For our final project, we want to implement volumetric rendering and photon mapping to our existing path tracer. Within volumetric rendering, some of the effects that we want to achieve or explore are fog/smoke effects and rendering a sunset/sky.  With photon mapping some of the effects we aim to achieve are the caustic and reflection effect.

We first plan on implementing volumetric rendering. From reading the slides and papers on volumetric rendering we understand that it involves ray marching instead of checking the closest intersection. We need to perform ray marching because we are treating clouds/fog differently than solid objects. Light can hit fog and still pass through. There are also two types of volumes, homogeneous and heterogeneous. We plan to render scenes with homogeneous and heterogeneous substances (ie fog or smoke). Finally, we would try to add implementations for atmospheric effects. If we are able to develop these aspects individually, we hope to render a more complex scene using these aspects.

To go more in depth with how we want to go about implementing volumetric rendering, we want to first implement single-scattering. Single scattering is easier to implement than multiscattering because it only interacts once with the medium before reaching the viewer. However, not all volumtetric objects exhibit single scattering properties. Clouds exhibit muti scattering behavior in which the light interacts with the object many times before being absorbed. This scattering behavior defines whether an object has high or low albedo.

While researching volumetric rendering,we also came across the delta tracking method in the 2017 SIGGRAPH Course by Pixar. It is said that delta tracking will improve the process compared to using ray marching. However, this comes as the cost of adding complexity to our code. We plan to start with ray marching (as explained on reference 7) as a beginning milestone for our exploration of the topic.  

After, if we have time, we plan on implementing caustics through photon mapping. To do so, we need to implement a kd-tree to store the photon mapping information. Then, we can attempt different effects such as caustics. Then we would try to build a more complicated scene with volumetric rendering and caustics. Our implementation would involve first constructing a photon map for the first pass. On the second pass we would use the photon map  to estimate the radiance of every pixel for the output image. We would then use the rendering equation to calculate the surface radiance and perform further ray tracing calculations.

Finally, we hope to combine volumetric rendering and caustics to see how the rendering will behave with both effects enabled. Scenes such as the underwater lighting scene should provide an opportunity for us to see both effects.

After reading through several papers and the CSE 168 website, we began by trying to implement ray marching so that we could step through our mediums. However, we went to our TA office hours and he guided us towards the CSE 272 slides and homework assignment on volumetric rendering. It was interesting that there was no specific mention of ray marching, as the implementation uses transmittance, probability sampling and integrals to check change over time.

Next, we moved on to "Multiple monochromatic homogeneous volumes with absorption and multiple-scattering using only phase function sampling, no surface lighting".

We saw that this was very similar to indirect lighting from previous homeworks in the sense that you could have multiple bounces. 

We actually spent the most time trying to render custom scenes with volumetric rendering / multiscattering at this point. The medium qualities (absorption, scattering, etc) meant that you had to be relatively close to emissive objects to see them in our scenes. 

Heres some custom images we rendered and some lessons/reflections we gained:

We would hope to expand on our current renderer in several aspects:

1. Exploring different phase functions: We would want to implement other phase functions other than the isotropic phase function, which would include Rayleigh Scattering and Henyey-Greenstein Scattering. This would change how light is sampled, as mentioned before (ie: the color wheel). This could allow us to go into more complex scenes, such as rendering the sky.

2. Adding NEE, MIS: Not every object is a medium, so we would end up merging this renderer into a NEE renderer to combine NEE sampling and allow different objects to exist (ie render the Cornell box with a sphere medium). 

3. Heterogeneous mediums: Continuing on, we would attempt to render heterogeneous volumes, such as smoke and fire. This might mean that absorption and scattering can vary on different parts of the medium.