Virtual characters have become crucial to many interactive 3D graphical virtual environment simulations in the context of virtual reality and computer games. One of the primary concerns of the designers of such environments is to model the interaction of the virtual characters with the users. The gaze of the virtual character forms a chief component of this interaction. When the gaze of the virtual character is directed correctly towards the users, they perceive a sense of presence inside the virtual environment, during their interactions with the virtual character. We present, in this paper, a simple idea to control the gaze of a virtual character based on the viewpoint of the user involved in the interaction, suitable both for Virtual Reality as well as Augmented Reality applications. We also place the idea in the context of methods to control gaze that already exist in literature by providing a summary of the existing works.