MagicGeo: Training-Free Text-Guided Geometric Diagram Generation

TL;DR

MagicGeo is a novel, training-free framework that generates accurate geometric diagrams from text descriptions by combining language models with formal mathematical solving, improving automation in educational and scientific contexts.

Contribution

It introduces MagicGeo, a training-free, coordinate optimization-based method for text-guided geometric diagram generation, and provides MagicGeoBench, a new benchmark dataset for evaluation.

Findings

Outperforms existing methods in qualitative assessments.

Achieves high geometric correctness through formal language solving.

Demonstrates scalability and accuracy in diagram generation.

Abstract

Geometric diagrams are critical in conveying mathematical and scientific concepts, yet traditional diagram generation methods are often manual and resource-intensive. While text-to-image generation has made strides in photorealistic imagery, creating accurate geometric diagrams remains a challenge due to the need for precise spatial relationships and the scarcity of geometry-specific datasets. This paper presents MagicGeo, a training-free framework for generating geometric diagrams from textual descriptions. MagicGeo formulates the diagram generation process as a coordinate optimization problem, ensuring geometric correctness through a formal language solver, and then employs coordinate-aware generation. The framework leverages the strong language translation capability of large language models, while formal mathematical solving ensures geometric correctness. We further introduce MagicGeoBench, a benchmark dataset of 220 geometric diagram descriptions, and demonstrate that MagicGeo outperforms current methods in both qualitative and quantitative evaluations. This work provides a scalable, accurate solution for automated diagram generation, with significant implications for educational and academic applications.