Split-and-Fit: Learning B-Reps via Structure-Aware Voronoi Partitioning

TL;DR

The paper presents Split-and-Fit, a top-down approach for B-Rep CAD reconstruction that first partitions space into a Voronoi diagram of GT primitives and then fits a single primitive per Voronoi cell. It introduces NVD-Net to predict Voronoi boundaries from input data, enabling a unique, structure-aware intermediate representation that simplifies primitive extraction and topology recovery. Compared to bottom-up and direct-CAD methods, the approach achieves superior geometric accuracy, topological consistency, and generalization on the ABC dataset, with robust handling of noise and real scans. This Voronoi-based intermediary reduces ambiguity in primitive counts and connections, improving the reliability and editability of reconstructed CAD models in practical applications.

Abstract

We introduce a novel method for acquiring boundary representations (B-Reps) of 3D CAD models which involves a two-step process: it first applies a spatial partitioning, referred to as the ``split``, followed by a ``fit`` operation to derive a single primitive within each partition. Specifically, our partitioning aims to produce the classical Voronoi diagram of the set of ground-truth (GT) B-Rep primitives. In contrast to prior B-Rep constructions which were bottom-up, either via direct primitive fitting or point clustering, our Split-and-Fit approach is top-down and structure-aware, since a Voronoi partition explicitly reveals both the number of and the connections between the primitives. We design a neural network to predict the Voronoi diagram from an input point cloud or distance field via a binary classification. We show that our network, coined NVD-Net for neural Voronoi diagrams, can effectively learn Voronoi partitions for CAD models from training data and exhibits superior generalization capabilities. Extensive experiments and evaluation demonstrate that the resulting B-Reps, consisting of parametric surfaces, curves, and vertices, are more plausible than those obtained by existing alternatives, with significant improvements in reconstruction quality. Code will be released on https://github.com/yilinliu77/NVDNet.

Figures (22)

• Figure 1: Overview of our method. Given an input model (i.e., a point cloud, mesh, or distance field), we first compute the Voronoi boundaries of the underlying shape and subsequently construct the Voronoi cells. Then we fit an elementary primitive for each Voronoi cell individually, with the cell boundary serving to naturally trim the primitive, and extract their corresponding connectivity from the Voronoi diagram. Finally, we reconstruct the CAD model (5 vertices, 4 lines and 2 circles in the figure) in B-Rep by combining the primitives and their topological relations.
• Figure 2: Overview of our network. We first voxelize the input UDF field. Each voxel contains 4 features $(d, g_x, g_y, g_z)$ which indicates the UDF value and the gradient vector of the UDF field. The voxel grid is split into overlapped local patches and fed into the standard UNet individually. A single channel binary flag is predicted within each voxel to indicate whether this voxel contains any Voronoi boundary.
• Figure 3: The relation between the Voronoi boundaries and the derivative of the UDF field.
• Figure 4: Qualitative comparisons of 5 representative shapes in ABC dataset.
• Figure 5: Qualitative comparisons of 5 randomly sampled shapes in ABC dataset.