We present a highly efficient approach to compute continuous shortest path vector fields on arbitrarily shaped 3D triangular meshes for robot navigation in complex real-world outdoor environments. The continuity of the vector field allows to query the shortest distance, direction and geodesic path to the goal at any point within the mesh triangles, resulting in accurate paths. In order to avoid impassable areas, our wavefront propagation method runs on a modular extendable multilayer map architecture taking different geometric cost layers into account. We describe the mathematical foundation of the geodesic distances and continuous vector field computation and demonstrate the performance in real-world and multilevel environments on our campus with a tunnel, ramps and staircases, and in a difficult, steep forest area with a stone quarry. For reproducibility, we provide a ready-to-use ROS software stack as well as Gazebo simulations.