This paper provides a detailed description of a set of algorithms to efficiently manipulate 3D geometric models to compute physical constraints and range observation models, data that is usually required in real-time mobile robotics or simulation. Our approach uses a standard file format to describe the environment and processes the model using the openGL library, a widely-used programming interface for 3D scene manipulation. The paper also presents results on a test model for benchmarking, and on a model of a real urban environment, where the algorithms have been effectively used for real-time localization in a large urban setting.