# Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search

arXiv: https://arxiv.org/abs/2205.02961 · HTML: https://mlsanity.com/paper/2205.02961/

## Key facts

- Cited by 67 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 64 references that are in the map.
- First posted on arXiv 5 May 2022.

## Builds on (most cited first, 13 of 13)

- [Soft Actor-Critic Algorithms and Applications](https://mlsanity.com/paper/1812.05905/) (2018)
- [SAPIEN: A SimulAted Part-based Interactive ENvironment](https://mlsanity.com/paper/2003.08515/) (2020)
- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Learning Shape Abstractions by Assembling Volumetric Primitives](https://mlsanity.com/paper/1612.00404/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Superquadrics Revisited: Learning 3D Shape Parsing beyond Cuboids](https://mlsanity.com/paper/1904.09970/) (2019)
- [Supervised Fitting of Geometric Primitives to 3D Point Clouds](https://mlsanity.com/paper/1811.08988/) (2018)
- [3D-PRNN: Generating Shape Primitives with Recurrent Neural Networks](https://mlsanity.com/paper/1708.01648/) (2017)
- [Learning Unsupervised Hierarchical Part Decomposition of 3D Objects from a Single RGB Image](https://mlsanity.com/paper/2004.01176/) (2020)
- [Robust Watertight Manifold Surface Generation Method for ShapeNet Models](https://mlsanity.com/paper/1802.01698/) (2018)
- [DeepMetaHandles: Learning Deformation Meta-Handles of 3D Meshes with Biharmonic Coordinates](https://mlsanity.com/paper/2102.09105/) (2021)
- [Deep Parametric Shape Predictions using Distance Fields](https://mlsanity.com/paper/1904.08921/) (2019)
- [Learning Generative Models of Shape Handles](https://mlsanity.com/paper/2004.03028/) (2020)

## Built on by (most cited first, 30 of 67)

- [Evaluating Real-World Robot Manipulation Policies in Simulation](https://mlsanity.com/paper/2405.05941/) (2024)
- [ManiSkill2: A Unified Benchmark for Generalizable Manipulation Skills](https://mlsanity.com/paper/2302.04659/) (2023)
- [ManiSkill3: GPU Parallelized Robotics Simulation and Rendering for Generalizable Embodied AI](https://mlsanity.com/paper/2410.00425/) (2024)
- [DexGraspNet: A Large-Scale Robotic Dexterous Grasp Dataset for General Objects Based on Simulation](https://mlsanity.com/paper/2210.02697/) (2022)
- [UniDexGrasp: Universal Robotic Dexterous Grasping via Learning Diverse Proposal Generation and Goal-Conditioned Policy](https://mlsanity.com/paper/2303.00938/) (2023)
- [PartSLIP: Low-Shot Part Segmentation for 3D Point Clouds via Pretrained Image-Language Models](https://mlsanity.com/paper/2212.01558/) (2022)
- [HumanoidBench: Simulated Humanoid Benchmark for Whole-Body Locomotion and Manipulation](https://mlsanity.com/paper/2403.10506/) (2024)
- [CAST: Component-Aligned 3D Scene Reconstruction from an RGB Image](https://mlsanity.com/paper/2502.12894/) (2025)
- [ManipTrans: Efficient Dexterous Bimanual Manipulation Transfer via Residual Learning](https://mlsanity.com/paper/2503.21860/) (2025)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Differentiable Physics Simulation of Dynamics-Augmented Neural Objects](https://mlsanity.com/paper/2210.09420/) (2022)
- [HUMOTO: A 4D Dataset of Mocap Human Object Interactions](https://mlsanity.com/paper/2504.10414/) (2025)
- [SemGrasp: Semantic Grasp Generation via Language Aligned Discretization](https://mlsanity.com/paper/2404.03590/) (2024)
- [Digital Twin Catalog: A Large-Scale Photorealistic 3D Object Digital Twin Dataset](https://mlsanity.com/paper/2504.08541/) (2025)
- [DexGrasp Anything: Towards Universal Robotic Dexterous Grasping with Physics Awareness](https://mlsanity.com/paper/2503.08257/) (2025)
- [NeuManifold: Neural Watertight Manifold Reconstruction with Efficient and High-Quality Rendering Support](https://mlsanity.com/paper/2305.17134/) (2023)
- [Dexonomy: Synthesizing All Dexterous Grasp Types in a Grasp Taxonomy](https://mlsanity.com/paper/2504.18829/) (2025)
- [DexVLG: Dexterous Vision-Language-Grasp Model at Scale](https://mlsanity.com/paper/2507.02747/) (2025)
- [InternScenes: A Large-scale Simulatable Indoor Scene Dataset with Realistic Layouts](https://mlsanity.com/paper/2509.10813/) (2025)
- [EFEM: Equivariant Neural Field Expectation Maximization for 3D Object Segmentation Without Scene Supervision](https://mlsanity.com/paper/2303.15440/) (2023)
- [Towards Physically Executable 3D Gaussian for Embodied Navigation](https://mlsanity.com/paper/2510.21307/) (2025)
- [ShapeGrasp: Zero-Shot Task-Oriented Grasping with Large Language Models through Geometric Decomposition](https://mlsanity.com/paper/2403.18062/) (2024)
- [BEHAVIOR Vision Suite: Customizable Dataset Generation via Simulation](https://mlsanity.com/paper/2405.09546/) (2024)
- [Do as I Do: Dexterous Manipulation Data from Everyday Human Videos](https://mlsanity.com/paper/2606.19333/) (2026)
- [Multi-GraspLLM: A Multimodal LLM for Multi-Hand Semantic Guided Grasp Generation](https://mlsanity.com/paper/2412.08468/) (2024)
- [ManiFoundation Model for General-Purpose Robotic Manipulation of Contact Synthesis with Arbitrary Objects and Robots](https://mlsanity.com/paper/2405.06964/) (2024)
- [Beyond Imitation: Reinforcement Learning-Based Sim-Real Co-Training for VLA Models](https://mlsanity.com/paper/2602.12628/) (2026)
- [DeepSimHO: Stable Pose Estimation for Hand-Object Interaction via Physics Simulation](https://mlsanity.com/paper/2310.07206/) (2023)
- [CORN: Contact-based Object Representation for Nonprehensile Manipulation of General Unseen Objects](https://mlsanity.com/paper/2403.10760/) (2024)
- [Convex Decomposition of Indoor Scenes](https://mlsanity.com/paper/2307.04246/) (2023)

## Abstract (arXiv)

Approximate convex decomposition aims to decompose a 3D shape into a set of almost convex components, whose convex hulls can then be used to represent the input shape. It thus enables efficient geometry processing algorithms specifically designed for convex shapes and has been widely used in game engines, physics simulations, and animation. While prior works can capture the global structure of input shapes, they may fail to preserve fine-grained details (e.g., filling a toaster's slots), which are critical for retaining the functionality of objects in interactive environments. In this paper, we propose a novel method that addresses the limitations of existing approaches from three perspectives: (a) We introduce a novel collision-aware concavity metric that examines the distance between a shape and its convex hull from both the boundary and the interior. The proposed concavity preserves collision conditions and is more robust to detect various approximation errors. (b) We decompose shapes by directly cutting meshes with 3D planes. It ensures generated convex hulls are intersection-free and avoids voxelization errors. (c) Instead of using a one-step greedy strategy, we propose employing a multi-step tree search to determine the cutting planes, which leads to a globally better solution and avoids unnecessary cuttings. Through extensive evaluation on a large-scale articulated object dataset, we show that our method generates decompositions closer to the original shape with fewer components. It thus supports delicate and efficient object interaction in downstream applications. We will release our implementation to facilitate future research.