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arXiv · 2502.13855

MagicGeo: Training-Free Text-Guided Geometric Diagram Generation

Junxiao Wang·Ting Zhang·Heng Yu·Jingdong Wang·Hua Huang
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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.

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Junxiao Wang, Ting Zhang, Heng Yu, Jingdong Wang, Hua Huang. 2025-02-19. MagicGeo: Training-Free Text-Guided Geometric Diagram Generation. https://arxiv.org/abs/2502.13855

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