CSG as an Intermediate Representation

Most code-CAD libraries hand you eager geometry: box(10, 10, 10) immediately calls into the kernel, returns a real B-Rep solid, and that solid sits in WASM memory until you .delete() it. Chain a few operations and you've allocated and freed dozens of intermediate shapes whose only purpose was to feed the next call.

brepjs's csg namespace offers a different surface for the same operations. Instead of materializing geometry, the builders construct a content-addressed DAG — a tree of IRNode values, each describing what to build without actually building it. Geometry is produced on demand by an Evaluator, which caches by structural hash so re-evaluating the same subtree is free.

A tree, not a shape

Every builder returns a plain data object:

import { csg } from 'brepjs/quick';

const node = csg.box(10, 20, 30);
// {
//   kind: 'Box',
//   x: NumLitExpr(10), y: NumLitExpr(20), z: NumLitExpr(30),
//   structuralHash: 0x9f3a...n,
//   freeParams: Set(0) {},
// }

No kernel call, no WASM allocation. Same for every builder — cylinder, sphere, fuse, cut, translate, even compound. The tree is just description.

import { csg } from 'brepjs/quick';

const tree = csg.cut(csg.box(100, 100, 100), csg.sphere(40));
// kind: 'Cut'
//   a: kind: 'Box' (100×100×100)
//   b: kind: 'Sphere' (radius 40)

The structure of the tree is the structure of the computation. Nothing has been computed yet.

Content-addressed hashing

Every node carries a structuralHash — a 64-bit FNV-1a Merkle hash of its kind plus its children's hashes. Two trees that describe the same geometry hash identically, regardless of how they were built:

import { csg } from 'brepjs/quick';

const a = csg.fuse(csg.box(10, 10, 10), csg.sphere(5));
const b = csg.fuse(csg.box(10, 10, 10), csg.sphere(5));

a.structuralHash === b.structuralHash; // true

Change any literal anywhere in the tree and the hash changes:

csg.box(10, 10, 10).structuralHash === csg.box(10, 10, 11).structuralHash;
// false — last dimension differs

The hash is computed once at build time and stored on the node, so cache lookups during evaluation are O(1) per node rather than O(subtree-size). The hash also normalizes -0 to +0 and serializes floats bit-exactly via DataView.setFloat64, so identical doubles always hash the same.

Free parameters propagate upward

Builders accept literal numbers or expressions. Expressions parameterize the tree — csg.param('w') is a placeholder bound at evaluation time. Each node tracks the set of parameter names it transitively depends on:

import { csg } from 'brepjs/quick';

const tree = csg.translate(csg.fuse(csg.box(csg.param('w'), 10, 10), csg.sphere(csg.param('r'))), [
  csg.param('dx'),
  0,
  0,
]);

[...tree.freeParams].sort(); // ['dx', 'r', 'w']

freeParams is computed bottom-up by the builders at build time. The evaluator uses it to project the env before computing the cache key — a node that doesn't reference dx will never see dx enter its cache key, so unrelated env edits cannot invalidate it. This is the core mechanism behind incremental re-evaluation:

When dx changes, only Translate invalidates. When r changes, Sphere + Fuse + Translate invalidate but Box survives. The granularity is structural: the cost of a parameter edit is proportional to the size of the subtrees that depend on it, not the size of the whole tree.

Output kinds and structural validity

The IR doesn't have separate node types for solids vs faces vs edges — there's one IRNode union with a kind discriminator. Output kind is derived structurally via outputKindOf:

import { csg } from 'brepjs/quick';

csg.outputKindOf(csg.box(10, 10, 10)); // 'Solid'
csg.outputKindOf(csg.translate(csg.box(10, 10, 10), [1, 0, 0])); // 'Solid'
csg.outputKindOf(csg.cut(csg.box(10, 10, 10), csg.sphere(3))); // 'Solid'
csg.outputKindOf(csg.circle(5)); // 'Edge'
csg.outputKindOf(
  csg.polygon([
    [0, 0, 0],
    [1, 0, 0],
    [0, 1, 0],
  ])
); // 'Face'

Booleans inherit the kind of their a argument; transforms inherit from target; primitives are fixed. There's no cross-kind boolean — fuse(box, circle) is rejected at the kernel boundary, not by the TypeScript types at v1.

Two equivalent ways to compute the same geometry

Both snippets produce the same 1000 - π·125 ≈ 477 mm³ solid:

Eager — topology API

import { box, sphere, cut, measureVolume, unwrap } from 'brepjs/quick';

const cube = box(10, 10, 10);
const ball = sphere(2.5);
const part = unwrap(cut(cube, ball));
const v = unwrap(measureVolume(part));
// 3 kernel allocations: cube, ball, part — all live until disposed

CSG IR

import { csg, measureVolume, unwrap } from 'brepjs/quick';

const tree = csg.cut(csg.box(10, 10, 10), csg.sphere(2.5));
using ev = new csg.Evaluator();
const v = unwrap(measureVolume(unwrap(ev.evaluate(tree))));
// 3 kernel allocations the first time. 0 on every subsequent ev.evaluate(tree).

The eager API is the right answer when you build a part once. The IR is the right answer when:

• the same tree shape gets re-evaluated with different parameter bindings (slider UIs, optimizer sweeps),
• multiple branches of a build share common subtrees that would otherwise be recomputed,
• you want to serialize the build recipe to JSON without serializing materialized B-Rep data,
• you want to inspect, simplify, or edit the build graph before evaluation.

If none of those apply, the topology API is leaner. The IR is a tool, not a replacement.

Where this fits in brepjs

The IR is purely a build-time abstraction layered on top of the kernel adapter — csg.Evaluator calls the same getKernel().fuseSolids(...) that the topology API does. Everything that works on a Solid works on the result of ev.evaluate(tree): finders, fillets, measurement, export. The IR is the parametric front of the pipeline; the topology API picks up where it leaves off.

The rest of the surface

The examples above touch box, sphere, cylinder, cut, fuse, and translate. The full builder set adds cone, torus, polygon, circle, line, vertex, mirror, scale, rotate, compound, plus the N-ary booleans fuseAll and cutAll. Expression helpers include add/mul shortcuts, unaryOp (sin, cos, sqrt, abs, neg), component for indexing vectors, and buildVec for constructing them from scalars. All exported from 'brepjs' under the csg.* namespace; see the API reference for type signatures.

Next steps

• Parametric CSG walkthrough — build a gridfinity-style bin with named parameters, change a slider, watch the cache absorb the unchanged subtrees.
• CSG caching internals — cacheStats, optimize, serialization, what the cache key actually contains, and what doesn't cache.
• Migrating from a hand-rolled cache — if you've built your own Map<key, Solid> cache around eager geometry, here's the IR equivalent and what you'd inherit by switching.