An octal tree subdivision recursively divides a bounded three-dimensional volume into octants about an internal division point. This scheme has been used to represent cellular or enumerated voxel models of solid objects. Given one or more sets of points sampled from the surface of a solid, an octal tree may be generated in which each leaf node contains m or less points. By specifying the tree traversal rule, the points are accessed in a sorted order. By defining m=3, a divide-and-conquer surface triangulation algorithm may be developed which does not require special sampling conditions (such as co-planarity) on subsets of the sample points. By assigning every polygon on a facetted surface to its containing octal element(octel) a pre-ordering is established on the faces. From any viewpoint, surface polygons can be visited in a priority ordered fashion by appropriate tree traversal. The pre-ordering established is shown to be useful in several graphics related contexts including: a viewpoint independent data structure leading to a hidden surface technique; a ray-tracing algorithm; a virtual frame buffer with reduced page faults; and, a simple geometric merging of sets of surface measurements containing no fiducial information.