1. Show that the WeightedReservoirSampler::Merge() method leaves the resulting reservoir with a sample that indeed is stored with probability equal to its weight divided by the sums of weights for all the samples in the two reservoirs.
  2. Modify the PiecewiseConstant1D implementation to use the adaptive CDF representation described by Lawrence et al. (2005), and experiment with how much more compact the CDF representation can be made without causing image artifacts. (Good test scenes include those that use ImageInfiniteLights, which use the PiecewiseConstant2D and, thus, PiecewiseConstant1D for sampling.) Can you measure an improvement in rendering speed due to more efficient searches through the approximated CDF?
  3. Extend SummedAreaTable to provide methods that efficiently compute 1D integrals along each dimension and then modify the WindowedPiecewiseConstant2D class’s Sample() method to use this capability for sampling the conditional CDF upper P left-parenthesis y vertical-bar x right-parenthesis . How is overall rendering performance affected by your change when rendering a scene that uses the PortalImageInfiniteLight? Profile pbrt and measure the change in performance of the Sample() method with your changes. What conclusions can you draw from your results?