A method for rendering parametric surface patches on a display screen includes receiving, at a processing unit, a computer-implemented representation of a first parametric surface patch, wherein the first parametric surface patch is a portion of a three-dimensional computer-implemented model that is desirably displayed at a first viewing perspective on the display screen. The first parametric patch is subdivided in the parameter domain to generate a plurality of subpatches, which are stored as quadtree coordinates in a memory. Thereafter, at least one pixel on the display screen is rendered based at least in part upon the quadtree coordinates in the memory.