Proximity-Preserving Neural Subdivision

[2608.14704] Proximity-Preserving Neural Subdivision Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Graphics arXiv:2608.14704 (cs) [Submitted on 10 Aug 2026] Title: Proximity-Preserving Neural Subdivision Authors: Hassan Ugail View a PDF of the paper titled Proximity-Preserving Neural Subdivision, by Hassan Ugail View PDF HTML (experimental) Abstract: Classical subdivision schemes are widely used because they are local, repeatable, and analytically tractable. A single stencil defines the entire refinement rule, and the behaviour of the resulting operator under iteration is well understood. This uniformity, however, means that fixed stencils tend to underfit localised geometric features, such as sharp ridges or soft edges, where curvature is concentrated. Neural mesh refinement can adapt to such features, yet unconstrained vertex prediction usually lacks the structural behaviour required of a subdivision operator once the refinement rule is applied to its own output. In this work, we introduce Proximity-Preserving Neural Subdivision, or PNS for short. PNS is a trainable refinement rule that augments Loop subdivision with a small, bounded, curvature-gated correction expressed in a covariant local frame. The construction is designed so that, for any finite network weights, the operator is exactly equivariant under rigid motion, reproduces planar input exactly, and remains inside a quadratic proximity envelope around the Loop stencil. At planar valence-k stars, the linearised operator agrees with Loop, and it therefore inherits Loop's tangent eigenspaces and Reif spectral gap at that reference configuration. All of these properties are architectural and hold before any training takes place. Empirically, PNS improves the approximation of localised ridge features while remaining inside its prescribed proximity envelope under repeated subdivision. An unconstrained neural baseline, in contrast, achieves stronger one-step fitting but develops high-frequency artefacts and leaves the subdivision regime once iterated. The overall message of this work is that learning can be introduced into subdivision without abandoning the structural constraints that make subdivision useful as a geometry-processing primitive. Subjects: Graphics (cs.GR) Cite as: arXiv:2608.14704 [cs.GR] (or arXiv:2608.14704v1 [cs.GR] for this version) https://doi.org/10.48550/arXiv.2608.14704 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Hassan Ugail [ view email ] [v1] Mon, 10 Aug 2026 22:42:17 UTC (2,269 KB) Full-text links: Access Paper: View a PDF of the paper titled Proximity-Preserving Neural Subdivision, by Hassan Ugail View PDF HTML (experimental) TeX Source view license Current browse context: cs.GR < prev | next > new | recent | 2026-08 Change to browse by: cs References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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