We present efficient network and geometry generation algorithms for the network element method. After providing sufficient conditions for existence of exact geometries i.e. reproducing first order polynomials without error, we describe a basic network generation algorithm fulfilling those conditions on demand. Then we explain how one can generate network geometries by solving a linear, well-posed problem replacing the original costly non-linear approach that was previously the main computational bottleneck of the network element workflow. We finally illustrate on challenging examples the good behavior of the overall updated network element workflow, from network generation to actual computation of PDE solutions.