1. In a computer system having a processor and a display, a computer implemented method for computing a subdivision surface by incrementally processing and outputting the subdivision surface to a final subdivision level to more accurately render a 3 dimensional (3D) surface, the method comprising the computer implemented steps of: a) pulling polygons from a polygon mesh of a 3D surface; b) storing the polygons into a 2 dimensional array such that the vertices of the polygons occupy nodes of the 2 dimensional array; c1) subdividing the polygons stored in a first portion of the 2 dimensional array into resulting polygons; c2) outputting the resulting polygons stored in the first portion to the graphics pipeline such that memory previously storing the first portion can be reused, wherein the resulting polygons stored in the first portion have been subdivided by at least three levels; c3) subdividing the polygons stored in a second portion of the 2 dimensional array into resulting polygons; c4) outputting the resulting polygons stored in the second portion to the graphics pipeline; and d) outputting the resulting polygons into a graphics pipeline wherein the graphics pipeline renders the resulting polygons into a 3D image on a computer display.