A robust and automatic discretization algorithm for complex conformal finite-difference time-domain (C-FDTD) simulation is presented in this publication. The targeted application range is to enable C-FDTD simulations for real-word engineering problems. Based on computer-graphics methods, complex CAD models with thousands of distinct parts can be efficiently and robustly discretized. A versatile concept is introduced to avoid numerical inaccuracies while calculating intersections, and to lead to a symmetric discretization without the overhead of "virtual lines." In addition, a necessary three-dimensional consistency check/correction, as well as merging of conformal cells of different CAD parts, are explained. The conformal geometric information is incorporated into the conventional FDTD algorithm using the conventional updating coefficients, which are conformally enhanced. Due to the derived stability criterion, the conformal updating scheme is always stable. The robustness and performance of the discretization algorithm presented is demonstrated with CAD models of increasing complexity towards real-world benchmarks. A conformal FDTD simulation with 80 million computational cells and 229 distinguished parts, representing a complete mobile phone and a head with hand, demonstrates the capabilities of the versatile technique.