1. With optically dense inhomogeneous volume regions, GridDensityMedium::Tr() may spend a lot of time finding the attenuation between lights and intersection points. One approach to reducing this expense is to take advantage of the facts that the amount of attenuation for nearby rays is generally smoothly varying and that the rays to a point or directional light source can be parameterized over a straightforward 2D domain. Given these conditions, it’s possible to use precomputed approximations to the attenuation. For example, Kajiya and Von Herzen (1984) computed the attenuation to a directional light source at a grid of points in 3D space and then found attenuation at any particular point by interpolating among nearby grid samples. A more memory-efficient approach was developed by Lokovic and Veach (2000) in the form of deep shadow maps, based on a clever compression technique that takes advantage of the smoothness of the attenuation. Implement one of these approaches in pbrt, and measure how much it speeds up rendering with the VolPathIntegrator. Under what sorts of situations do approaches like these result in noticeable image errors?
  2. Another effective method for speeding up GridDensityMedium::Tr() is to use Russian roulette: if the accumulated transmittance Tr goes below some threshold, randomly terminate it and return 0 transmittance; otherwise, scale it based on 1 over the survival probability. Modify pbrt to optionally use this approach, and measure the change in Monte Carlo efficiency. How does varying the termination threshold affect your results?
  3. Read the papers by Yue et al. (2010, 2011) on improving delta-tracking’s efficiency by decomposing inhomogeneous media using a spatial data structure and then applying delta tracking separately in each region of space. Apply their approach to the GridDensityMedium, and measure the change in efficiency compared to the current implementation.
  4. The current sampling algorithm in the GridDensityMedium is based purely on sampling based on the accumulated attenuation. While this is more effective than sampling uniformly, it misses the factor that it’s desirable to sample scattering events at points where the scattering coefficient is relatively large as well, as these points contribute more to the overall result. Kulla and Fajardo (2012) describe an approach based on sampling the medium at a number of points along each ray and computing a PDF for the product of the transmittance and the scattering coefficient. Sampling from this distribution gives much better results than sampling based on the transmittance alone. Implement Kulla and Fajardo’s technique in pbrt, and compare the Monte Carlo efficiency of their method to the method currently implemented in GridDensityMedium. Are there scenes where their approach is less effective?
  5. As described in Section 15.3.1, the current VolPathIntegrator implementation will spend unnecessary effort computing ray–primitive intersections in scenes with optically dense scattering media: closer medium interactions will more often be sampled than the surface intersections. Modify the system so that medium interactions are sampled before ray–primitive intersections are tested. Reduce the ray’s tMax extent when a medium interaction is sampled before performing primitive intersections. Measure the change in performance for scenes with both optically thin and optically thick participating media. (Use a fairly geometrically complex scene so that the cost of ray–primitive intersections isn’t negligible.) If your results show that the most efficient approach varies depending on the medium scattering properties, implement an approach to automatically choose between the two strategies at run time based on the medium’s characteristics.
  6. The Medium abstraction currently doesn’t make it possible to represent emissive media, and the volume-aware integrators don’t account for volumetric emission. Modify the system so that emission from a 3D volume can be described, and update one or more Integrator implementations to account for emissive media in their lighting calculations. For the code related to sampling incident radiance, it may be worthwhile to read the paper by Villemin and Hery (2013) on Monte Carlo sampling of 3D emissive volumes.
  7. Compare rendering subsurface scattering with a BSSRDF to brute force integration of the same underlying medium properties with the VolPathIntegrator. (Recall that in high-albedo media, paths of hundreds or thousands of bounces may be necessary to compute accurate results.) Compare scenes with a variety of scattering properties, including both low and high albedos. Render images that demonstrate cases where the BSSRDF approximation introduces noticeable error but Monte Carlo computes a correct result. How much slower is the Monte Carlo approach for cases where the BSSRDF is accurate?
  8. Donner et al. (2009) performed extensive numerical simulation of subsurface scattering from media with a wide range of scattering properties and then computed coefficients to fit an analytical model to the resulting data. They have shown that rendering with this model is more efficient than full Monte Carlo integration, while handling well many cases where the approximations of many BSSRDF models are unacceptable. For example, their model accounts for directional variation in the scattered radiance and handles media with low and medium albedos well. Read their paper and download the data files of coefficients. Implement a new BSSRDF in pbrt that uses their model, and render images showing cases where it gives better results than the current BSSRDF implementation.