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Signed Distance Functions & Ray-Marching

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! -------------------- Join the Sum and Product Discord:   / discord   Follow Sum And Product on Twitter:   / sumandproduct   ...or Instagram:   / sum_and_product   Or buy me a coffee: https://ko-fi.com/sumandproduct -------------------- Resources, references & further reading material: Animations were made with CindyJS: https://cindyjs.org/ Signed Distance Functions on Wikipedia: https://en.wikipedia.org/wiki/Signed_... Octrees on Wikipedia: https://en.wikipedia.org/wiki/Octree Calculating perpendiculars via dot product: https://en.wikipedia.org/wiki/Vector_... Inigo Quilez' Website: https://iquilezles.org/ Inigo Quilez' YouTube channel:    / @inigoquilez   Inigo Quilez' article on wrong interior SDFs when using mimimums: https://iquilezles.org/articles/inter... Giovanni Russo & Smereka (2000), A Remark on Computing Distance Functions: https://www.sciencedirect.com/science... Phong reflection on Wikipedia: https://en.wikipedia.org/wiki/Phong_r... Blog post by Vassilis Poulopoulos on how to use SDFs to render text: https://renderdiagrams.org/2017/12/28... Music: "Shade" by Josh Woodward. Free download: http://joshwoodward.com/ -------------------- Chapters: [00:00] Introduction [01:36] Ray-Marching [04:51] Definition & Calculations [14:25] Manipulating SDFs [18:53] Basic Lighting & Actual Rendering