The construction of online vectorized High-Definition (HD) maps is critical for downstream prediction and planning. Recent efforts have built strong baselines for this task, however, shapes and relations of instances in urban road systems are still under-explored, such as parallelism, perpendicular, or rectangle-shape. In our work, we propose GeMap ($\textbf{Ge}$ometry $\textbf{Map}$), which end-to-end learns Euclidean shapes and relations of map instances beyond basic perception. Specifically, we design a geometric loss based on angle and distance clues, which is robust to rigid transformations. We also decouple self-attention to independently handle Euclidean shapes and relations. Our method achieves new state-of-the-art performance on the NuScenes and Argoverse 2 datasets. Remarkably, it reaches a 71.8% mAP on the large-scale Argoverse 2 dataset, outperforming MapTR V2 by +4.4% and surpassing the 70% mAP threshold for the first time. Code is available at https://github.com/cnzzx/GeMap
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