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.

Abstract: A system for verifying that the proper ingredient-containing transport containers have been assembled at a particular soup-blending kettle, in which a hole-coded metal key is permanently affixed to each container and provided with an array of machine-readable holes corresponding to a number unique to each container. At the ingredient-dispensing station, a key-reader reads out the identifying number of the container and transmits it to that kettle station to which the container is to be delivered. The transport container is then delivered to the kettle station, where the key code is again machine read; the container number thus read out at the kettle station is compared with that previously transmitted from the ingredient-dispensing station, and if they both represent the same number then the proper container has been delivered to the kettle station and its contents are dumped into the kettle.