I.8 - SPACE-FILLING CURVES AND A MEASURE OF COHERENCE

Abstract

This chapter focuses on space-filling curves and a measure of coherence. Some space- filling curves can exploit coherence in two dimensions despite a range of object area sizes. As fractals, they are self-similar at multiple resolutions. Thus, if they do a good job of visiting all the pixels corresponding to a particular object area at one scale, then they may have this advantage for much larger or smaller object areas. As topologically continuous curves, areas visited always are adjacent. Peano curves are recursive boustrophedonic patterns. They snake back and forth at multiple recursion levels, filling the plane. Because each pattern enters and exits from opposite rectangle corners, they implicitly use serpentines with an odd number of swaths, a minimum of three. Both the Peano and Hilbert curves far exceed the coherence = 1.00 measure of conventional scanline traversal. The Hilbert curve appears superior, and is easier to generate. Better performance from a real renderer can be expected simply by choosing either of these alternative traversal sequences.