Multimodal Large Language Models (MLLMs) have achieved remarkable progress but continue to struggle with geometric reasoning, primarily due to the perception bottleneck regarding fine-grained visual elements. While formal languages have aided plane geometry understanding, solid geometry which requires spatial understanding remains largely unexplored. In this paper, we address this challenge by designing a unified formal language that integrates plane and solid geometry, comprehensively covering geometric structures and semantic relations. We construct GDP-29K, a large-scale dataset comprising 20k plane and 9k solid geometry samples collected from diverse real-world sources, each paired with its ground-truth formal description. To ensure syntactic correctness and geometric consistency, we propose a training paradigm that combines Supervised Fine-Tuning with Reinforcement Learning via Verifiable Rewards. Experiments show that our approach achieves state-of-the-art parsing performance. Furthermore, we demonstrate that our parsed formal descriptions serve as a critical cognitive scaffold, significantly boosting MLLMs' capabilities for downstream geometry reasoning tasks. Our data and code are available at Geoparsing.
@article{arxiv.2604.11600,
title = {Geoparsing: Diagram Parsing for Plane and Solid Geometry with a Unified Formal Language},
author = {Peijie Wang and Ming-Liang Zhang and Jun Cao and Chao Deng and Dekang Ran and Hongda Sun and Pi Bu and Xuan Zhang and Yingyao Wang and Jun Song and Bo Zheng and Fei Yin and Cheng-Lin Liu},
journal= {arXiv preprint arXiv:2604.11600},
year = {2026}
}