Polygonal meshes are ubiquitous, but have only played a relatively minor role in the deep learning revolution. State-of-the-art neural generative models for 3D shapes learn implicit functions and generate meshes via expensive iso-surfacing. We overcome these challenges by employing a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core operation of BSP involves recursive subdivision of 3D space to obtain convex sets. By exploiting this property, we devise BSP-Net, a network that learns to represent a 3D shape via convex decomposition without supervision. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built over a set of planes, where the planes and convexes are both defined by learned network weights. BSP-Net directly outputs polygonal meshes from the inferred convexes. The generated meshes are watertight, compact (i.e., low-poly), and well suited to represent sharp geometry. We show that the reconstruction quality by BSP-Net is competitive with those from state-of-the-art methods while using much fewer primitives. We also explore variations to BSP-Net including using a more generic decoder for reconstruction, more general primitives than planes, as well as training a generative model with variational auto-encoders. Code is available at https://github.com/czq142857/BSP-NET-original.

通过使用计算机图形学经典空间数据结构BSP，我们设计了一种名为BSP-Net的网络模型，它能够无监督地学习表示一个3D形状，并通过检测一组面来重构一个多边形网格。该模型生成的网格既密封又紧凑，适合表示尖锐的几何体，并且使用更少的基本元素即可达到与其他现有方法相同的重构质量。

基于二叉空间划分树网络的网格表示学习