无需训练即可根据文字生成精准几何图，解决数学教育中的制图难题
MagicGeo: Training-Free Text-Guided Geometric Diagram Generation
- 将绘图转为坐标优化问题，用形式化语言求解保证几何正确性
- 在220个几何描述上验证，生成效果优于现有方法
- 适合教育工具、学术出版等需要高精度图形的场景
几何图示在传达数学与科学概念中至关重要，但传统生成方式依赖人工且耗时。尽管文本到图像生成在写实图像方面取得进展，但准确生成几何图仍面临挑战，原因在于需精确的空间关系，且缺乏几何专用数据集。本文提出 MagicGeo，一种无需训练的文本引导几何图生成框架。该框架将绘图过程建模为坐标优化问题，通过形式化语言求解器确保几何正确性，并结合坐标感知生成。框架利用大语言模型强大的语义理解能力，同时以形式化数学求解保障准确性。我们还构建了 MagicGeoBench 基准数据集，包含 220 个几何图描述，实验表明 MagicGeo 在定性和定量评估中均优于当前方法。本工作为自动化绘图提供了可扩展、高精度的解决方案，对教育和学术应用具有重要意义。
原文摘要 · Abstract (English)
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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