Object-centric process mining (OCPM) is gaining traction in both academia and industry due to its ability to model real-world processes more accurately than traditional case-centric approaches. By considering multiple interacting objects, object-centric Petri nets (OCPNs) offer a richer process representation, but this also introduces unique challenges for visualization. The presence of multiple object types, variable arcs, and complex interactions complicates the creation of clear and interpretable layouts. In this paper, we address these challenges by presenting a dedicated layout algorithm tailored to the structural characteristics of OCPNs. Inspired by the Sugiyama framework, the algorithm balances aesthetic and functional criteria, guided by a set of domain-specific quality metrics. We implemented our approach in an open-source web-based tool, OCPN Visualizer, and a reusable JavaScript library for integration into third-party applications. A user study confirms the practical relevance of our approach and highlights its effectiveness in improving the interpretability of object-centric process visualizations.