A system and method for traversing and rendering a graphic primitive represented in screen space, employing block- and band-oriented traversal algorithms in texture mapping. Improved performance is achieved through burst-mode texture access and texture caching in connection with a texture map subdivided into squares. Block- and band-oriented traversal facilitates minimization of page breaks and texture cache swap-out. Improved determinism is facilitated by obviating the need for pixel sorting algorithms. Improved re-use of retrieved data segments in burst-mode access is facilitated.