To enable automated software testing, the ability to automatically navigate to a state of interest and to explore all, or at least sufficient number of, instances of such a state is fundamental. When testing a computer game the problem has an extra dimension, namely the virtual world where the game is played on. This world often plays a dominant role in constraining which logical states are reachable, and how to reach them. So, any automated testing algorithm for computer games will inevitably need a layer that deals with navigation on a virtual world. Unlike e.g. navigating through the GUI of a typical web-based application, navigating over a virtual world is much more challenging. This paper discusses how concepts from geometry and graph-based path finding can be applied in the context of game testing to solve the problem of automated navigation and exploration. As a proof of concept, the paper also briefly discusses the implementation of the proposed approach.