Haotian Yin

Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk et al.

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/.

Haotian Yin, Aleksander Plocharski, Michal Jan Wlodarczyk et al.

We introduce a finite-difference framework for curvature regularization in neural signed distance field (SDF) learning. Existing approaches enforce curvature priors using full Hessian information obtained via second-order automatic differentiation, which is accurate but computationally expensive. Others reduced this overhead by avoiding explicit Hessian assembly, but still required higher-order differentiation. In contrast, our method replaces these operations with lightweight finite-difference stencils that approximate second derivatives using the well known Taylor expansion with a truncation error of O(h^2), and can serve as drop-in replacements for Gaussian curvature and rank-deficiency losses. Experiments demonstrate that our finite-difference variants achieve reconstruction fidelity comparable to their automatic-differentiation counterparts, while reducing GPU memory usage and training time by up to a factor of two. Additional tests on sparse, incomplete, and non-CAD data confirm that the proposed formulation is robust and general, offering an efficient and scalable alternative for curvature-aware SDF learning.

Haotian Yin, Przemyslaw Musialski

Neural signed distance functions (SDFs) have become a powerful representation for geometric reconstruction from point clouds, yet they often require both gradient- and curvature-based regularization to suppress spurious warp and preserve structural fidelity. FlatCAD introduced the Off-Diagonal Weingarten (ODW) loss as an efficient second-order prior for CAD surfaces, approximating full-Hessian regularization at roughly half the computational cost. However, FlatCAD applies a fixed ODW weight throughout training, which is suboptimal: strong regularization stabilizes early optimization but suppresses detail recovery in later stages. We present scheduling strategies for the ODW loss that assign a high initial weight to stabilize optimization and progressively decay it to permit fine-scale refinement. We investigate constant, linear, quintic, and step interpolation schedules, as well as an increasing warm-up variant. Experiments on the ABC CAD dataset demonstrate that time-varying schedules consistently outperform fixed weights. Our method achieves up to a 35% improvement in Chamfer Distance over the FlatCAD baseline, establishing scheduling as a simple yet effective extension of curvature regularization for robust CAD reconstruction.