The author gives the outline of an algorithm to cut down on computing time when updating a picture frame while the camera is static. By splitting the screen into small squares and appending to each square a table of the rays passing through pixels in the square, one needs only to check which pixels do change color (by becoming hidden or uncovered) and to redraw the rays passing through these pixels. The first frame naturally must be drawn in the traditional way, touching all pixels. A number of considerations for memory management are given for further reduction of computer time and to make the algorithm independent of resolution. The author’s unpublished algorithm is reported to have cut down computing time for a 350-frame sequence with a static camera by about 73 percent. The paper ends with some indications on how to adapt the memory management scheme to the case of a moving camera.