A graphical display system and a method for Z-subdivision of polygons into quadrilaterals and triangles whose vertices are arranged between two adjacent Z planes. This slicing allows both atmospheric and texture parameters to be interpolated linearly with minimal error within each quadrilateral or triangle slice. Object data from a host computer is processed by four pipelined graphics subsystems before being displayed on a display screen. Each object is decomposed into a set of primitives. Each primitive may intersect one or more Z planes thereby producing a set of component portions of the primitive. Once a primitive is sliced into component portions, a texture is mapped onto each component portion by interpolating texture parameters to points on or within the component portion. Finally, the textured component portions are rendered on a display device thereby creating a seamless complete object.