FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models
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Date
2025
Journal Title
Journal ISSN
Volume Title
Publisher
The Eurographics Association and John Wiley & Sons Ltd.
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 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/.
Description
CCS Concepts: Computing methodologies → Shape modeling; Regularization; Machine learning algorithms
@article{10.1111:cgf.70249,
journal = {Computer Graphics Forum},
title = {{FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models}},
author = {Yin, Haotian and Plocharski, Aleksander and Wlodarczyk, Michal Jan and Kida, Mikolaj and Musialski, Przemyslaw},
year = {2025},
publisher = {The Eurographics Association and John Wiley & Sons Ltd.},
ISSN = {1467-8659},
DOI = {10.1111/cgf.70249}
}