• Process
• Tile Classification
• Integrate for Pixels Support Importance Sample BRDF
• Overall Process
• Detailed Process
• BxDF Sampling
• Generate Uniform Distributed Sample

Process

On a technical level, the entire Integrate process includes two steps:

1. Tile Classification
2. Integrate for classified tiles

The first step is to improve parallelism by dividing the screen into 8x8 pixel tiles and then organizing them into three lists in different ways according to the Integrate method.

The second step is to perform Integrate calculations on each of these three lists separately.

This engineering design helps to improve parallelism, meaning that there won't be situations where some threads in the same group have heavy workloads while others have light workloads, and the entire group still needs to wait for the slowest thread to finish its work.

Tile Classification

Integrate for Pixels Support Importance Sample BRDF

In our Diffuse Cube test, all pixels were identified as 'Support Importance Sample BRDF', so we proceeded with the process for this part.

Overall Process

Overall, this step includes three sub-phases:

1. Blending Phase: blend and interpolate four probes corresponding to each pixel.
2. Calculate Diffuse Indirect Lighting.
3. Calculate Rough Specular Indirect Lighting.

In principle, Indirect Lighting actually contains three components:

• Fully Diffuse Reflection Component.
• Rough Specular Reflection Component.
• Fully Specular Reflection Component.

Since the first two components involve integral calculation, they are completed in this step. The last component does not involve integral calculation and will be completed in the later Lumen Reflection section.

If we try to integrate the red Radiance in each image mathematically, it will be impossible to complete.

Therefore, the method of Importance Sampling is used to estimate the results through sampling.

For each sub-step, there is a similar process:

• Generate a random factor E
• Sample BxDF
• Calculate Radiance based on the sampled BxDF sample
• Weighted sum

Detailed Process

BxDF Sampling

⚠️

This section involves quite a lot of mathematical details related to sampling. In order to avoid deviating from the main topic, I will avoid discussing the mathematical details of "why a certain function is written in a certain way". There are many resources that can help you learn more, such as:

Importance Sampling techniques for GGX with Smith Masking-Shadowing: Part 1

Today I’ll be writing about importance sampling the GGX BRDF. GGX used with the Smith masking-shadowing function has become ubiquious in the game industry so it was the first specular model I wanted to implement in the path tracer I’m writing. About two weeks before I wrote this blog post I sat down and googled “importance sampling ggx” and while I was able to find a number of articles and papers that described specific details of the technique I was left a little unsure about whether I was combining the pieces together correctly. This blog post is a result of my investigation that followed and will hopefully provide enough details along the way that anyone in the future who searches for a similar phrase will be confident in their implementation.

schuttejoe.github.io

2D Sampling with Multidimensional Transformations

pbr-book.org

Generate Uniform Distributed Sample

In this step, Lumen first generates random sampling sample information, mainly through the ComputeIndirectLightingSampleE function. It should be noted that Hammersley sequence is used here to generate sample points, which can produce more uniform random samples.