Reach For the Spheres:
Tangency-Aware Surface Reconstruction of SDFs

Silvia Sellán, University of Toronto

Christopher Batty, University of Waterloo

Oded Stein, University of Southern California

Figure 1. Reconstructing a mesh from the discrete signed distance field (SDF) of a koala (source, rightmost). By using global information from all sample points at once, our method recovers the shape even in low resolutions where methods like Marching Cubes and Neural Dual Contouring (NDCx) produce very coarse shapes (left trio), and it recovers surface detail at higher resolutions that Marching Cubes and NDCx miss (middle trio). Our method is purely geometric, and does not require any training or storing of weights (unlike NDCx).


Signed distance fields (SDFs) are a widely used implicit surface representation, with broad applications in computer graphics, computer vision, and applied mathematics. To reconstruct an explicit triangle mesh surface corresponding to an SDF, traditional isosurfacing methods, such as Marching Cubes and and its variants, are typically used. However, these methods overlook fundamental properties of SDFs, resulting in reconstructions that exhibit severe oversmoothing and feature loss. To address this shortcoming, we propose a novel method based on a key insight: each SDF sample corresponds to a spherical region that must lie fully inside or outside the surface, depending on its sign, and that must be tangent to the surface at some point. Leveraging this understanding, we formulate an energy that gauges the degree of violation of tangency constraints by a proposed surface. We then employ a gradient flow that minimizes our energy, starting from an initial triangle mesh that encapsulates the surface. This algorithm yields superior reconstructions to previous methods, even with sparsely sampled SDFs. Our approach provides a more nuanced understanding of SDFs and offers significant improvements in surface reconstruction.

Cite as

      title={Reach For the Spheres: Tangency-Aware Surface Reconstruction of SDFs}, 
      author={Silvia Sellán and Christopher Batty and Oded Stein},


This work is funded in part by the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-2021-02524), an NSERC Vanier Scholarship and an Adobe Research Fellowship.

We thank Abhishek Madan for technical help and for proofreading. We thank Aravind Ramakrishnan, and Hsueh-Ti Derek Liu for proofreading. The first author would also like to thank the second and third authors for inviting her to visit their respective institutions, which served as the foundation for this collaboration.

We acknowledge the authors of the 3D models used throughout this paper and thank them for making them available for academic use. See the paper for a detailed list.