Abstract: In an interactive three-dimensional graphics system, objects are defined by a plurality of Bezier patches. Said patches are approximated by polygons for the purpose of rendering and rendering occurs on a patch by patch basis. Ordering for the rendering of patches is performed by precalculating order lists. An order list is produced by dividing each area which forms part of an object into a set of polygons and performing a topological sort on said polygons to produce a rendering list for said polygons. An order list is produced for the Bezier patches by considering the first occurence of a polygon from each area set of polygons.