2026/07/03 by Nicole Feng, Nicole C. Feng, Ioannis Gkioulekas +1 · 1 voice
Computer Science · Engineering · #3D Shape Modeling and Analysis #Computer Graphics and Visualization Techniques #Curvature #Normal #Offset (computer science) #Point (geometry) #Point cloud #Pointwise #Signed distance function #Surface (topology) #Surface reconstruction #Topological and Geometric Data Analysis #cs.CV #cs.GR
paper · pdf · open access · doi:10.1145/3811385
published in ACM Transactions on Graphics 45(4), 1-24 (Association for Computing Machinery)
openalex publication_date 2026/07/03 · openalex created_date 2026/07/04 · openalex updated_date 2026/08/05
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.