Photon Mapping Caustics

CSC 572 Spring 2017

By: Justin Kehl

Overview

I chose to implement caustics because I am interested in water and light and how they interact. I chose photon mapping for this because we read "A Practical Guide to Global Illumination using Photon Map" by H. Jensen., et al this quarter. This paper provides the theoretical foundation for photon mapping and one of the scenes in the paper interested me enough to want to attempt to reproduce it.

What are caustics?

Caustics are the rays of light reflected or refracted by a curved surface. When light passes through water it refracts, reflects, and scatters to produce the interesting patterns seen above.

Project Goal

For my project I wanted to reproduce the caustics visible through the glass of cognac in the scene above from the Photon Mapping paper.

Photon Mapping Theory Overview

In this section I will describe the approach to Photon Mapping described by Jensen in the paper above. Jensen's Photon Mapping uses two passes to generate the scene:

• First Pass - Generate the global photon map
• Fire a large number of photons (determined by light strength) in all directions from any lights in the scene.
• When a photon hits an object use a roullete system to determine whether the photon is reflected, refracted, or absorbed.
• Store information about every collision in a global illumination photon map.
• Photons continue bouncing around the scene storing information until they are all absorbed or they bounce a certain (settable threshold) number of times.


• Second Pass - Generate the caustic photon map
• Fire a large number of photons from each light source towards objects of interest in the scene.
• These photons behave similarly to those described above, but information about their collisions is stored in a separate caustics photon map.

Once the two photon maps have been built, Monte Carlo Ray Tracing is used to render the scene. However, the ray tracing is sped up significantly by pulling data from the pre-generated photon maps to determine where more detail is necessary (directly visible objects illuminated by direct light) and areas where the global photon map approximation can be used instead (indirectly illuminated objects, corners, shadows, etc.). The data from the caustic photon map is used directly as the high density of photons used in its generation supplies enough information to accurately depict the caustic lighting. This approach produces very realistic scenes with modest efficiency improvements to pure Monte Carlo Ray Tracing. Full details can be found in the paper, "A Practical Guide to Global Illumination using Photon Map" by H. Jensen., et al.

My Approach

I chose to focus on the caustics photon map exclusively so I skip the entire first pass of the photon mapping algorithm, use a simple ray tracer rather than Monte Carlo, and light the majority of the scene with a simple Blinn-Phong lighting model rather than computing radiance. The images below show some visualizations of my implementation with images on the left using about a tenth of the number of photons as their counterparts on the right.

These images show the trace of each individual photon as it refracts through the spheres. Since each photon supplies such a small amount of light and even with denser samples the caustic is not very smooth, I increased the energy of each photon and then distribute the light from each photon across neighboring pixels. This 'blurs' the caustic a bit, but also helps to define the shadow produced by the sphere.

In these images I have added a more solid shadow since the 'shadow' effect produced by my blurring of the caustic photon map did not quite produce enough of a visible and clear shadow. The addition of the ground plane also helps round off the scene a bit more.

These next images show an initial full scene. The image on the left uses fewer photons with less bluring which produces a more accurate, but pixelated caustic. The scene on the right uses 10x more photons with additional bluring. These two pictures show some of the interesting variation that can be achieved by tweaking the number of photons, strength of photons, and blur amount. In particular, the photons in both of these scenes are slightly overpowered which produces more of a fake-looking, monochromatic caustic.

These last images show the final result of my project (on the right) compared against the reference caustic I wanted to recreate. Ignoring the glass and textured ground plane, my rendered spheres and caustics do look somewhat similar, particulry the sphere on the left with the brighter portion of the caustic towards one side of the shadow away from the light.

What I learned

• Realistic lighting is tricky to get right and very obvious when it is off.
• I gained a lot more experience with ray tracing and learned how light is refracted through materials.
• Realistic, complex scenes are difficult to render and take time even with efficient implementations of rendering.
• I learned about photon mapping for global illumination, efficient data structures like balanced k-d trees, and how lighting can be calculated more accurately using radiance.

Struggles and Future Work

• I would like to implement a Monte Carlo Ray Tracer to render a more realistic final scene.
• I struggled to store photon data as a more efficient data structure, instead using 2D arrays to represent direct illumination and caustic data. The original paper describes a method for storing all the photon data efficiently in a balanced k-d tree. I had a hard time grasping exactly how this data structure would work and since I was only using a simple ray tracer with very few photons (relatively) the efficiency gains were not particularly important for me.
• I would like to learn how to accurately render transparent materials like glass. The realism of my scene suffers from the spheres appearing so solid, although the cognac in the reference scene is fairly dark and solid as well.
• I would ultimately like to implement a complete photon mapping solution to render a more accurate and interesting scene.

References

"A Practical Guide to Global Illumination using Photon Maps" (H. Jensen., et al)