# Draw it like Euclid: Teaching transformer models to generate CAD profiles using ruler and compass construction steps

arXiv: https://arxiv.org/abs/2601.09428 · HTML: https://mlsanity.com/paper/2601.09428/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 36 references that are in the map.
- First posted on arXiv 14 Jan 2026.

## Builds on (most cited first, 23 of 23)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [ABC: A Big CAD Model Dataset For Geometric Deep Learning](https://mlsanity.com/paper/1812.06216/) (2018)
- [DeepCAD: A Deep Generative Network for Computer-Aided Design Models](https://mlsanity.com/paper/2105.09492/) (2021)
- [ReMax: A Simple, Effective, and Efficient Reinforcement Learning Method for Aligning Large Language Models](https://mlsanity.com/paper/2310.10505/) (2023)
- [SkexGen: Autoregressive Generation of CAD Construction Sequences with Disentangled Codebooks](https://mlsanity.com/paper/2207.04632/) (2022)
- [BrepGen: A B-rep Generative Diffusion Model with Structured Latent Geometry](https://mlsanity.com/paper/2401.15563/) (2024)
- [Beyond A*: Better Planning with Transformers via Search Dynamics Bootstrapping](https://mlsanity.com/paper/2402.14083/) (2024)
- [The Optimal Reward Baseline for Gradient-Based Reinforcement Learning](https://mlsanity.com/paper/1301.2315/) (2013)
- [Computer-Aided Design as Language](https://mlsanity.com/paper/2105.02769/) (2021)
- [IconShop: Text-Guided Vector Icon Synthesis with Autoregressive Transformers](https://mlsanity.com/paper/2304.14400/) (2023)
- [SketchGraphs: A Large-Scale Dataset for Modeling Relational Geometry in Computer-Aided Design](https://mlsanity.com/paper/2007.08506/) (2020)
- [SketchGen: Generating Constrained CAD Sketches](https://mlsanity.com/paper/2106.02711/) (2021)
- [Vitruvion: A Generative Model of Parametric CAD Sketches](https://mlsanity.com/paper/2109.14124/) (2021)
- [Engineering Sketch Generation for Computer-Aided Design](https://mlsanity.com/paper/2104.09621/) (2021)
- [CADCrafter: Generating Computer-Aided Design Models from Unconstrained Images](https://mlsanity.com/paper/2504.04753/) (2025)
- [Chain of Thought Imitation with Procedure Cloning](https://mlsanity.com/paper/2205.10816/) (2022)
- [Seek-CAD: A Self-refined Generative Modeling for 3D Parametric CAD Using Local Inference via DeepSeek](https://mlsanity.com/paper/2505.17702/) (2025)
- [cadrille: Multi-modal CAD Reconstruction with Reinforcement Learning](https://mlsanity.com/paper/2505.22914/) (2025)
- [NeuroNURBS: Learning Efficient Surface Representations for 3D Solids](https://mlsanity.com/paper/2411.10848/) (2024)
- [Aligning Constraint Generation with Design Intent in Parametric CAD](https://mlsanity.com/paper/2504.13178/) (2025)

## Built on by (most cited first, 1 of 1)

- [Pointer-CAD v2: Plan-Then-Construct CAD Generation with Dimension-Aware Parametric Precision](https://mlsanity.com/paper/2606.29301/) (2026)

## Abstract (arXiv)

We introduce a new method of generating Computer Aided Design (CAD) profiles via a sequence of simple geometric constructions including curve offsetting, rotations and intersections. These sequences start with geometry provided by a designer and build up the points and curves of the final profile step by step. We demonstrate that adding construction steps between the designer's input geometry and the final profile improves generation quality in a similar way to the introduction of a chain of thought in language models. Similar to the constraints in a parametric CAD model, the construction sequences reduce the degrees of freedom in the modeled shape to a small set of parameter values which can be adjusted by the designer, allowing parametric editing with the constructed geometry evaluated to floating point precision. In addition we show that applying reinforcement learning to the construction sequences gives further improvements over a wide range of metrics, including some which were not explicitly optimized.