Draw it like Euclid: Teaching transformer models to generate CAD profiles using ruler and compass construction steps
Fuente:
arXiv
Saved in:
| Main Authors: | , , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909990310117376 |
|---|---|
| author | Li, Siyi Lambourne, Joseph G. Zhang, Longfei Jayaraman, Pradeep Kumar Willis, Karl. D. D. |
| author_facet | Li, Siyi Lambourne, Joseph G. Zhang, Longfei Jayaraman, Pradeep Kumar Willis, Karl. D. D. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_09428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Draw it like Euclid: Teaching transformer models to generate CAD profiles using ruler and compass construction steps Li, Siyi Lambourne, Joseph G. Zhang, Longfei Jayaraman, Pradeep Kumar Willis, Karl. D. D. Machine Learning Graphics 65D17 (Primary) 68U07, 68T05 (Secondary) J.6 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. |
| title | Draw it like Euclid: Teaching transformer models to generate CAD profiles using ruler and compass construction steps |
| topic | Machine Learning Graphics 65D17 (Primary) 68U07, 68T05 (Secondary) J.6 |
| url | https://arxiv.org/abs/2601.09428 |