Speaker: Torsten Möller (Simon Fraser University, Canada)
In this talk we investigate the effects of function composition in the form g(f(x)) = h(x) by means of a spectral analysis of h. We decompose the spectral description of h(x) into a scalar product of the spectral description of g(x) and a term that solely depends on f(x) and that is independent of g(x). We then use the method of stationary phase to derive the essential maximum frequency of g(f(x)) bounding the main portion of the energy of its spectrum. This limit is the product of the maximum frequency of g(x) and the maximum derivative of f(x). This leads to a proper sampling of the composition h of the two functions g and f. We apply our theoretical results to a fundamental open problem in volume rendering -- the proper sampling of the rendering integral after the application of a transfer function.