Abstract Neural 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 finite‐difference 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/ .
Yin et al. (Sat,) studied this question.
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