A method and apparatus includes primitive setup circuitry for determining a plurality of functions for an input graphics primitive, including an edge function associated with each edge of the input graphics primitive and a depth function associated with the input graphics primitive. Rasterization circuitry performs a rasterization operation in order to calculate position data for a plurality of graphics fragments to be used to represent the input graphics primitive. In a default mode of operation, depth bound clipping circuitry performs a depth bound clipping operation by determining, for each graphics fragment in said plurality of graphics fragments, a depth value for said graphics fragment using the depth function, and determining whether said depth value resides within a valid depth range of a view frustum, the graphics fragment being discarded from further processing if its depth value does not reside within said valid depth range.