TangramPuzzle: Benchmarking Geometric Constraint-Based Compositional Spatial Reasoning in MLLMs

Multimodal Large Language Models (MLLMs) have achieved remarkable progress in visual recognition and semantic understanding, yet precise compositional spatial reasoning under geometric constraints remains underexplored. Existing benchmarks mainly assess coarse spatial relations and rarely support rigorous geometric verification or multiple valid solutions in constructive tasks. To address these limitations, we introduce TangramPuzzle, a benchmark comprising 668 validated configurations and 1,336 instances for evaluating compositional spatial reasoning under geometric constraints. We formulate the Tangram Construction Expression (TCE) to encode tangram configurations with machine-verifiable geometric specifications, together with a multi-solution-aware verifier that separately evaluates geometric validity and silhouette fidelity. TangramPuzzle covers two complementary evaluation tasks: part-to-whole Outline Prediction and whole-to-part End-to-End Assembly Generation. We conduct extensive evaluation experiments on advanced open-source and proprietary models, revealing an interesting insight: MLLMs tend to prioritize matching the target silhouette while neglecting geometric constraints, leading to distortions or deformations of the pieces.