Abstract: A system which enables the user to visualize directly an object in 3-D Lobachevskian, 4-D Euclidean, or other geometries. The system includes an input device (10), a transducer (11), a processing device (11), and an output device (12). The transducer (11) determines incident angles of light rays from each object point with respect to the coordinate axes of the system eye, employing geometric relationships to the alternative geometry. Then, using those incident angles, it defines new rays which produce an image constituting a direct representation on the human retina of the original object in the space of the alternative geometry. The processing device (11) them assembles the image points and delivers them to an output device (12) to be viewed by the user.