13 HN users recommended this tutorial10 months2021–2025score 12
Years with an HN recommendation, 2007–2026
HN repeatedly calls it a mind-blowing and accessible introduction to SDFs and procedural art from a master explainer.
Inigo Quilez live-codes a cartoon character painting entirely from math, using signed distance fields in a Shadertoy shader. He explains each step of building the image from formulas.
“he's a master of this stuff and a great explainer.” (HN, 2022)
This was a mind blowing example of math and art from last year - perhaps the live coding of the method was even more impressive than the outcome: [this video]
If you don't have an understanding of signed distance fields, [this video] is an amazing demo of their power. There are more videos about the fundamentals of SDFs at [link] The interesting thing about this paper is that they replace the mathematical SDF with a neural net that computes SDF_NN(x,y,z) => -1/1 and use this as a compression system for mesh based inputs. This feels like a graphical version of the [link] for NN-based text compression.
Great write up. If anyone wants to explore SDFs more, check out Inigo Quilez - he's a master of this stuff and a great explainer. Painting a Character with Maths: [this video] And plenty more on his website in article form: [link] Finally, Shadertoy, a graphics shader playground where you can see (and try!) a lot of this kind of stuff: [link]
Master explainer of SDFs painting a character with maths
I see a Inigo Quilez link, I upvote! He's one of those incredible artist-engineer out there always pushing boundaries further and sharing his ideas and techniques publicly. If you have some time today, watch a few of his videos on his youtube channel, it's incredible to see his creation process in action: [link] For example, "Painting a character with maths" is mind-blowing and packed with SO MUCH educative content: [this video]
Mind-blowing, packed with educational content on creating art with maths
Demos are almost always generated and displayed at runtime. The music is composed of samples generated at runtime by additive synthesis which is just adding waveforms of differing frequencies together when you get down to it. It doesn't take many lines of code to produce CD quality instruments that can be arranged as a soundtrack. Today's 64k intros offload their drawing onto the GPU using shaders and a technique called raymarching which is a form of fixed-step raytracing that can be done in real time. Essentially the objects you see are painted with math: instead of thousands of vertices for a 3d fractal or a complex object, a formula is fed in to the ray marcher and it returns a shape with colors and lighting. Combining shapes using unions and intersections is then done and often the shape formula will take time as a parameter as well. To play with this concept yourself go to [link] and see how shader programs are rendered into incredible scenes with astonishingly few lines of code. For a wonderful look at the creation process, see the grandfather of raymarching Inigo Quilez create a selfie of a girl from scratch using formulas here: [this video]
Inigo Quilez, the author of this slide, also has made in-depth videos [1] [2] which might be more accessible to who aren't familiar with shader languages. [1] [this video] [2] [link]
Good to see high quality articles gaining traction. If the article looks too verbose, be sure to check out, as the author cites, Inigo Quilez's videos Painting a Landscape with Maths - [link] Painting a Character with Maths - [this video] Bonus: Painting with Maths in Google Sheets - [link]
I don't think that people only value the output. Take "Selfie Girl"[0] by Inigo Quilez people appreciate that it's a shader, even people that are not into programming (though they'd need to see the making of video[1]). [0] [link] [1] [this video]
He has a YouTube channel as well: [this video] Also you may like Marble Marcher made by Code Parade, it's a game that uses a similar approach to rendering: [link]
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