发表机构
Carnegie Mellon University（卡内基梅隆大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种计算点云符号距离的方法，通过用环面局部拟合点云，利用预训练网络输出参数，无需全局优化和空间离散化且易并行化，基于新理论统一相关方法，可直接用于点云应用，无需显式重建。
AI 中文摘要
我们描述了一种计算到点云的符号距离的方法，该方法允许在任意空间分辨率下进行快速逐点评估。作为输入，我们的方法采用带有法线的点云；作为输出，它提供了一种解析参数化，允许在任意点查询到近似潜在表面的符号距离，同时提供重建和距离。我们的关键思想是通过用环面局部拟合点云来重建形状，环面具有闭式符号距离函数。环面以前馈方式拟合，使用预训练网络输出逐点曲率和偏移参数。重要的是，我们的方法不需要昂贵的全局优化或空间离散化，并且易于并行化。我们的方法基于一种新理论，该理论将符号距离与缠绕数和泊松表面重建的经典重建方法统一起来。我们用我们的方法计算到由摄影测量、网格、3D高斯和神经隐式表示产生的点云的符号距离。我们的方法允许点云直接用于应用中，而无需显式表面重建：例如，我们对点云进行偏移，应用形态学和布尔运算，并使用球体追踪直接可视化偏移表面。
英文摘要
We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points - simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.
CommentsPublished in ACM Transactions on Graphics, volume 45 (2026). For associated presentations and code, see https://nzfeng.github.io/research/PointsAsTori
Journal refACM Transactions on Graphics, volume 45 (2026), article number 53
DOI：10.1145/3811385
