The swept horn grammar

Procedural geometry in this toolbox starts from the horn: a cross-section (profile) swept along a curve and warped by an ordered stack of transforms — bend, twist, scale — then optionally instanced into towers and whorls by the structural ops stack and branch. It is a clean re-derivation of the FormGrow horn grammar from the long-running Todd–Latham collaboration, rebuilt here as a lazy, typed geometry expression-IR (see decision record ADR-0010).

The defining property is that a horn is pointwise closed-form:

$\mathrm{eval}(s,\ \theta)\ \rightarrow\ (\text{position},\ \text{normal})$

for a sweep coordinate $s \in [0,1]$ (base → tip) and a spoke coordinate $\theta \in [0,2\pi)$ (around the profile). There is no marching or recurrence along the sweep, so the same expression is compiled two ways that agree by construction: a CPU golden (s, θ) loop, and a per-vertex WGSL kernel generated from the same IR. A parity test pins them together to within 1e-4.

Live demo — the Mutator breeding grid

The grammar’s parameters are ordinary numbers, so they breed. This demo is a Todd–Latham Mutator grid: each of the nine cells is a horn, you select parents and breed a new generation, and the grid eases between genotypes with the toolbox’s own one-pole trait-damping.

▶ Open the horn Mutator — a full-page interactive demo (opens in this tab; use your browser’s back button to return).

• Drag anywhere to orbit all nine cells; scroll to zoom.
• Click a cell to select it as the parent; ⇧-click to add more parents.
• Breed produces a generation of mutated offspring around the selected elite; Randomize scatters fresh genotypes.
• Open the folded parameters panel to edit a specimen’s genes directly and read the equivalent horn(…) chain.

Note

The demo imports the library directly and renders on WebGPU — each cell’s horn is evaluated by the codegen’d swept GPU kernel (createSweptGpu) into resident buffers the render pass binds directly, with no CPU tessellation. Because the kernel reads gene values from a uniform buffer (structure baked, values as data), all nine cells share one pipeline and morph smoothly; the structural stack/branch ops instance that leaf as a single GPU instanced draw (one base buffer + a per-cell matrix buffer), so the grid breeds both the horn’s shape and its structure. Breeding is breed over a TraitSpace from src/evo; the easing is the library’s OnePole trait-damping. Structural counts are continuous: the control snaps to whole numbers, but a fractional count folds a member in/out by its smoothstep weight (and branch re-spaces its whorl), so a bred change to stack/branch grows an arm in smoothly rather than popping it. It needs WebGPU and fails gracefully without it. Still designed-for, not yet built: recursion (sub), heterogeneous trees, and a composable profile sub-grammar.