MagicGeo: Training-Free Text-Guided Geometric Diagram Generation
Journal:
arXiv
Published Date:
Feb 19, 2025
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.
