Building suitable representations for diversified environments to enable robot autonomous navigation is a complicated task, especially for large-scale environments, where the captured vast amount of data will give rise to computation and storage bottlenecks. In this letter, we first propose the random mapping method (RMM), which can efficiently project the irregular points in the low-dimensional data set into the high-dimensional one, where the points are approximately linearly separable or distributed. In the mapped space, we then propose a unified environment modeling framework in the form of linear parametric model, which can represent the occupancy maps and terrain models consistently. Adopting the idea of parallel computing, we then apply our method to the large-scale environment modeling to reduce the wall-clock time of calculation without losing much accuracy. Experiments were fully conducted to evaluate the proposed random mapping method and the proposed environmental modeling method, showing their better comprehensive performance compared to the typical methods and state-of-the-art methods.