# Sketch2PQ: Freeform Planar Quadrilateral Mesh Design via a Single Sketch

arXiv: https://arxiv.org/abs/2201.09367 · HTML: https://mlsanity.com/paper/2201.09367/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 65 references that are in the map.
- First posted on arXiv 23 Jan 2022.

## Builds on (most cited first, 11 of 11)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [AtlasNet: A Papier-Mach'e Approach to Learning 3D Surface Generation](https://mlsanity.com/paper/1802.05384/) (2018)
- [MarrNet: 3D Shape Reconstruction via 2.5D Sketches](https://mlsanity.com/paper/1711.03129/) (2017)
- [Sketch2Model: View-Aware 3D Modeling from Single Free-Hand Sketches](https://mlsanity.com/paper/2105.06663/) (2021)
- [3D Shape Reconstruction from Sketches via Multi-view Convolutional Networks](https://mlsanity.com/paper/1707.06375/) (2017)
- [3D Sketching using Multi-View Deep Volumetric Prediction](https://mlsanity.com/paper/1707.08390/) (2017)
- [Better Patch Stitching for Parametric Surface Reconstruction](https://mlsanity.com/paper/2010.07021/) (2020)
- [On Linear Spaces of Polyhedral Meshes](https://mlsanity.com/paper/1303.4110/) (2013)

## Built on by (most cited first, 6 of 6)

- [What's the Situation with Intelligent Mesh Generation: A Survey and Perspectives](https://mlsanity.com/paper/2211.06009/) (2022)
- [Point2Quad: Generating Quad Meshes from Point Clouds via Face Prediction](https://mlsanity.com/paper/2504.19545/) (2025)
- [Deep Sketch-Based 3D Modeling: A Survey](https://mlsanity.com/paper/2603.03287/) (2026)
- [Make Your Brief Stroke Real and Stereoscopic: 3D-Aware Simplified Sketch to Portrait Generation](https://mlsanity.com/paper/2302.06857/) (2023)
- [Strokes2Surface: Recovering Curve Networks From 4D Architectural Design Sketches](https://mlsanity.com/paper/2306.07220/) (2023)
- [Reconstruction of a 3D wireframe from a single line drawing via generative depth estimation](https://mlsanity.com/paper/2604.13549/) (2026)

## Abstract (arXiv)

The freeform architectural modeling process often involves two important stages: concept design and digital modeling. In the first stage, architects usually sketch the overall 3D shape and the panel layout on a physical or digital paper briefly. In the second stage, a digital 3D model is created using the sketch as a reference. The digital model needs to incorporate geometric requirements for its components, such as the planarity of panels due to consideration of construction costs, which can make the modeling process more challenging. In this work, we present a novel sketch-based system to bridge the concept design and digital modeling of freeform roof-like shapes represented as planar quadrilateral (PQ) meshes. Our system allows the user to sketch the surface boundary and contour lines under axonometric projection and supports the sketching of occluded regions. In addition, the user can sketch feature lines to provide directional guidance to the PQ mesh layout. Given the 2D sketch input, we propose a deep neural network to infer in real-time the underlying surface shape along with a dense conjugate direction field, both of which are used to extract the final PQ mesh. To train and validate our network, we generate a large synthetic dataset that mimics architect sketching of freeform quadrilateral patches. The effectiveness and usability of our system are demonstrated with quantitative and qualitative evaluation as well as user studies.