# Intuitive and Efficient Roof Modeling for Reconstruction and Synthesis

arXiv: https://arxiv.org/abs/2109.07683 · HTML: https://mlsanity.com/paper/2109.07683/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2021.

## Built on by (most cited first, 14 of 14)

- [3D Line Mapping Revisited](https://mlsanity.com/paper/2303.17504/) (2023)
- [Smooth Non-Rigid Shape Matching via Effective Dirichlet Energy Optimization](https://mlsanity.com/paper/2210.02870/) (2022)
- [Learning to Construct 3D Building Wireframes from 3D Line Clouds](https://mlsanity.com/paper/2208.11948/) (2022)
- [RoofDiffusion: Constructing Roofs from Severely Corrupted Point Data via Diffusion](https://mlsanity.com/paper/2404.09290/) (2024)
- [3D detection of roof sections from a single satellite image and application to LOD2-building reconstruction](https://mlsanity.com/paper/2307.05409/) (2023)
- [Intelligent Generation of Graphical Game Assets: A Conceptual Framework and Systematic Review of the State of the Art](https://mlsanity.com/paper/2311.10129/) (2023)
- [PolyRoof: Precision Roof Polygonization in Urban Residential Building with Graph Neural Networks](https://mlsanity.com/paper/2503.10913/) (2025)
- [AutoPoly: Predicting a Polygonal Mesh Construction Sequence from a Silhouette Image](https://mlsanity.com/paper/2203.15233/) (2022)
- [ZRG: A Dataset for Multimodal 3D Residential Rooftop Understanding](https://mlsanity.com/paper/2304.13219/) (2023)
- [Polygonizing Roof Segments from High-Resolution Aerial Images Using Yolov8-Based Edge Detection](https://mlsanity.com/paper/2503.09187/) (2025)
- [AIM2PC: Aerial Image to 3D Building Point Cloud Reconstruction](https://mlsanity.com/paper/2503.18527/) (2025)
- [Flatten The Complex: Joint B-Rep Generation via Compositional k-Cell Particles](https://mlsanity.com/paper/2601.17733/) (2026)
- [Patchwork: A compact representation for 3D polygonal shapes](https://mlsanity.com/paper/2605.16266/) (2026)
- [Diffusion Transformers for Roof Graph Synthesis and Reconstruction](https://mlsanity.com/paper/2608.25652/) (2026)

## Abstract (arXiv)

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.