CAST: Cast-Admissible Generative Design and Shape Optimization with Paired Depth Images

Deep generative design can produce complex geometries, but unconstrained representations may create undercuts that prevent release from a two-part mold. We present CAST, which reformulates three-dimensional shape generation under a selected mold-opening constraint as a two-dimensional image generation problem using paired top and bottom depth images. Each valid depth pair defines one material interval along a selected mold-opening direction, so reconstructions exclude undercuts in that direction by construction. Diffusion models generate candidate shapes in this representation, and a finite element analysis (FEA) guided optimizer refines the same two boundaries. We evaluate diffusion-based generation with limited training data comprising 211 SimJEB bracket designs. On SimJEB brackets, FEA-guided refinement with a volume penalty reduced compliance in 193 of 200 generated candidates. The median reduction across all candidates was 36.8 percent in the optimization FEA model. Reconstruction of existing brackets revealed a mass--stiffness trade-off: filling occluded regions increased material volume and reduced displacement under the evaluated loads. Paired depth images thus connect generative exploration and structural refinement in a shared design space that preserves the selected pull-direction restriction.