# Codimensional Incremental Potential Contact

arXiv: https://arxiv.org/abs/2012.04457 · HTML: https://mlsanity.com/paper/2012.04457/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Dec 2020.

## Built on by (most cited first, 30 of 34)

- [VideoPhy: Evaluating Physical Commonsense for Video Generation](https://mlsanity.com/paper/2406.03520/) (2024)
- [SDF-StyleGAN: Implicit SDF-Based StyleGAN for 3D Shape Generation](https://mlsanity.com/paper/2206.12055/) (2022)
- [HOOD: Hierarchical Graphs for Generalized Modelling of Clothing Dynamics](https://mlsanity.com/paper/2212.07242/) (2022)
- [DiffCloth: Differentiable Cloth Simulation with Dry Frictional Contact](https://mlsanity.com/paper/2106.05306/) (2021)
- [PhysAvatar: Learning the Physics of Dressed 3D Avatars from Visual Observations](https://mlsanity.com/paper/2404.04421/) (2024)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [Simplicits: Mesh-Free, Geometry-Agnostic, Elastic Simulation](https://mlsanity.com/paper/2407.09497/) (2024)
- [ChatGarment: Garment Estimation, Generation and Editing via Large Language Models](https://mlsanity.com/paper/2412.17811/) (2024)
- [Dressing Avatars: Deep Photorealistic Appearance for Physically Simulated Clothing](https://mlsanity.com/paper/2206.15470/) (2022)
- [Motion Guided Deep Dynamic 3D Garments](https://mlsanity.com/paper/2209.11449/) (2022)
- [GarmentDreamer: 3DGS Guided Garment Synthesis with Diverse Geometry and Texture Details](https://mlsanity.com/paper/2405.12420/) (2024)
- [Learning Keypoints for Robotic Cloth Manipulation using Synthetic Data](https://mlsanity.com/paper/2401.01734/) (2024)
- [PICA: Physics-Integrated Clothed Avatar](https://mlsanity.com/paper/2407.05324/) (2024)
- [Neural Garment Dynamics via Manifold-Aware Transformers](https://mlsanity.com/paper/2407.06101/) (2024)
- [MPMAvatar: Learning 3D Gaussian Avatars with Accurate and Robust Physics-Based Dynamics](https://mlsanity.com/paper/2510.01619/) (2025)
- [Understanding Physical Effects for Effective Tool-use](https://mlsanity.com/paper/2206.14998/) (2022)
- [Human 3D Avatar Modeling with Implicit Neural Representation: A Brief Survey](https://mlsanity.com/paper/2306.03576/) (2023)
- [NeuralClothSim: Neural Deformation Fields Meet the Thin Shell Theory](https://mlsanity.com/paper/2308.12970/) (2023)
- [3D Generative Model Latent Disentanglement via Local Eigenprojection](https://mlsanity.com/paper/2302.12798/) (2023)
- [Neural Volumetric Mesh Generator](https://mlsanity.com/paper/2210.03158/) (2022)
- [SENC: Handling Self-collision in Neural Cloth Simulation](https://mlsanity.com/paper/2407.12479/) (2024)
- [Advances in 4D Representation: Geometry, Motion, and Interaction](https://mlsanity.com/paper/2510.19255/) (2025)
- [SwinGar: Spectrum-Inspired Neural Dynamic Deformation for Free-Swinging Garments](https://mlsanity.com/paper/2308.02827/) (2023)
- [PhysiFormer: Learning to Simulate Mechanics in World Space](https://mlsanity.com/paper/2606.27364/) (2026)
- [A Comparative Study of Garment Draping Techniques](https://mlsanity.com/paper/2405.11056/) (2024)
- [Neural Garment Dynamic Super-Resolution](https://mlsanity.com/paper/2412.06285/) (2024)
- [ReWeaver: Towards Simulation-Ready and Topology-Accurate Garment Reconstruction](https://mlsanity.com/paper/2601.16672/) (2026)
- [Ani3DHuman: Photorealistic 3D Human Animation with Self-guided Stochastic Sampling](https://mlsanity.com/paper/2602.19089/) (2026)
- [Tac2Real: Reliable and GPU Visuotactile Simulation for Online Reinforcement Learning and Zero-Shot Real-World Deployment](https://mlsanity.com/paper/2603.28475/) (2026)
- [AIpparel: A Multimodal Foundation Model for Digital Garments](https://mlsanity.com/paper/2412.03937/) (2024)

## Abstract (arXiv)

We extend the incremental potential contact (IPC) model for contacting elastodynamics to resolve systems composed of codimensional DOFs in arbitrary combination. This enables a unified, interpenetration-free, robust, and stable simulation framework that couples codimension-0,1,2, and 3 geometries seamlessly with frictional contact. Extending IPC to thin structures poses new challenges in computing strain, modeling thickness and determining collisions. To address these challenges we propose three corresponding contributions. First, we introduce a C2 constitutive barrier model that directly enforces strain limiting as an energy potential while preserving rest state. This provides energetically-consistent strain limiting models (both isotropic and anisotropic) for cloth that enable strict satisfaction of strain-limit inequalities with direct coupling to both elastodynamics and contact via minimization of the incremental potential. Second, to capture the geometric thickness of codimensional domains we extend the IPC model to directly enforce distance offsets. Our treatment imposes a strict guarantee that mid-surfaces (resp. mid-lines) of shells (resp. rods) will not move closer than applied thickness values. This enables us to account for thickness in the contact behavior of codimensional structures and so robustly capture challenging contacting geometries; a number of which, to our knowledge, have not been simulated before. Third, codimensional models, especially with modeled thickness, mandate strict accuracy requirements that pose a severe challenge to all existing continuous collision detection (CCD) methods. To address these limitations we develop a new, efficient, simple-to-implement additive CCD (ACCD) method that applies conservative advancement to iteratively refine a lower bound for deforming primitives, converging to time of impact.