NeurCADRecon: Neural Representation for Reconstructing CAD Surfaces by Enforcing Zero Gaussian Curvature

TL;DR

NeurCADRecon tackles the challenge of reconstructing high-fidelity CAD surfaces from low-quality unoriented point clouds by leveraging the principle that CAD surfaces are piecewise developable. The method learns a neural SDF in a self-supervised manner, combining Dirichlet and Eikonal fidelity with a Gaussian curvature based developability constraint, augmented by a double-trough function to tolerate tip points and a dynamic sampling strategy for incomplete data. This yields SDFs that reveal sharp CAD features, enabling easy extraction of feature-aligned meshes and patch-based CAD design recovery. Experiments across four open CAD datasets show significant gains over state-of-the-art methods in accuracy and robustness, validating the practical impact for reverse engineering and design workflows.

Abstract

Despite recent advances in reconstructing an organic model with the neural signed distance function (SDF), the high-fidelity reconstruction of a CAD model directly from low-quality unoriented point clouds remains a significant challenge. In this paper, we address this challenge based on the prior observation that the surface of a CAD model is generally composed of piecewise surface patches, each approximately developable even around the feature line. Our approach, named NeurCADRecon, is self-supervised, and its loss includes a developability term to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points. Noticing that the Gaussian curvature is non-zero at tip points, we introduce a double-trough curve to tolerate the existence of these tip points. Furthermore, we develop a dynamic sampling strategy to deal with situations where the given points are incomplete or too sparse. Since our resulting neural SDFs can clearly manifest sharp feature points/lines, one can easily extract the feature-aligned triangle mesh from the SDF and then decompose it into smooth surface patches, greatly reducing the difficulty of recovering the parametric CAD design. A comprehensive comparison with existing state-of-the-art methods shows the significant advantage of our approach in reconstructing faithful CAD shapes.

Figures (25)

• Figure 1: Despite being mathematically correct, enforcing the rank of the Hessian matrix to be 1 may lead to numerical instability. In this paper, we propose to reconstruct CAD shapes by minimizing the overall absolute Gaussian curvature.
• Figure 2: A gallery of reconstruction results by our NeurCADRecon. The central idea is to encourage the Gaussian curvature toward 0 while ensuring fidelity to the input points.
• Figure 3: (a) The Gaussian curvature field on the cube model shows significant deviations from 0 at the tip points. (b) To accommodate the non-zero Gaussian curvature at the tip points, we advocate the use of a double-trough function. This function is designed to permit the desired Gaussian curvature to assume values of either 0 or approximately $\pi/2$.
• Figure 4: By utilizing a specially designed double-trough (DT) curve, we allow the presence of non-zero Gaussian curvature, but are more inclined to favor zero Gaussian curvature. Without the usage of the tolerating technique, bulges may arise around the tip points.
• Figure 5: We use an annealing factor to gradually reduce the influence of the Gaussian curvature, such that the fidelity can be preserved even for (a) non-developable surfaces and (b) tiny structures.