CoMesh: Constrained Progressive Mesh Generation for Engineering Design

Engineering shape design calls for models that explicitly generate meshes, which preserve broad geometric freedom and interface naturally with downstream physical simulations. Yet existing mesh generation approaches struggle to reconcile with spatial engineering constraints, achieve simulation-level quality, and often require costly autoregressive modeling over long refinement histories. We introduce *CoMesh*, a framework that starts with a prescribed seed mesh that hard-encodes engineering constraints and progressively introduces new geometric degrees of freedom through edge splits. Its key component is a novel serialization algorithm that constructs refinement trajectories for training in the same forward direction as generation, using a shared scheduler to select the edge refined at each step. We establish sufficient conditions for self-intersection free refinement, and translate them into a dihedral-based procedure for placing new vertices. Compared to baseline serializations, our approach guarantees that hard constraints can be embedded and reduces each refinement action to a 2D local displacement. This turns autoregressive generation into a local, state-conditioned problem, enabling an efficient, compact model independent of refinement history. Across three engineering families, mounting brackets, transonic wings, and ship hulls, CoMesh consistently generates diverse meshes with substantially improved constraint validity and element quality, while enabling markedly more efficient training and inference. These results demonstrate that using a deterministic refinement schedule with learned local geometry provides an efficient formulation for mesh-level generative design.