# Implicit-ARAP: Efficient Handle-Guided Neural Field Deformation via Local Patch Meshing

arXiv: https://arxiv.org/abs/2405.12895 · HTML: https://mlsanity.com/paper/2405.12895/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 57 references that are in the map.
- First posted on arXiv 21 May 2024.

## Builds on (most cited first, 30 of 31)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [D-NeRF: Neural Radiance Fields for Dynamic Scenes](https://mlsanity.com/paper/2011.13961/) (2020)
- [NICE: Non-linear Independent Components Estimation](https://mlsanity.com/paper/1410.8516/) (2014)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [CLIP-NeRF: Text-and-Image Driven Manipulation of Neural Radiance Fields](https://mlsanity.com/paper/2112.05139/) (2021)
- [Neural Unsigned Distance Fields for Implicit Function Learning](https://mlsanity.com/paper/2010.13938/) (2020)
- [Editing Conditional Radiance Fields](https://mlsanity.com/paper/2105.06466/) (2021)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [GaussianEditor: Editing 3D Gaussians Delicately with Text Instructions](https://mlsanity.com/paper/2311.16037/) (2023)
- [HyperDiffusion: Generating Implicit Neural Fields with Weight-Space Diffusion](https://mlsanity.com/paper/2303.17015/) (2023)
- [4DComplete: Non-Rigid Motion Estimation Beyond the Observable Surface](https://mlsanity.com/paper/2105.01905/) (2021)
- [Learning Deformable Tetrahedral Meshes for 3D Reconstruction](https://mlsanity.com/paper/2011.01437/) (2020)
- [NeuroMorph: Unsupervised Shape Interpolation and Correspondence in One Go](https://mlsanity.com/paper/2106.09431/) (2021)
- [Neural Surface Reconstruction of Dynamic Scenes with Monocular RGB-D Camera](https://mlsanity.com/paper/2206.15258/) (2022)
- [Neural Non-Rigid Tracking](https://mlsanity.com/paper/2006.13240/) (2020)
- [A Level Set Theory for Neural Implicit Evolution under Explicit Flows](https://mlsanity.com/paper/2204.07159/) (2022)
- [ARAPReg: An As-Rigid-As Possible Regularization Loss for Learning Deformable Shape Generators](https://mlsanity.com/paper/2108.09432/) (2021)
- [Predicting Loose-Fitting Garment Deformations Using Bone-Driven Motion Networks](https://mlsanity.com/paper/2205.01355/) (2022)
- [DeepMetaHandles: Learning Deformation Meta-Handles of 3D Meshes with Biharmonic Coordinates](https://mlsanity.com/paper/2102.09105/) (2021)
- [GSEdit: Efficient Text-Guided Editing of 3D Objects via Gaussian Splatting](https://mlsanity.com/paper/2403.05154/) (2024)
- [Neural Shape Deformation Priors](https://mlsanity.com/paper/2210.05616/) (2022)
- [ParticleNeRF: A Particle-Based Encoding for Online Neural Radiance Fields](https://mlsanity.com/paper/2211.04041/) (2022)
- [Marching-Primitives: Shape Abstraction from Signed Distance Function](https://mlsanity.com/paper/2303.13190/) (2023)
- [Neural Implicit Surface Evolution](https://mlsanity.com/paper/2201.09636/) (2022)
- [Accurate Differential Operators for Hybrid Neural Fields](https://mlsanity.com/paper/2312.05984/) (2023)
- [Variational Barycentric Coordinates](https://mlsanity.com/paper/2310.03861/) (2023)

## Built on by (most cited first, 5 of 5)

- [FUSE: A Flow-based Mapping Between Shapes](https://mlsanity.com/paper/2511.13431/) (2025)
- [Deep Feature Deformation Weights](https://mlsanity.com/paper/2601.12527/) (2026)
- [As-Rigid-As-Possible Regularization for Implicit Surfaces](https://mlsanity.com/paper/2608.15933/) (2026)
- [RADmesh: Remesh-Aware Mesh Deformation](https://mlsanity.com/paper/2608.17182/) (2026)
- [Cepheid: Decoupling Scale from Structure for Cross-Family Motion Completion](https://mlsanity.com/paper/2610.18871/) (2026)

## Abstract (arXiv)

Neural fields have emerged as a powerful representation for 3D geometry, enabling compact and continuous modeling of complex shapes. Despite their expressive power, manipulating neural fields in a controlled and accurate manner -- particularly under spatial constraints -- remains an open challenge, as existing approaches struggle to balance surface quality, robustness, and efficiency. We address this by introducing a novel method for handle-guided neural field deformation, which leverages discrete local surface representations to optimize the As-Rigid-As-Possible deformation energy. To this end, we propose the local patch mesh representation, which discretizes level sets of a neural signed distance field by projecting and deforming flat mesh patches guided solely by the SDF and its gradient. We conduct a comprehensive evaluation showing that our method consistently outperforms baselines in deformation quality, robustness, and computational efficiency. We also present experiments that motivate our choice of discretization over marching cubes. By bridging classical geometry processing and neural representations through local patch meshing, our work enables scalable, high-quality deformation of neural fields and paves the way for extending other geometric tasks to neural domains.