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

2026-01-14

AI Summary

This work addresses the challenge of enabling Transformer-based models to generate high-quality, editable CAD sketches while preserving design intent and parametric control. Inspired by classical compass-and-straightedge constructions, the authors propose modeling sketch generation as a sequence of geometric construction steps—such as offsetting, rotation, and intersection—and introduce, for the first time, a “chain-of-thought”-like sequence of geometric operations. The generation process is optimized via reinforcement learning and implemented using a Transformer architecture capable of handling floating-point parameters, thereby supporting fine-grained parametric editing. Experimental results demonstrate that the proposed method significantly outperforms existing baselines in terms of sketch quality, editability, and multiple evaluation metrics, with consistent improvements even on metrics not explicitly optimized during training.

Technology Category

• Computer Vision: Diffusion Models for Vision
• Natural Language Processing: Generation
• Machine Learning: Deep Neural Architectures and Foundation Models

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information

Abstract

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.

Problem

• CAD generation
• geometric construction
• parametric modeling
• transformer models
• ruler and compass

Innovation

• geometric construction
• parametric CAD
• chain-of-thought reasoning
• reinforcement learning
• transformer models