We present BSP-Net, a network that generates compact and structured 3D meshes via Binary Space Partitioning (BSP). The key idea is to learn to recursively partition space using a set of hyperplanes, decomposing a shape into a collection of convex components. BSP-Net produces meshes that are compact (low polygon count), watertight, and directly usable without post-processing, in contrast to implicit methods that require expensive iso-surface extraction (e.g., Marching Cubes). Our network achieves comparable or better reconstruction quality with significantly fewer polygons.

3D shape generation is a core task in computer graphics and vision. Current deep learning approaches predominantly use voxel grids, point clouds, or implicit functions as 3D representations. However, voxel grids are memory-intensive and resolution-limited, point clouds lack surface connectivity, and implicit methods require post-hoc iso-surface extraction that produces dense, unstructured meshes. The ideal output should be a compact polygon mesh directly usable in downstream applications.

We propose to leverage Binary Space Partitioning (BSP), a classical computational geometry technique that recursively divides space using hyperplanes into convex regions. BSP-Net learns to predict a set of hyperplanes and their grouping into convex components, which are then combined via Boolean union to form the final shape. This produces compact meshes with guaranteed watertightness by construction.

Implicit shape representations such as Occupancy Networks and DeepSDF learn continuous signed distance or occupancy functions, enabling arbitrary resolution output. However, they require Marching Cubes for mesh extraction, producing meshes with hundreds of thousands of faces. Template deformation methods like Pixel2Mesh deform a sphere mesh to match the target shape, but are limited to genus-0 topologies. Primitive-based methods approximate shapes with geometric primitives, but produce non-watertight results due to primitive overlaps.

BSP-Net consists of three stages: (1) a BSP-plane generator that predicts N hyperplane parameters from a shape encoding, (2) a convex selector that groups planes into K convex components via a binary selection matrix, and (3) a shape assembler that combines convex components through Boolean union. The network is trained with a reconstruction loss comparing the predicted occupancy with ground truth occupancy. The entire pipeline is differentiable, enabling end-to-end training.

Each convex component is defined as the intersection of half-spaces determined by a subset of hyperplanes. The inside/outside classification of a point with respect to a convex is computed as the product of its classifications with respect to each constituent plane. To enable gradient flow, we replace the hard indicator functions with sigmoid approximations during training. The final shape is the union of all convex components, computed as 1 minus the product of (1 minus each convex's occupancy).

We evaluate BSP-Net on ShapeNet across 13 categories for 3D shape autoencoding and single-image reconstruction. Compared to Occupancy Networks, BSP-Net achieves comparable IoU (Intersection over Union) while producing meshes with 50x to 100x fewer polygons. For example, on the chair category, BSP-Net generates meshes with ~600 polygons vs. ~100,000 from Marching Cubes. The output meshes are guaranteed watertight by construction and exhibit meaningful structural decomposition into semantic parts.

Ablation studies show that increasing the number of planes N from 32 to 256 improves IoU but with diminishing returns. The convex decomposition learned by BSP-Net often aligns with semantically meaningful parts — for instance, chair legs, seat, and back are separated into distinct convex groups without any part-level supervision. Compared to SQ (superquadrics) and CvxNet, BSP-Net produces more faithful reconstructions with tighter surface fitting.

We have introduced BSP-Net, a novel approach that leverages Binary Space Partitioning for deep 3D shape generation. The method directly produces compact, watertight polygon meshes without requiring iso-surface extraction. By decomposing shapes into learned convex components via hyperplane arrangement, BSP-Net bridges the gap between classical computational geometry and modern deep learning, offering a principled and efficient solution for 3D shape generation.