I attended my first GDC in 2016 and gave a talk on Fixed Point Iteration (FPI)! The video is available here for those with vault creds: http://www.gdcvault.com/play/1023320/Fixed-Point-Iteration-A-Simple . I have also attached a pre-print version of the slides, which has slide notes: FPI_GDC2016_preprint .
Going forwards I will add additional thoughts and notes and further reading links to this page.
Examples / diagram shaders
Shader with just a gerstner wave framed: MstSRN
My general graphing shader (includes gerstner solve): Msl3Ws
Raymarch overview diagram from slide 39: 4sdSR8
Raymarch render diagram with Secant Step alternating on and off, from slide 57: Mdj3W3
‘Milky’ shader (header image) which uses the Secant Step for fast and accurate convergence, from slide 64: Msy3D1
Multiple Solutions
The biggest omission from this talk (due to time constraints) was a discussion of the behaviour in the presence of multiple solutions. Intuitively, the iteration converges to the ‘closest’ solution. We published a paper [3] that describes and illustrates this, and also provides a technique to catch all possible solutions. We used this to do reprojection of images, spatially to do a stereoscopic post-conversion and temporally to do a 30-60Hz upsampler.
References
[1] Bowles, H. and Zimmermann, D. Oceans on a Shoestring: Shape Representation, Meshing and Shading, Advances in Real-Time Rendering in Games course, SIGGRAPH 2013. Project page here.
[2] Gonzales-Ochoa, C. Water Technology of Uncharted, GDC 2012
[3] Bowles, H., Mitchell, K., Sumner, B., Moore, J. and Gross, M.. Iterative Image Warping, Eurographics 2012. Project page here.
[4] Torres, G. and Ricour, H. Technical Challenges of Assassin’s Creed III: Real-Time Water Simulation and High-Quality Linear Gameplay Sequences, SIGGRAPH Asia 2012
[5] Keinert, B., Schaefer, H., Korndoerfer, J., Ganse, U. and Stamminger, M., Enhanced Sphere Tracing, STAG 2014
[6] Tessendorf, J. Simulating Ocean Water, SIGGRAPH 2001
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Thanks for the comment! I’m super glad if others find it useful. It’s been a great tool for me that I’ve used a number of times, and it changed the way i think about iterative methods in general and has been a pleasure to learn about. And thanks for the compliment about the website, I’ll try to update it again soon!