Incremental and Hierarchical Hilbert Order Edge Equation Polygon Rasterization

Abstract

A rasterization algorithm must efficiently generate pixel fragments from geometric descriptions of primitives. ln order to accomplish per-pixel shading, shading parameters must also be interpolated across the primitive in a perspective-correct manner. lf some of these parameters are to be interpreted in later stages of the pipeline directly or indirectly as texture coordinates, then translating spatial and parametric coherence into temporal coherence will improve texture cache performance. Finally, if framebuffer access is also organized around cached blocks, then organizing rasterization so fragments are generated in block-sequential order will maximize framebuffer cache performance. Hilbert-order rasterization accomplishes these goals, and also permits efficient incrementale valuation of edge and interpolation equations.