# Combinatorial 3D Shape Generation via Sequential Assembly

arXiv: https://arxiv.org/abs/2004.07414 · HTML: https://mlsanity.com/paper/2004.07414/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2020.

## Built on by (most cited first, 13 of 13)

- [Generating Physically Stable and Buildable Brick Structures from Text](https://mlsanity.com/paper/2505.05469/) (2025)
- [Brick-by-Brick: Combinatorial Construction with Deep Reinforcement Learning](https://mlsanity.com/paper/2110.15481/) (2021)
- [Planning Assembly Sequence with Graph Transformer](https://mlsanity.com/paper/2210.05236/) (2022)
- [Neural Assembler: Learning to Generate Fine-Grained Robotic Assembly Instructions from Multi-View Images](https://mlsanity.com/paper/2404.16423/) (2024)
- [Physics-Aware Combinatorial Assembly Sequence Planning using Data-free Action Masking](https://mlsanity.com/paper/2408.10162/) (2024)
- [BrickNet: Graph-Backed Generative Brick Assembly](https://mlsanity.com/paper/2604.22984/) (2026)
- [Budget-Aware Sequential Brick Assembly with Efficient Constraint Satisfaction](https://mlsanity.com/paper/2210.01021/) (2022)
- [A Lightweight and Transferable Design for Robust LEGO Manipulation](https://mlsanity.com/paper/2309.02354/) (2023)
- [Learning to Assemble Geometric Shapes](https://mlsanity.com/paper/2205.11809/) (2022)
- [Stable and Consistent Prediction of 3D Characteristic Orientation via Invariant Residual Learning](https://mlsanity.com/paper/2306.11406/) (2023)
- [TreeSBA: Tree-Transformer for Self-Supervised Sequential Brick Assembly](https://mlsanity.com/paper/2407.15648/) (2024)
- [Putting 3D Spatially Sparse Networks on a Diet](https://mlsanity.com/paper/2112.01316/) (2021)
- [AssemblyComplete: 3D Combinatorial Construction with Deep Reinforcement Learning](https://mlsanity.com/paper/2410.15469/) (2024)

## Abstract (arXiv)

Sequential assembly with geometric primitives has drawn attention in robotics and 3D vision since it yields a practical blueprint to construct a target shape. However, due to its combinatorial property, a greedy method falls short of generating a sequence of volumetric primitives. To alleviate this consequence induced by a huge number of feasible combinations, we propose a combinatorial 3D shape generation framework. The proposed framework reflects an important aspect of human generation processes in real life -- we often create a 3D shape by sequentially assembling unit primitives with geometric constraints. To find the desired combination regarding combination evaluations, we adopt Bayesian optimization, which is able to exploit and explore efficiently the feasible regions constrained by the current primitive placements. An evaluation function conveys global structure guidance for an assembly process and stability in terms of gravity and external forces simultaneously. Experimental results demonstrate that our method successfully generates combinatorial 3D shapes and simulates more realistic generation processes. We also introduce a new dataset for combinatorial 3D shape generation. All the codes are available at urlhttps://github.com/POSTECH-CVLab/Combinatorial-3D-Shape-Generation.