Frequency Analysis and Sheared Filtering for Multidimensional Effects in Rendering

Many of the most expensive effects in rendering are those that require integrating complex multidimensional signals. Computation for a single pixel can require hundreds of samples, and standard methods do not provide a mathematically sound way to share samples between pixels with overlapping integrands. This thesis first analyzes the underlying signals for motion blur and occlusion and identifies the sparse structure of these signals in the Fourier domain. We then leverage this information to design a sheared filter that is customized to each pixel's frequency content. We finally present practical algorithms that share samples between pixels, reduce sampling requirements by an order of magnitude, and provide significant speedups for many of the most expensive computations in computer graphics.