A Complexity Analysis for Directional Parametric Height Field Ray Tracing

Abstract

It has been shown that height field ray tracing efficiency can be improved by traversing rays in steps across evenly spaced inverted cones of empty space centered above height field cells. This approach, referred to as linear parametric height field ray tracing, has previously been extended by directionalizing the inverted cones, i.e., by allowing the opening angles of the inverted cones to vary between sectors. This paper provides a mathematical analysis of parametric ray tracing complexity as a function of cone sector width and height field resolution. Empirical data on ray tracing run-times and mean lengths of traversal steps along rays during ray tracing is presented. It is shown that parametric height field ray tracing can be substantially more efficient than other popular height field ray tracing methods when cones with narrow sectors are used.