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This paper introduces a novel visual attention model to compute user's gaze position automatically, i.e. without using a gaze-tracking system. Our model is specifically designed for real-time first-person exploration of 3D virtual environments. It is the first model adapted to this context which can compute, in real-time, a continuous gaze point position instead of a set of 3D objects potentially observed by the user. To do so, contrary to previous models which use a mesh-based representation of visual objects, we introduce a representation based on surface-elements. Our model also simulates visual reflexes and the cognitive process which takes place in the brain such as the gaze behavior associated to first-person navigation in the virtual environment. Our visual attention model combines the bottom-up and top-down components to compute a continuous gaze point position on screen that hopefully matches the user's one. We have conducted an experiment to study and compare the performance of our method with a state-of-the-art approach. Our results are found significantly better with more than 100% of accuracy gained. This suggests that computing in realtime a gaze point in a 3D virtual environment is possible and is a valid approach as compared to object-based approaches.