How do you optimize your Monte Carlo rendering code for performance and scalability?

1 Use importance sampling

One of the main challenges of Monte Carlo rendering is dealing with high variance, which causes noise and artifacts in the final image. To reduce variance, you need to sample the scene more intelligently, focusing on the most relevant light sources and directions. This is called importance sampling, and it can significantly improve the quality of your rendering with fewer samples. Importance sampling requires you to evaluate the probability distribution function (PDF) of the scene, which describes how likely a certain ray is to contribute to the final color. You can use different methods to estimate the PDF, such as using the BRDF, the light intensity, or the visibility.

2 Use multiple importance sampling

Sometimes, using a single PDF for importance sampling is not enough, as different components of the scene may have different characteristics and importance. For example, a glossy material may have a narrow PDF for the BRDF, while a point light may have a wide PDF for the light intensity. In this case, using only one of them may result in either missing some important rays or wasting samples on irrelevant ones. To solve this problem, you can use multiple importance sampling (MIS), which combines different PDFs with appropriate weights to balance the sampling efficiency. MIS can help you reduce variance and noise even further, especially for complex scenes with multiple light sources and materials.

3 Use adaptive sampling

Another way to optimize your Monte Carlo rendering code is to use adaptive sampling, which means adjusting the number of samples per pixel according to the local variance. Instead of using a fixed number of samples for the whole image, you can use more samples where the variance is high, and less samples where the variance is low. This way, you can achieve a more uniform noise distribution and a better trade-off between quality and speed. Adaptive sampling requires you to measure the variance of each pixel or region, which can be done by using different estimators, such as the standard deviation, the median absolute deviation, or the contrast.

4 Use parallel computing

Monte Carlo rendering is inherently parallelizable, as each pixel or sample can be computed independently from the others. This means that you can use parallel computing techniques to speed up your rendering code and scale it to larger scenes and resolutions. Parallel computing can be done on different levels, such as using multiple threads, multiple cores, multiple processors, or multiple machines. Depending on your hardware and software, you can use different frameworks and libraries to implement parallel computing, such as OpenMP, MPI, CUDA, or OpenCL.