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.

本研究提出了一种基于局部补丁网格表示的神经符号距离场方法，结合 3D 神经场和约束集，实现高效的几何变形，并在结果质量和稳定性方面取得显著改进。通过局部补丁网格化，我们解决了高分辨率网格的几何处理问题，并为将其他几何任务应用于隐式曲面领域铺平了道路。