In this work, we present the local patch mesh representation for neural signed distance fields. This technique allows to discretize local regions of the level sets of an input SDF by projecting and deforming flat patch meshes onto the level set surface, using exclusively the SDF information and its gradient. Our analysis reveals this method to be more accurate than the standard marching cubes algorithm for approximating the implicit surface. Then, we apply this representation in the setting of handle-guided deformation: we introduce two distinct pipelines, which make use of 3D neural fields to compute As-Rigid-As-Possible deformations of both high-resolution meshes and neural fields under a given set of constraints. We run a comprehensive evaluation of our method and various baselines for neural field and mesh deformation which show both pipelines achieve impressive efficiency and notable improvements in terms of quality of results and robustness. With our novel pipeline, we introduce a scalable approach to solve a well-established geometry processing problem on high-resolution meshes, and pave the way for extending other geometric tasks to the domain of implicit surfaces via local patch meshing.

翻译：本文提出了一种用于神经符号距离场的局部面片网格表示方法。该技术通过将平面面片网格投影并变形至等值面表面，实现对输入SDF等值面局部区域的离散化处理，整个过程仅需利用SDF信息及其梯度。分析表明，该方法在逼近隐式曲面时比经典行进立方体算法具有更高精度。随后，我们将此表示应用于手柄引导变形场景：提出了两条独立处理管线，利用三维神经场计算给定约束条件下高分辨率网格与神经场的尽可能刚性变形。通过对本方法及多种神经场与网格变形基线方案的全面评估，两条管线均展现出卓越的计算效率，并在结果质量与鲁棒性方面取得显著提升。通过这一创新管线，我们为解决高分辨率网格上长期存在的几何处理问题提供了可扩展方案，并为通过局部面片网格化技术将其他几何任务拓展至隐式曲面领域开辟了新路径。