Typed mates, not raw transforms, are what make LLM-driven 3D assembly actually work

Most 3D generators produce a single opaque surface with no concept of parts, no sharp edges, and no way to change a dimension without sculpting the mesh directly. Procedura takes a different route: it writes the object as a parametric program in constructive solid geometry, where every face is an exact plane or cylinder, so edges stay crisp and every part is a named, editable module.

The core mechanism is typed mates. Rather than letting a language model guess raw transforms from a rendered image, Procedura defines a closed vocabulary of twelve mate types — nine static, three kinematic — and solves placement algebraically from the mated frames. Two parts that share a peg-socket mate derive their shared dimension from one parameter plus a signed fit offset; an edit to one side cannot orphan the other. This is what prior code-based agents skip, and it is why they produce objects where parts float or collide.

The build is incremental. One LLM call adds one part at a time, seeing the already-compiled program as text and a parts-coloured render of the partial assembly from up to twelve viewpoints. A three-gate verification stack — compile, mate registration, and a span-based connectivity check — must pass before any part is committed. The span check matters on its own terms: a thin detached panel has near-zero enclosed volume but a large bounding-box span, so a volume threshold misses it while the span threshold catches it.

Refinement uses a decoupled critic — a separate vision call that has never seen the code it is judging — to diagnose the rendered build against a reference image. A hard latch enforces one diagnosis before one edit; without it, the system issued edits against diagnoses at a ratio well above one-to-one, whereas the gated loop holds the diagnose-to-edit ratio at one-to-one. The critic is history-aware, so it can verify that earlier fixes landed rather than re-reporting closed issues.

On MechBench-36, a 36-object hard-surface benchmark the authors introduce, Procedura leads every method on the judge's geometry and aesthetics axes and ships the sharpest edges of any system measured. On P3D-Bench the composite margin over the strongest comparable entry is several times the confidence intervals. Domain-tuned CAD coders collapse entirely on many-part objects, shipping no mesh on a substantial fraction of cases.

The same mate graph drives articulation: kinematic mates live alongside static ones, so a hinge axis is the relation that seated the part, not a value fitted to a finished surface afterward. Validation runs headless in Isaac Sim; the reported set clears every dynamics phase for the majority of articulated objects tested.

Honest limits: the agent perceives geometry only through rendered images, so occluded interiors can hide from every camera. CSG is a poor fit for organic or freeform surfaces. And a mate the plan never declares cannot be verified.