# Concise Plane Arrangements for Low-Poly Surface and Volume Modelling

arXiv: https://arxiv.org/abs/2404.06154 · HTML: https://mlsanity.com/paper/2404.06154/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 36 references that are in the map.
- First posted on arXiv 9 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [BSP-Net: Generating Compact Meshes via Binary Space Partitioning](https://mlsanity.com/paper/1911.06971/) (2019)
- [Thingi10K: A Dataset of 10,000 3D-Printing Models](https://mlsanity.com/paper/1605.04797/) (2016)
- [CvxNet: Learnable Convex Decomposition](https://mlsanity.com/paper/1909.05736/) (2019)
- [Points2Surf: Learning Implicit Surfaces from Point Cloud Patches](https://mlsanity.com/paper/2007.10453/) (2020)
- [Approximate Convex Decomposition for 3D Meshes with Collision-Aware Concavity and Tree Search](https://mlsanity.com/paper/2205.02961/) (2022)
- [CSG-Stump: A Learning Friendly CSG-Like Representation for Interpretable Shape Parsing](https://mlsanity.com/paper/2108.11305/) (2021)
- [D2CSG: Unsupervised Learning of Compact CSG Trees with Dual Complements and Dropouts](https://mlsanity.com/paper/2301.11497/) (2023)
- [Reconstructing Compact Building Models from Point Clouds Using Deep Implicit Fields](https://mlsanity.com/paper/2112.13142/) (2021)
- [A Survey and Benchmark of Automatic Surface Reconstruction from Point Clouds](https://mlsanity.com/paper/2301.13656/) (2023)

## Built on by (most cited first, 4 of 4)

- [Parametric Point Cloud Completion for Polygonal Surface Reconstruction](https://mlsanity.com/paper/2503.08363/) (2025)
- [HaloGS: Loose Coupling of Compact Geometry and Gaussian Splats for 3D Scenes](https://mlsanity.com/paper/2505.20267/) (2025)
- [Unified Primitive Proxies for Structured Shape Completion](https://mlsanity.com/paper/2601.00759/) (2026)
- [Hierarchical Space Partition for Surface Reconstruction](https://mlsanity.com/paper/2606.04891/) (2026)

## Abstract (arXiv)

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire scenes: (i) an ordering scheme for the plane insertion and (ii) the direct use of input points during arrangement construction. Both ingredients reduce the number of unwanted splits, resulting in improved scalability of the construction mechanism by up to two orders of magnitude compared to existing algorithms. We further introduce a remeshing and simplification technique that allows us to extract low-polygon surface meshes and lightweight convex decompositions of volumes from the arrangement. We show that our approach leads to state-of-the-art results for the aforementioned tasks by comparing it to learning-based and traditional approaches on various different datasets. Our implementation is available at https://github.com/raphaelsulzer/compod .