用形式化语言和优化算法，让文字生成精准几何图。
GeoLoom: High-quality Geometric Diagram Generation from Textual Input
- 将自然语言转为专用形式语言GeoLingua，再用蒙特卡洛优化求坐标。
- 在结构保真度上显著超越现有方法，误差更低。
- 适合需要高精度几何图的教育或工程场景。
高质量几何图生成兼具挑战与机遇：既要保证严格的空间准确性，又具备可引导生成的明确约束。受近期几何问题求解中使用形式语言和符号求解器提升正确性和可解释性的启发，我们提出GeoLoom，一种面向几何领域的文本到图形生成新框架。GeoLoom包含两个核心组件：一个自动形式化模块，将自然语言转化为专为生成设计的形式语言GeoLingua；一个坐标求解器，利用高效的蒙特卡洛优化将形式化约束映射为精确坐标。为支持该框架，我们构建了GeoNF数据集，对齐自然语言几何描述与形式化GeoLingua描述。我们还提出基于约束的评估指标，量化结构偏差，为迭代优化提供数学基础的监督。实验结果表明，GeoLoom在结构保真度上显著优于现有最佳基线，为可解释且可扩展的图表生成提供了原则性基础。
原文摘要 · Abstract (English)
High-quality geometric diagram generation presents both a challenge and an opportunity: it demands strict spatial accuracy while offering well-defined constraints to guide generation. Inspired by recent advances in geometry problem solving that employ formal languages and symbolic solvers for enhanced correctness and interpretability, we propose GeoLoom, a novel framework for text-to-diagram generation in geometric domains. GeoLoom comprises two core components: an autoformalization module that translates natural language into a specifically designed generation-oriented formal language GeoLingua, and a coordinate solver that maps formal constraints to precise coordinates using the efficient Monte Carlo optimization. To support this framework, we introduce GeoNF, a dataset aligning natural language geometric descriptions with formal GeoLingua descriptions. We further propose a constraint-based evaluation metric that quantifies structural deviation, offering mathematically grounded supervision for iterative refinement. Empirical results demonstrate that GeoLoom significantly outperforms state-of-the-art baselines in structural fidelity, providing a principled foundation for interpretable and scalable diagram generation.
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