A graphics rendering chip serially renders a stream of geometric primitives to image regions called chunks. A set-up processor in the chip parses rendering commands and the stream of geometric primitives and computes edge equation parameters. A scan-convert processor receives the edge equation parameters from the set-up processor and scan converts the geometric primitives to produce pixel records and fragment records. An internal, double-buffered pixel buffer stores pixel records for fully covered pixel addresses and also stores references to fragment lists stored in a fragment buffer. A pixel engine performs hidden surface removal and controls storage of pixel and fragment records to the pixel and fragment buffers, respectively. An anti-aliasing engine resolves pixel data for one pixel buffer while the pixel engine fills the other pixel buffer with pixel data for the next chunk.