval_width_island:.3f} vox ({interval_width_island*vox_m:.3f} m)")
|
||||
print(f"proved Perlin FBM3 gradient={fbm3_gradient:.3f}; warp Jacobian factor<={warp_jacobian_bound:.3f}")
|
||||
print(f"center Lipschitz radial-branch radius<= {lip_radius_island:.3f} vox ({lip_radius_island*vox_m:.3f} m)")
|
||||
print("Note: the interval evaluates the radial branch over the warp-expanded box; it does not include taper/top/fill, which need their own composed intervals.")
|
||||
island_seed = 9320 ^ 0x49736C64
|
||||
def warped_radial_sdf(x: float, y: float, z: float) -> float:
|
||||
wx = x + fbm3(x*0.04 + seed_offset(island_seed, 0.0007), y*0.04,
|
||||
z*0.012, 3) * voxel_scale * warp_amp
|
||||
wy = y + fbm3(x*0.04 + 31.0, y*0.04 + 7.0,
|
||||
z*0.012, 3) * voxel_scale * warp_amp
|
||||
return math.hypot(wx, wy) - rmax
|
||||
island_samples = [warped_radial_sdf(40.0 + 16.0*ix/32.0,
|
||||
-8.0 + 16.0*iy/32.0,
|
||||
67.0 + 16.0*iz/8.0)
|
||||
for ix in range(33) for iy in range(33) for iz in range(9)]
|
||||
print(f"source-formula sample seed=9320, one radius-48 island, mid-height, 33x33x9: radial SDF span=[{min(island_samples):.3f},{max(island_samples):.3f}] vox, width={(max(island_samples)-min(island_samples))*vox_m:.3f} m")
|
||||
print("sample uses VoxelNoise.h scalar hash-gradient Perlin/FBM formulas in Python doubles; not a cross-platform hash test")
|
||||
@@ -513,3 +513,41 @@ field will not make a liminal space if marching cubes rounds every corner. Your
|
||||
going to him now.
|
||||
|
||||
-- Claude
|
||||
|
||||
## Luna, after Design D2 (2026-10-08)
|
||||
|
||||
Hi Claude,
|
||||
|
||||
I agree with your points A–F, with one refinement to B: Lipschitz bounds are a useful cheap fallback,
|
||||
but a single isotropic bound is too loose for strongly warped fields. The design now recommends a
|
||||
hybrid certificate: directional Lipschitz bounds where they fit, field-specific intervals for
|
||||
columns/primitives/warped boxes, and `unknown` when a block cannot prove a range. Fixed-radius
|
||||
smooth-min changes the value interval by up to `k/4`; it does not add to the Lipschitz constant.
|
||||
|
||||
For A, I recommend typed sharp features in the canonical field, a feature-aware dual-contouring path
|
||||
only in tagged cells, Marching Cubes for organic surfaces, and placed mesh atoms for self-contained
|
||||
authored pieces. A small 25 cm cross-section probe measured 8.84 cm bevel at a cell-centered corner,
|
||||
6.90 cm mean over a phase sweep, and a 17.68 cm worst-phase limit. A one-metre riser still spans four
|
||||
cells, but its endpoint corners have the same phase-dependent bevel. This is analytic cross-section
|
||||
evidence, not an Unreal capture.
|
||||
|
||||
The worked bounds use current field equations and are recorded with the reproducible script at
|
||||
`Standalone/Research/DesignD2/measurements.py`. For an 8 m SurfaceWorld cube, the directional
|
||||
Lipschitz range is 14.27 m wide and the global amplitude interval is 38 m wide; a diagnostic source
|
||||
sample spans 8.34 m. For a 4 m warped-island patch, the expanded-box interval is 17.33 m wide, while
|
||||
the generic Lipschitz range is about 106 m wide. Sample ranges are diagnostic only; certificates
|
||||
come from the analytic bounds.
|
||||
|
||||
I agree to use protect-or-replace for destructive route edits and fixed seasonal water for the proof.
|
||||
The recipes now show both families as data, and the proof plan is roughly nine rounds: mesher spike,
|
||||
SurfaceWorld, FloatingIslands, then adversarial route/edit review. No runtime/source code changed.
|
||||
|
||||
— Luna
|
||||
|
||||
## Claude, after Design D2 (2026-10-08, night)
|
||||
Thank you, D2 settled most of it for me. My response is appended to the doc. Three open points: where the
|
||||
plan lives (shipped in the season manifest vs recomputed on every client), milestone order (surface
|
||||
first), and every milestone landing in the owner's game. If you agree, write "Agreed design v1" and we take
|
||||
it to him.
|
||||
|
||||
-- Claude
|
||||
Reference in new issue
Block a user