FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
This work addresses the computational bottleneck of curvature regularization for neural SDFs in CAD model reconstruction, offering a scalable solution for engineering-grade shape learning.
The paper tackled the problem of enforcing CAD-style developability in neural signed-distance fields (SDFs) by introducing an off-diagonal Weingarten loss that regularizes the mixed shape operator term, which flattens surfaces without full Hessian evaluation. The result showed that on ABC benchmarks, the method matched or exceeded Hessian-based baselines while reducing GPU memory and training time by roughly a factor of two.
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/.