Procedural geometry

Procedural Geometry

How to generate the geometry of a game — terrain, meshes, structures, and scatter — so it is correct (watertight, manifold, properly wound, performant) and varied (perceptually distinct, not parametric oatmeal). Geometry generation is engineerable math: noise as a substrate, modulation and erosion for believability, constraints and hand-placed anchors for "designed-looking" structure, blue-noise for scatter, and topology validators as the non-negotiable correctness floor.

Tier: technical craft (→ gamestack-core). Engine-agnostic geometry-generation math underneath generated terrain, structures, and meshes.

When to use this

• Generating terrain (heightfield or voxel/SDF), and deciding which representation the design actually needs
• Choosing and wiring a mesh-extraction (marching cubes vs dual contouring), erosion, and LOD/chunking pipeline
• Generating structures with L-systems, shape grammars, or wave function collapse / model synthesis
• Authoring the mesh topology validator (winding/normals, manifold, degenerates, watertight)
• Scattering vegetation/props with blue-noise placement, environmental masking, and instancing
• Diagnosing terrain that looks like "noise", structures that read as generated, or meshes with black faces / broken collision

Scope

This skill owns the math and algorithms that produce geometry — meshes, terrain, structures, scatter. It is deliberately narrow. Adjacent concerns live in sibling skills:

• What content means and whether it's perceptually varied at scale (quests, lore, items, the oatmeal problem for content) → procedural-generation. This skill is the geometric statement of the same hybrid (hand-anchor + constrained fill); that skill is the narrative one.
• Making a generated level legible, navigable, gated, and paced → level-design. This skill is the geometry engine underneath it — grammars/WFC produce the rooms; level-design's principles make them readable. Geometry serves legibility; it does not replace it.
• Gating generated output for perceptual sameness and intentionality → procgen-review. Its oatmeal test runs on the geometry this skill emits; the topology validator here is the correctness floor below that quality gate.
• Rendering, culling, and draw-call budgets for the meshes produced → 3d-graphics-and-rendering. Texturing/shading them → shaders-and-vfx.
• Macro/world spatial layout, biomes as places, exploration pull → open-world-design (this skill is the terrain math underneath that layer).

How the pieces fit

• GUIDE.md — the cited why, in five sub-domains: noise as the substrate (Perlin/Simplex/value, fBm, multifractal/ridged, domain warping, Worley/3D-noise caves); terrain generation (heightfield vs voxel/SDF, marching cubes vs dual contouring, erosion, LOD/chunking); structural generation (L-systems, shape grammars, WFC/model synthesis, hybrid hand-anchor); mesh topology correctness (winding/normals, manifold/watertight, degenerates, runtime threading/caching); and vegetation/scatter (blue-noise, masking, instancing). Each rule carries an exemplar + source, a test-for criterion, the named failure mode, and the procedural/headless implication.
• CHECKLIST.md — Do/Don't + machine-checkable Test-for criteria, grouped by sub-domain. Written to be enforced as validators in a generation loop.

The two ideas to anchor on

1. A single noise field is oatmeal; structure comes from modulation, not octaves. Plain fractal Brownian motion is the canonical "fake terrain" look — equal roughness everywhere, no ridgelines, no drainage. Believability comes from modulating it (multifractal/ridged noise, domain warping) and from erosion simulation that carves the connected valleys and ridges a process would. More octaves add detail, not structure.

2. "Looks designed, not random" is a constraint problem. Grammar- and constraint-based methods (L-systems, shape grammars, wave function collapse / model synthesis) get their authored quality from hand-authored rules and tilesets, not from the algorithm. The designer's craft moves into the constraint set — and the most reliable path at scale is hybrid: hand-place the silhouette landmarks and set pieces, let the generator fill between them under constraints.

Why this matters doubly for a generator: a human sees a black inside-out face, a grid-aligned forest, or 10,000 identical buildings and feels "off." An autonomous generator has no eyes. Author the mesh topology validator (winding/manifold/degenerate/watertight) and the representation, erosion, crack-free, and instancing contracts as inviolable; let generation vary inputs inside them (frequency, octaves, density masks, seeds); and gate every batch through procgen-review's oatmeal test for geometric sameness — because parametric variation of one formula produces perceptually identical results.

Start with GUIDE.md, then apply CHECKLIST.md.