A Frequency Analysis of Monte-Carlo and other Numerical Integration Schemes

The numerical calculation of integrals is central to many computer graphics algorithms such as Monte-Carlo Ray Tracing. We show that such methods can be studied using Fourier analysis. Numerical error is shown to correspond to aliasing and the link between properties of the sampling pattern and the integrand is studied. The approach also permits the unified study of image aliasing and numerical integration, by considering a multidimensional domain where some dimensions are integrated while others are sampled