TU Wien Rendering #37 - Manifold Exploration
That pesky torus enclosed in the glass cube again! Since it contains lots of SDS light paths, it is the bane of many rendering algorithms. However, it is no match for Wenzel Jakob's Manifold Exploration technique that explicitly looks for these paths and runs an equation solving system to find and render these light paths that are difficult or impossible to render with traditional techniques.

About the course:
This course aims to give an overview of basic and state-of-the-art methods of rendering. Offline methods such as ray and path tracing, photon mapping and many other algorithms are introduced and various refinement are explained. 

The basics of the involved physics, such as geometric optics, surface and media interaction with light and camera models are outlined. 

The apparatus of Monte Carlo methods is introduced which is heavily used in several algorithms and its refinement in the form of stratified sampling and the Metropolis-Hastings method is explained. 

At the end of the course students should be familiar with common techniques in rendering and find their way around the current state-of-the-art of the field. Furthermore the exercises should deepen the attendees' understanding of the basic principles of light transport and enable them to write a simple rendering program themselves.

These videos are the recordings of the lectures of 2015 at the Teschnische Universität Wien by Károly Zsolnai and Thomas Auzinger

Course website and slides → http://www.cg.tuwien.ac.at/courses/Rendering/
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Web → https://cg.tuwien.ac.at/~zsolnai/
Twitter → https://twitter.com/karoly_zsolnai
 This is the work of Vensal Jakob, he's a super smart, really brilliant guy. He extended the beach metropolis algorithm to handle SDS transport better. Now how is this possible? What I have written here is the very scientific way of stating what is really happening. The most difficult parts form a manifold in path space and you can grab this manifold and sample this exhaustively with an equation solving system. Let's take a look at the intuition. This is super useful but very challenging to understand and implement for ordinary people. What is exactly happening here? So we have a diffuse bounce. This is xb and we hit the light source after that which is xc on the upper right. And between the b and the c we have two specular bounces. And imagine that I am fixing the xb and xc. These are two fixed vertices. And if I have this glass egg in between that is perfectly specular, then I can write an algorithm that computes what should be the exact outgoing direction from this diffuse vertex in order to exactly hit that xc point. There is only one possible path because we have perfectly specular inter-reflections in between. So what should be this outgoing direction from xb? This is the equation solving system that we are interested in. How do the results look like? Well you can compare it to Metropolis light transport that is either very noisy or it misses some of the light paths completely in these very difficult test cases. The manifold exploration path eraser outperforms all of the existing algorithms. PSSMLT is the Kalamaz time MLT, MLT is the original feature Metropolis. One more example. A, Vitch Metropolis B, ERPT. I will tell you in a second what that is. C, Kalamaz Metropolis light transport algorithm, and D, manifold exploration path tracing. Vancell was kind enough to put I think 20 minutes talk about this work on his website so make sure to check it out. It is really well illustrated. It is really well explained. Make sure to check it out. Let's take a look how the algorithm converges in time. Take a look at this beauty. Lots of SDS light paths and in the first 10 minutes you already have some degree of convergence that would take days or possibly forever with other algorithms. Pretty amazing. Pretty amazing. One of my favorites out there. Here you can see side by side. Elements Metropolis light transport versus manifold exploration path tracing. It's difficult not to get excited about this right?
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