# Robust Biharmonic Skinning Using Geometric Fields

arXiv: https://arxiv.org/abs/2406.00238 · HTML: https://mlsanity.com/paper/2406.00238/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 108 references that are in the map.
- First posted on arXiv 1 Jun 2024.

## Builds on (most cited first, 30 of 37)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [3D Gaussian Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2308.04079/) (2023)
- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Implicit Geometric Regularization for Learning Shapes](https://mlsanity.com/paper/2002.10099/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neuralangelo: High-Fidelity Neural Surface Reconstruction](https://mlsanity.com/paper/2306.03092/) (2023)
- [Physics-informed neural networks with hard constraints for inverse design](https://mlsanity.com/paper/2102.04626/) (2021)
- [SNARF: Differentiable Forward Skinning for Animating Non-Rigid Neural Implicit Shapes](https://mlsanity.com/paper/2104.03953/) (2021)
- [Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks](https://mlsanity.com/paper/2104.08426/) (2021)
- [MagicPony: Learning Articulated 3D Animals in the Wild](https://mlsanity.com/paper/2211.12497/) (2022)
- [S3: Neural Shape, Skeleton, and Skinning Fields for 3D Human Modeling](https://mlsanity.com/paper/2101.06571/) (2021)
- [Learning Skeletal Articulations with Neural Blend Shapes](https://mlsanity.com/paper/2105.02451/) (2021)
- [Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modeling](https://mlsanity.com/paper/2109.06407/) (2021)
- [Fast Tetrahedral Meshing in the Wild](https://mlsanity.com/paper/1908.03581/) (2019)
- [Implicit Neural Spatial Representations for Time-dependent PDEs](https://mlsanity.com/paper/2210.00124/) (2022)
- [RigNet: Neural Rigging for Articulated Characters](https://mlsanity.com/paper/2005.00559/) (2020)
- [Neural Point-based Shape Modeling of Humans in Challenging Clothing](https://mlsanity.com/paper/2209.06814/) (2022)
- [Scaling physics-informed hard constraints with mixture-of-experts](https://mlsanity.com/paper/2402.13412/) (2024)
- [NiLBS: Neural Inverse Linear Blend Skinning](https://mlsanity.com/paper/2004.05980/) (2020)
- [SkinningNet: Two-Stream Graph Convolutional Neural Network for Skinning Prediction of Synthetic Characters](https://mlsanity.com/paper/2203.04746/) (2022)
- [Cubic Stylization](https://mlsanity.com/paper/1910.02926/) (2019)
- [Grid-Free Monte Carlo for PDEs with Spatially Varying Coefficients](https://mlsanity.com/paper/2201.13240/) (2022)
- [A Unified Hard-Constraint Framework for Solving Geometrically Complex PDEs](https://mlsanity.com/paper/2210.03526/) (2022)
- [Accurate Differential Operators for Hybrid Neural Fields](https://mlsanity.com/paper/2312.05984/) (2023)
- [Walk on Stars: A Grid-Free Monte Carlo Method for PDEs with Neumann Boundary Conditions](https://mlsanity.com/paper/2302.11815/) (2023)
- [Physics-informed attention-based neural network for solving non-linear partial differential equations](https://mlsanity.com/paper/2105.07898/) (2021)
- [Boundary Value Caching for Walk on Spheres](https://mlsanity.com/paper/2302.11825/) (2023)
- [VINECS: Video-based Neural Character Skinning](https://mlsanity.com/paper/2307.00842/) (2023)

## Built on by (most cited first, 6 of 6)

- [MagicArticulate: Make Your 3D Models Articulation-Ready](https://mlsanity.com/paper/2502.12135/) (2025)
- [Puppeteer: Rig and Animate Your 3D Models](https://mlsanity.com/paper/2508.10898/) (2025)
- [Geometry in Style: 3D Stylization via Surface Normal Deformation](https://mlsanity.com/paper/2503.23241/) (2025)
- [Operator Learning Using Weak Supervision from Walk-on-Spheres](https://mlsanity.com/paper/2603.01193/) (2026)
- [FreeForm: Reduced-Order Deformable Simulation from Particle-Based Skinning Eigenmodes](https://mlsanity.com/paper/2605.29318/) (2026)
- [Variational Green's Functions for Volumetric PDEs](https://mlsanity.com/paper/2602.12349/) (2026)

## Abstract (arXiv)

Bounded bihramonic weights are a popular tool used to rig and deform characters for animation, to compute reduced-order simulations, and to define feature descriptors for geometry processing. They necessitate tetrahedralizing the volume bounded by the surface, introducing the possibility of meshing artifacts or tetrahedralization failure. We introduce a mesh-free and robust automatic skinning technique that generates weights comparable to the current state of the art, but works reliably even on open surfaces, triangle soups, and point clouds where current methods fail. We achieve this through the use of a specialized Lagrangian representation enabled by the advent of hardware ray-tracing, which circumvents the need for finite elements while optimizing the biharmonic energy and enforcing boundary conditions. The flexibility of our formulation allows us to integrate artistic control through weight painting during the optimization. We offer a thorough qualitative and quantitative evaluation of our method.