An apparatus and a method for generating 3-dimensional computer graphic images. The image is first sub-divided into a plurality of rectangular areas. A display list memory is loaded with object data for each rectangular area. The image and shading data for each picture element of each rectangular area are derived from the object data in the image synthesis processor and a texturizing and shading processor. A depth range generator derives a depth range for each rectangular area from the object data as the imaging and shading data is derived. This is compared with the depth of each new object to be provided to the image synthesis processor and the object may be prevented from being provided to the image synthesis processor independence on the result of the comparison.