Methods and apparatus render images of digital objects or prepare digital objects for subsequent processing. The method includes sorting data representative of positions of at least three vertices of polygons of a digital object, then determining whether the orientation of the vertices of each polygon from a specific reference point differs from the actual, or original, orientation of the vertices. Such a determination may be made by generating an orientation decision variable based on the relative positions of the vertices and calculating a cross product term (CPT) after the vertex data has been sorted. The CPT may also be used in other operations involving the polygon, such as in imparting appearance characteristics to the polygon. The method may be embodied as a computer program that controls the operation of a processor. Processors, computers, and systems that practice the method are also contemplated.