FlatCAD: Fast Curvature Regularization of Neural SDFs for CAD Models

TL;DR

FlatCAD introduces a novel, efficient regularization method for neural SDFs that enforces CAD-style developability by focusing on mixed shape operator terms, reducing computational costs while maintaining geometric accuracy.

Contribution

The paper proposes a new off-diagonal Weingarten loss for neural SDFs that simplifies curvature regularization, making it faster and more memory-efficient without sacrificing accuracy.

Findings

Matches or exceeds Hessian-based baselines in benchmarks.

Reduces GPU memory and training time by about 50%.

Enables scalable curvature-aware shape reconstruction.

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/.