FormalAnalyticGeo Generates Multimodal Geometry Problems.

Despite advancements in Multimodal Large Language Models (MLLMs) for math reasoning, analytic geometry remains underexplored due to a lack of annotated datasets. Existing diagram generation methods struggle with the precision and constraint-driven layouts required for analytic geometry. This paper introduces FormalAnalyticGeo, a novel neural-symbolic framework designed for the fully automatic generation of multimodal analytic geometry problems. The core of FormalAnalyticGeo is the Condition Description Language (CDL), a formal intermediate representation that seamlessly connects free-form problem text with accurate diagram rendering. This rendering is achieved through a Signed Distance Field (SDF) engine, ensuring geometric precision for elements like conic curves. The framework employs four specialized LLM components: a Generator for diverse problems, a Formalizer to convert problems into CDL, a Measurer to extract ground-truth answers from rendered diagrams, and a Quality Verifier that provides structured feedback for automatic retries, creating a closed-loop system that eliminates human annotation. This scalable approach has yielded AnalyticGeo7K, a dataset of over 7,000 verified problems with high accuracy, demonstrating a significant step forward in generating complex math reasoning data.