Spectral analysis of function composition

Before rendering, data values f(x) at given spatial positions x have to be assigned optical properties and visibility. In mathematical terms this corresponds to function composition g(f(x)). We describe the composition as a linear operator and conduct a spectral analysis to estimate a suitable sampling frequency in x to reconstruct the composed signal. We put the theoretical insight to practical effect by implementing a raycaster with an adaptive sampling scheme based on our new estimate.