Polygonal meshes are ubiquitous in the digital 3D domain, yet they have only played a minor role in the deep learning revolution. Leading methods for learning generative models of shapes rely on implicit functions, and generate meshes only after expensive iso-surfacing routines. To overcome these challenges, we are inspired by a classical spatial data structure from computer graphics, Binary Space Partitioning (BSP), to facilitate 3D learning. The core ingredient of BSP is an operation for recursive subdivision of 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. Importantly, BSP-Net is unsupervised since no convex shape decompositions are needed for training. The network is trained to reconstruct a shape using a set of convexes obtained from a BSP-tree built on a set of planes. The convexes inferred by BSP-Net can be easily extracted to form a polygon mesh, without any need for iso-surfacing. The generated meshes are compact (i.e., low-poly) and well suited to represent sharp geometry; they are guaranteed to be watertight and can be easily parameterized. We also show that the reconstruction quality by BSP-Net is competitive with state-of-the-art methods while using much fewer primitives. Code is available at https://github.com/czq142857/BSP-NET-original.

中文翻译：

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BSP-Net：通过二进制空间分区生成紧凑网格

多边形网格在数字 3D 领域无处不在，但它们在深度学习革命中只发挥了次要作用。学习形状生成模型的领先方法依赖于隐式函数，并且仅在昂贵的等值曲面处理程序之后生成网格。为了克服这些挑战，我们受到了计算机图形学中的经典空间数据结构二进制空间分区 (BSP) 的启发，以促进 3D 学习。BSP 的核心成分是对空间进行递归细分以获得凸集的操作。通过利用这一特性，我们设计了 BSP-Net，这是一种通过凸分解学习表示 3D 形状的网络。重要的是，BSP-Net 是无监督的，因为训练不需要凸形分解。该网络经过训练，可以使用从构建在一组平面上的 BSP 树获得的一组凸面来重建形状。BSP-Net 推断出的凸面可以很容易地提取形成多边形网格，而无需等值曲面。生成的网格很紧凑（即低多边形），非常适合表示锐利的几何图形；它们保证是防水的，并且可以很容易地参数化。我们还表明，BSP-Net 的重建质量与最先进的方法相比具有竞争力，同时使用的原语要少得多。代码可在 https://github.com/czq142857/BSP-NET-original 获得。它们保证是防水的，并且可以很容易地参数化。我们还表明，BSP-Net 的重建质量与最先进的方法相比具有竞争力，同时使用的原语要少得多。代码可在 https://github.com/czq142857/BSP-NET-original 获得。它们保证是防水的，并且可以很容易地参数化。我们还表明，BSP-Net 的重建质量与最先进的方法相比具有竞争力，同时使用的原语要少得多。代码可在 https://github.com/czq142857/BSP-NET-original 获得。