Syntopia, the maker of Fragmentarium, did a series of blog posts on raymarching 3D fractals using distance estimation. You may find it helpful. Here's the first one:
http://blog.hvidtfeldts.net/index.php/2011/06/distance-estimated-3d-fractals-part-i/Each post contains a link to the next one at the bottom of the page.
You can also take a peek at the DE-Raytracer and Mandelbox scripts that come with Fragmentarium.
If you have any questions, we'll be happy to answer them. For example, if you want to know how to find the ray direction for a pixel, or how to derive the Distance Estimation formula for the Mandelbox.
I've been reading that article for quite a while now. The problem is that syntopia is kinda assuming people reading have the same level of mathematical knowledge and programming experience as him.
There is really for nothing complete beginner noobs.
I mean in contrast you can find many articles that step by step explain how a draw a Mandelbrot while all explaining all the mathematical principles along the way with highly commented code written to learn from and not optimised to hell.
People like syntopia are on a completely different level, they are more interested in extreme optimisation and really talking about problems they are solving for highly optimised super efficient code.
Seriously their explanations are virtually impossible to understand without doing tonnes of background research. I just gave up when I first read that, it didn't help me to understand how to draw a mandelbox.
Reading an expert ponder how they are optimising the mathematics or code for their program is fascinating
But totally and utterly useless for the beginner. Honestly the commercial optimised code in programs like fragmentarium is useless for the beginner to learn from, I've tried.
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Luckily we have shadertoy now and can instantly run glsl code and get immediate results in a browser!
The problem here is the code is by super "demo coding" experts with deep knowledge and it's virtually impossible to reverse engineer the code in amazing demos in shader Toy.
But if someone actually programmed a mandel box shader step by step teaching all the maths along the way this is clearly the most perfect environment we've had - as we can get instant results from c like code in shader Toy. ( I know its actually read shader code that gets compiled into the graphic card)
Just need someone to actually comment and explain each function and the maths behind it.
I found a good starting point this is the only post below I can find on the *entire internet* that tries to explains a raymarcher with commented shadertoy glsl code.
I mean if you can help extend and explain this further this would be great.
Then you can explain a highly readable totally unoptimised distance estimator for a mandelbox, designed to learn from. Not theory actual shader toy real code, line by line.
Which can then plugged into previously explained code the ray-marcher code as a distance estimator.
I don't think there are many people interested in education and teaching though.
This is the only thing I've found that almost makes me understand sphere tracing shader.
Here have a look:
http://www.reddit.com/r/twotriangles/comments/1hy5qy/tutorial_1_writing_a_simple_distance_field/It would be great to get a working fully commented explained version of this on shader toy that explains more.
As it's important to get real working code to learn and play with.
Although unfortunately the link for this code is broken!
It is frustrating that no line by line code with explanations and teaching exists for noobs.
Now I fully understand why, Not many people enjoy teaching.
Plus this forum is clearly experts with tonnes and years and years if knowledge.
They aren't gonna waste time writing noob code for beginners.
It's almost like if you weren't into this from the beginning for many years you aren't gonna learn anything quick.