Learning to Build Shapes by Extrusion

TL;DR

This work reframes 3D mesh generation as learning sequences of geometric extrusions rather than primitive-level token predictions. By introducing Text Encoded Extrusions (TEE) and leveraging fine-tuned LLMs, the method builds and edits quadrilateral FEQ meshes without fixed output grids, enabling arbitrarily detailed, manifold meshes. The approach combines a formal FEQ-based building methodology with a learned, text-based extrusion language, yielding high-fidelity generation, editable outputs, and scalable representations (K ≈ 20,000). Datasets based on MANO, DFAUST, and FEQ-derived meshes support diverse shape synthesis, with quantitative metrics (FID) showing strong gains over transformer-based baselines. Overall, the paper demonstrates a practical, controllable path from high-level extrusion plans to detailed, editable 3D geometries, with broad potential for artistic and engineering workflows.

Abstract

We introduce Text Encoded Extrusion (TEE), a text-based representation that expresses mesh construction as sequences of face extrusions rather than polygon lists, and a method for generating 3D meshes from TEE using a large language model (LLM). By learning extrusion sequences that assemble a mesh, similar to the way artists create meshes, our approach naturally supports arbitrary output face counts and produces manifold meshes by design, in contrast to recent transformer-based models. The learnt extrusion sequences can also be applied to existing meshes - enabling editing in addition to generation. To train our model, we decompose a library of quadrilateral meshes with non-self-intersecting face loops into constituent loops, which can be viewed as their building blocks, and finetune an LLM on the steps for reassembling the meshes by performing a sequence of extrusions. We demonstrate that our representation enables reconstruction, novel shape synthesis, and the addition of new features to existing meshes.

Figures (11)

• Figure 1: Method overview: Our method takes as input an FEQ mesh, which is decomposed into the individual face-loops and a building manual for assembling it again from its components.
• Figure 2: Two meshes, each with a single face loop highlighted in blue. The face loop on the right is self-intersecting.
• Figure 3: Generic extrusion: A set of faces highlighted in blue on an extended base patch to the left, and the boundary curve of the face set mapped to 2D and illustrated on the generic extrusion to the right
• Figure 4: Extruding the base patch:. The extrusion of the vertices in green of the extended base patch is determined by the extrusion vectors (blue) mapped to a local basis at each of the boundary vertices of the base patch (red).
• Figure 5: Applying extrusions: Three different extrusions are applied to the same base patch, creating three different extruded sets of faces.