Tell me how far away something is, and I tell you what it looks like!
This one took a while. Mostly due to other things in my life. But also because I stumbled over quite a few problems when trying to implement SDFs for the animation. As a consequence, I learned more, but I also had to rewrite the script a lot to convey the things I learned properly. Still feels much rougher around the edges than my other videos.
Moreover, this video is in 4k and 60 fps. Is it worth it? Doesn't make the development of the video much longer, so, I'll probably continue with it...
Lastly, this video is also my submission for the Summer of Math Exposition 2023. If you search for #SoME3 on YouTube, you will find many fantastic videos by the other participants!
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Resources, references & further reading material:
Animations were made with CindyJS:
https://cindyjs.org/
Signed Distance Functions on Wikipedia:
https://en.wikipedia.org/wiki/Signed_distance_function
Octrees on Wikipedia:
https://en.wikipedia.org/wiki/Octree
Calculating perpendiculars via dot product:
https://en.wikipedia.org/wiki/Vector_projection
Inigo Quilez' Website:
https://iquilezles.org/
Inigo Quilez' YouTube channel:
https://www.youtube.com/channel/UCdmAhiG8HQDlz8uyekw4ENw
Inigo Quilez' article on wrong interior SDFs when using mimimums:
https://iquilezles.org/articles/interiordistance/
Giovanni Russo & Smereka (2000), A Remark on Computing Distance Functions:
https://www.sciencedirect.com/science/article/abs/pii/S0021999100965537
Phong reflection on Wikipedia:
https://en.wikipedia.org/wiki/Phong_reflection_model
Blog post by Vassilis Poulopoulos on how to use SDFs to render text:
https://renderdiagrams.org/2017/12/28/signed-distance-fields/
Music:
"Shade" by Josh Woodward. Free download: http://joshwoodward.com/
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Chapters:
[00:00] Introduction
[01:36] Ray-Marching
[04:51] Definition & Calculations
[14:25] Manipulating SDFs
[18:53] Basic Lighting & Actual Rendering