Raymarching SDFs (Signed Distance Fields) is slowly getting popular, because it's a simple, elegant and powerful way to represent 3D objects and even render 3D scenes. SDFs are a type of implicit surface representation, and so its origins can be tracked back very far in the history of computer graphics. While not SDFs per-se, the first paper that's been brought to my attention showing boolean operations in implicit surfaces by combining them through the min() and max() operators dates back to 1972, by A.Ricci and later by B.Wyvill and G.Wyvill in 1989. The first mention of raymarching SDFs seems to be also from that time - the paper by Sandin, Hart and Kauffman, which used it for rendering 3D fractals, although they never coined the term "SDF". Seven years later in 1995 C.Hart himself documented the raymarching technique once again (but unfortunately miscalled it "Sphere Tracing" - usually we trace rays, cylinders or cones, but definitely not spheres!).

My story with SDFs starts around 2001. Like many other demosceners of that time, I experimented a lot with raymarching Signed Fields (without the "D") to render fractals and metaballs as part of our demos. However it was only after I read Alex Evan's work from 2006 and Keenan Crane's work from 2005 that I got excited about exploring the consequences of constraining a Signed Field to be an Euclidean Distance. And so, in 2007 I dived in, and explored, and then produced the first results that we'd recognizable as modern SDF, including the four images at the bottom of this page that demonstrated non-trivial but art directed content, and demonstrated techniques for efficient soft shadows, smooth blending and domain repetition.


A raymarched procedural SDF, step by step modeling, shading and lighting
Now, although raymarching SDFs can definitely render regular polygonal meshes, as a lover of compression and procedural content myself, my focus became to implement the SDFs directly as list of primitives rather than as volumetric data, which is where many folks' first instinct seem to go, despite the unresolvable precision issues, probably because their mindset is that of rendering in video games. However, primitive based SDF offer the infinite sharpness and precision that is crucial both for CAD and professional graphic design. Unlike volume based approaches of constant access time, rendering unlimited number of primitives and their CSG (boolean) operations that define the SDF requires some acceleration structures and more complex techniques than volumes. But coincidentally, back in 2007, the timing for such a procedural/math and compute based approach was great - First, GPUs were evolving their compute/ALU capabilities faster than their memory bandwidth, a trend that has only continued in the last 20 years, so pure mathematical SDFs started to be competitive against a backed representations. Second, I personal had an interest in doodling around and finding the required maths to express different shapes and effects. Third, I was also very much interested in improving my artistic skills, so procedural content was a great fit. And fourth, as a demoscener, I was naturally captivated by procedural content generation and its potential for reduced memory footprint (RAM and disk). As it turns, pretty rendering, procedural content and small memory footprint was also in high demand at Pixar, I learnt a couple of years later, but that's a story for another day.

And so, for the next 5 years, the demoscene and the Shadertoy communities we pushed the SDF raymarching technique further, creating more and better looking content. With each new demo and Shadertoy piece, we proved SDFs did not have to be limited to just funny fractals or metaballs or toy cities of ever repeating buildings, but content could be created that was art directed, and included sophisticated modeling, proper shading with filtering, lighting and animation. As the volume of works grew, a case started to emerge for SDFs as a legit professional representation for 3D graphics, at least in certain applications. And about 5 years later academia noticed this, and started working on the area as well. Another 5 years or so later the industry itself also joined in, and we started seeing the emergence of professional modeling and design tools based on SDFs.

Anyways, to end this already long post, since 1998 I've been documenting some of the discoveries/inventions I did around SDFs, or just tricks or simple observations that could be interesting to others, both in this very website and my Youtube channel. So here are some pointers if you want to start learning the basics of SDFs:

• Articles on Raymarching on this site
• My video tutorials and streams about raymarching SDFs on Youtube
• The lecture called "Rendering Worlds with Two Triangles" that I have 2008 on the topic
• All my Shadertoy examples, some of which I list below:

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