1. Replace ratio tracking in the VolPathIntegrator::SampleLd() method with delta tracking. After you confirm that your changes converge to the correct result, measure the difference in performance and MSE in order to compare the Monte Carlo efficiency of the two approaches for a variety of volumetric data sets. Do you find any cases where delta tracking is more efficient? If so, can you explain why?
  2. Residual ratio tracking can compute transmittance more efficiently than ratio tracking in dense media; it is based on finding lower bounds of sigma Subscript normal t in regions of space, analytically computing that portion of the transmittance, and then using ratio tracking for the remaining variation (Novák et al. 2014). Implement this approach in pbrt and measure its effectiveness. Note that you will need to make modifications to both the Medium’s RayMajorantSegment representation and the implementation of the VolPathIntegrator in order to do so.
  3. The current implementation of SampleT_maj() consumes a new uniform random value for each RayMajorantSegment returned by the medium’s iterator. Its sampling operation can alternatively be implemented using a single uniform value to sample a total optical thickness and then finding the point along the ray where that optical thickness has been accumulated. Modify SampleT_maj() to implement that approach and measure rendering performance. Is there a benefit compared to the current implementation?
  4. It is not possible to directly sample emission in volumes with the current Medium interface. Thus, integrators are left to include emission only when their random walk through a medium happens to find a part of it that is emissive. This approach can be quite inefficient, especially for localized bright emission. Add methods to the Medium interface that allow for sampling emission and modify the direct lighting calculation in the VolPathIntegrator to use them. For inspiration, it may be worthwhile to read the papers by Villemin and Hery (2013) and Simon et al. (2017) on Monte Carlo sampling of 3D emissive volumes. Measure the improvement in efficiency with your approach. Are there any cases where it hurts performance?
  5. While sampling distances in participating media according to the majorant is much more effective than sampling uniformly, it does not account for other factors that vary along the ray, such as the scattering coefficient and phase function or variation in illumination from light sources. Implement the approach described by Wrenninge and Villemin (2020) on product sampling based on adapting the majorant to account for multiple factors in the integrand and then randomly selecting among weighted sample points. (You may find weighted reservoir sampling (Section A.2) a useful technique to apply in order to avoid the storage costs of maintaining the candidate samples.) Measure the performance of your implementation as well as how much it improves image quality for tricky volumetric scenes.
  6. Add the capability to specify a bump or normal map for the bottom interface in the LayeredBxDF. (The current implementation applies bump mapping at the top interface only.) Render images that show the difference between perturbing the normal at the top interface and having a smooth bottom interface and vice versa.
  7. Investigate the effect of improving the sampling patterns used in the LayeredBxDF—for example, by replacing the uniform random numbers used with low-discrepancy points. You may need to pass further information through the BSDF evaluation routines to do so, such as the current pixel, pixel sample, and current ray depth. Measure how much error is reduced by your changes as well as their performance impact.
  8. Generalize the LayeredBxDF to allow the specification of an arbitrary number of layers with different media between them. You may want to review the improved sampling techniques for this case that were introduced by Gamboa et al. (2020). Verify that your implementation gives equivalent results to nested application of the LayeredBxDF and measure the efficiency difference between the two approaches.