# CvxNet: Learnable Convex Decomposition

arXiv: https://arxiv.org/abs/1909.05736 · HTML: https://mlsanity.com/paper/1909.05736/

## Key facts

- Cited by 174 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Sep 2019.

## Built on by (most cited first, 30 of 174)

- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Neural Geometric Level of Detail: Real-time Rendering with Implicit 3D Shapes](https://mlsanity.com/paper/2101.10994/) (2021)
- [Advances in Neural Rendering](https://mlsanity.com/paper/2111.05849/) (2021)
- [LucidDreamer: Domain-free Generation of 3D Gaussian Splatting Scenes](https://mlsanity.com/paper/2311.13384/) (2023)
- [NEAT: Neural Attention Fields for End-to-End Autonomous Driving](https://mlsanity.com/paper/2109.04456/) (2021)
- [Flexible Isosurface Extraction for Gradient-Based Mesh Optimization](https://mlsanity.com/paper/2308.05371/) (2023)
- [D2NeRF: Self-Supervised Decoupling of Dynamic and Static Objects from a Monocular Video](https://mlsanity.com/paper/2205.15838/) (2022)
- [NeSF: Neural Semantic Fields for Generalizable Semantic Segmentation of 3D Scenes](https://mlsanity.com/paper/2111.13260/) (2021)
- [A-SDF: Learning Disentangled Signed Distance Functions for Articulated Shape Representation](https://mlsanity.com/paper/2104.07645/) (2021)
- [Neural Kernel Surface Reconstruction](https://mlsanity.com/paper/2305.19590/) (2023)
- [Neural Parts: Learning Expressive 3D Shape Abstractions with Invertible Neural Networks](https://mlsanity.com/paper/2103.10429/) (2021)
- [3DILG: Irregular Latent Grids for 3D Generative Modeling](https://mlsanity.com/paper/2205.13914/) (2022)
- [POCO: Point Convolution for Surface Reconstruction](https://mlsanity.com/paper/2201.01831/) (2022)
- [What's in your hands? 3D Reconstruction of Generic Objects in Hands](https://mlsanity.com/paper/2204.07153/) (2022)
- [Decomposing 3D Scenes into Objects via Unsupervised Volume Segmentation](https://mlsanity.com/paper/2104.01148/) (2021)
- [LOLNeRF: Learn from One Look](https://mlsanity.com/paper/2111.09996/) (2021)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [SALAD: Part-Level Latent Diffusion for 3D Shape Generation and Manipulation](https://mlsanity.com/paper/2303.12236/) (2023)
- [CAPRI-Net: Learning Compact CAD Shapes with Adaptive Primitive Assembly](https://mlsanity.com/paper/2104.05652/) (2021)
- [Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields](https://mlsanity.com/paper/2106.05187/) (2021)
- [Neural Fields as Learnable Kernels for 3D Reconstruction](https://mlsanity.com/paper/2111.13674/) (2021)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [Neural Marching Cubes](https://mlsanity.com/paper/2106.11272/) (2021)
- [A Skeleton-Driven Neural Occupancy Representation for Articulated Hands](https://mlsanity.com/paper/2109.11399/) (2021)
- [3D Convex Splatting: Radiance Field Rendering with 3D Smooth Convexes](https://mlsanity.com/paper/2411.14974/) (2024)
- [Triangle Splatting for Real-Time Radiance Field Rendering](https://mlsanity.com/paper/2505.19175/) (2025)
- [SECAD-Net: Self-Supervised CAD Reconstruction by Learning Sketch-Extrude Operations](https://mlsanity.com/paper/2303.10613/) (2023)
- [Unsupervised Learning for Cuboid Shape Abstraction via Joint Segmentation from Point Clouds](https://mlsanity.com/paper/2106.03437/) (2021)
- [Reconstructing editable prismatic CAD from rounded voxel models](https://mlsanity.com/paper/2209.01161/) (2022)
- [Deep Implicit Surface Point Prediction Networks](https://mlsanity.com/paper/2106.05779/) (2021)

## Abstract (arXiv)

Any solid object can be decomposed into a collection of convex polytopes (in short, convexes). When a small number of convexes are used, such a decomposition can be thought of as a piece-wise approximation of the geometry. This decomposition is fundamental in computer graphics, where it provides one of the most common ways to approximate geometry, for example, in real-time physics simulation. A convex object also has the property of being simultaneously an explicit and implicit representation: one can interpret it explicitly as a mesh derived by computing the vertices of a convex hull, or implicitly as the collection of half-space constraints or support functions. Their implicit representation makes them particularly well suited for neural network training, as they abstract away from the topology of the geometry they need to represent. However, at testing time, convexes can also generate explicit representations -- polygonal meshes -- which can then be used in any downstream application. We introduce a network architecture to represent a low dimensional family of convexes. This family is automatically derived via an auto-encoding process. We investigate the applications of this architecture including automatic convex decomposition, image to 3D reconstruction, and part-based shape retrieval.