Points as Tori: Fast Pointwise Signed Distance for Point Clouds
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 cos...
| Authors | Nicole Feng, Ioannis Gkioulekas, Keenan Crane |
|---|---|
| Primary category | cs.GR |
| Published | 18 July 2026 |
| Last updated at source | 18 July 2026 |
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