FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models

• URL: http://arxiv.org/abs/2506.16627v2
• Date: Sun, 24 Aug 2025 19:14:03 GMT
• Title: FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
• Authors: Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk, Mikolaj Kida, Przemyslaw Musialski,
• Abstract summary: We introduce an off-diagonal Weingarten loss that regularizes only the mixed shape operator term.<n>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.<n>The method is drop-in and framework-agnostic, enabling scalable curvature-aware SDF learning for engineering-grade shape reconstruction.
• Score: 37.56003520528009
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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/.

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