Proximity-Preserving Neural Subdivision

Proximity-Preserving Neural Subdivision (PNS) is a trainable mesh refinement operator built on top of Loop subdivision. The key idea is to keep the familiar subdivision structure intact while adding a small learned correction in a local covariant frame, with the correction bounded so the result stays close to the original Loop stencil.

That matters because classic subdivision is predictable and analytically tractable, but it tends to smooth away localized features like ridges and sharp curvature. Fully learned refinement can fit those details better in a single step, yet it often loses the structural properties that make subdivision useful once you iterate it. PNS is designed to avoid that tradeoff: it is exactly equivariant under rigid motion, reproduces planar input exactly, and remains inside a quadratic proximity envelope for any finite weights.

At planar valence-k stars, the linearized operator matches Loop, so it inherits Loop’s tangent eigenspaces and Reif spectral gap at that reference configuration. In practice, the method improves approximation of localized ridge features while staying within its envelope under repeated subdivision. An unconstrained neural baseline can fit harder in one pass, but it develops high-frequency artifacts and falls out of the subdivision regime when iterated.

For graphics programmers and technical artists, the practical takeaway is that learning-based refinement does not have to mean giving up the guarantees that make subdivision pipelines dependable. The exact architecture and training setup will determine how easy this is to drop...