1. A method, comprising: presenting, by a computer, multiple interactive items on a display coupled to the computer; projecting a light toward a scene that includes a user of the computer; capturing and processing the projected light returned from the scene so as to reconstruct an initial three-dimensional (3D) map containing at least a head of the user of the computer; capturing and processing a two dimensional (2D) image containing reflections of the projected light from a fundus and a cornea of an eye of the user; extracting, from the initial 3D map, 3D coordinates of the head; identifying, based on the 3D coordinates of the head and the reflections of the projected light from the fundus and the cornea of the eye, a direction of a gaze of the user; selecting, in response to the gaze direction, one of the multiple interactive items; subsequent to selecting the one of the interactive items, receiving a sequence of three-dimensional (3D) maps containing at least a hand of the user; analyzing the 3D maps to detect a gesture performed by the user; and performing an operation on the selected interactive item in response to the gesture.