  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.
