Yin, HaotianPlocharski, AleksanderWlodarczyk, Michal JanKida, MikolajMusialski, PrzemyslawChristie, MarcPietroni, NicoWang, Yu-Shuen2025-10-072025-10-0720251467-8659https://doi.org/10.1111/cgf.70249https://diglib.eg.org/handle/10.1111/cgf70249Neural signed-distance fields (SDFs) are a versatile backbone for neural geometry representation, but enforcing CAD-style developability usually requires Gaussian-curvature penalties with full Hessian evaluation and second-order differentiation, which are costly in memory and time. We introduce an off-diagonal Weingarten loss that regularizes only the mixed shape operator term that represents the gap between principal curvatures and flattens the surface. We present two variants: a finitedifference version using six SDF evaluations plus one gradient, and an auto-diff version using a single Hessian-vector product. Both converge to the exact mixed term and preserve the intended geometric properties without assembling the full Hessian. On the ABC benchmarks the losses match or exceed Hessian-based baselines while cutting GPU memory and training time by roughly a factor of two. The method is drop-in and framework-agnostic, enabling scalable curvature-aware SDF learning for engineering-grade shape reconstruction. Our code is available at https://flatcad.github.io/.CCS Concepts: Computing methodologies → Shape modeling; Regularization; Machine learning algorithmsComputing methodologies → Shape modelingRegularizationMachine learning algorithms10.1111/cgf.7024912 pages