1. A computer executable area subdivision methodology for visible surface determination of elements of an image frame of a digital scene wherein the elements are represented by geometric interval functions stored within virtual memory, the steps comprising: (a) executing, by means of interval arithmetic, a robust and non-heuristic area analysis of a screen or pixel coordinate system of the image frame in furtherance of ascertaining at least a portion of a visible solution set of an element of the elements of the image frame; and, (b) computing said at least a portion of the visible solution set of the element of the elements of the image frame.