PhaseSurf introduces a neural volume rendering framework that uses Metric-Phase Fields (MPFs) to handle thin structures and sign-ambiguous geometry. MPFs combine a nonnegative metric field for unsigned proximity with a continuous phase field that softly indicates sign, producing a signed composite implicit function with stable gradients. The method includes specialized training losses for metric consistency and phase transition stability, enabling robust iso-surface extraction and outperforming both SDF- and UDF-based approaches on multi-view datasets with challenging geometry.
By Junkai Deng, Jiayi Kong, Xuhui Chen, Guanli Hou, Fei Hou, Junhui Hou, Wenping Wang, Ying He
The paper introduces Spectrally Optimised Neural Discretisations (SpeND), a mesh‑free framework that learns discretisation weights from local stencil geometry on unstructured point clouds. By embedding discrete moment conditions into the network architecture, SpeND guarantees polynomial consistency and allows the weights to be optimised for spectral accuracy over a chosen wavenumber band, using an unsupervised Fourier‑mode loss. The resulting operators are PDE‑agnostic, perform well on Poisson, Burgers, and Navier–Stokes equations, and can reduce wall‑clock time by 3–20× compared to existing mesh‑free methods at the same accuracy.
By Lucas Gerken Starepravo, Henry Broadley, Steven Lind, Jack R. C. King
M-plicits introduces a multiscale framework for neural implicit surfaces that models a surface as a residual sum of MLPs trained on nested neighborhoods. By localizing supervision to narrow bands around previous zero-level sets, the method achieves robustness to noisy input, avoids costly mesh extraction, and enables a multiscale sphere-tracing algorithm with analytical normal computation. Experiments on Stanford and Thingi32 show superior Chamfer distance and IoU metrics compared to existing methods while using far fewer parameters.
By Vin\'icius da Silva, Isabelle Melo, Matheus Bessa, Guilherme Schardong, Luiz Schirmer, Andr\'e Ara\'ujo, Nuno Gon\c{c}alves, H\'elio Lopes, Alberto Raposo, Luiz Velho, Tiago Novello
Boundary representation (B‑rep) is the standard format for parametric 3D models in CAD systems, yet the same solid can be encoded by different B‑reps due to varying operations, kernel rebuilds, or export settings. Existing B‑rep encoders fail to handle these variations, collapsing on standard benchmarks and real‑world perturbations. The authors introduce the canonical region graph, an input representation derived directly from the solid, which offers theoretical invariance to repartitioning and rigid motions and performs as well as the best baseline while remaining stable across all tested perturbations.
The paper examines how boundary representation (B‑rep) encoders for CAD models fail to handle variations that do not change the underlying solid, such as different modeling operations or software export settings. By demonstrating that existing encoders collapse under these perturbations, the authors introduce the canonical region graph, a representation derived directly from the solid that is theoretically invariant to repartitioning and rigid motions. This new input format matches the best baseline on standard benchmarks and remains stable across all tested perturbations.
By Heinrich Jiang, Hager Yasser Mohamed, Alexander Hitt, Valeriia Lomakina, Henning Jiang, Jennifer Jang
Implicit Neural Representations (INRs) have become the standard for continuous 2D shape modeling, but they suffer from black-box uneditability, vulnerability to noise, and high parameter counts that severely hinder deployment on edge devices. We introduce Fluid-SDF, a highly compressed, differentiable Constructive Solid Geometry (CSG) framework that models shapes using explicit geometric primitives blended via a smooth minimum function.