Math and modelling. Procedural

Hi folks.
Can anybody suggest where to learn MATH for object in space?
I’m interested in both procedural textures and animations nodes, I have many questions and ideas like:
– how to create tree branch algorithm
– how to create custom shapes from coordinate inputs (like snake scales, or hexagons)
etc.
Yes there are some tutorials which just give final formula/solution – post links here.
But my real interest is to create my own formulas, procedural shapes.

PS: ps don’t post tutorials on how to use nodes. I rather need how to mathematically describe shapes, common algorithm tricks…

I found a very interesting topic - L-systems. its a way to generate procedural organic shapes. And most importantly there is a plugin for blender called tissue in which we are able to build these L-system organic shapes.
This is an answer to tree branch algorithm question

Still looking for some decent math tutorials for building procedural shapes having only coordinates system from 0 to 1.

Also, https://www.desmos.com/calculator is a very useful tool to play with math and see what shape it generates before going into blender.
For example I have built procedural math model of snake scales here

It’s a very interesting topic to me, also.

An important thing to distinguish, though, is whether an algorithm can be efficiently evaluated locally (and thus can be used directly in material nodes), or not. I, e.g. doubt that it is possible to reasonably implement a nontrivial L-system in nodes.

If you are able to skip the former requirement, it becomes much easier. Then you can create a couple of base shapes (with beziers, or whatever) and use an algorithm which places (scaled, rotated, distorted) copies into whatever pattern. I couldn’t find a decent, free tool, though, which can do that nicely and interactively.

Building directly with nodes also is fun, but creating more complex shapes quickly ends in insanity. More basic things can be done alone with highschool-level knowledge of geometry and trigonometry. (Note that ‘math for objects is space’ is just a different term for ‘geometry’ :wink: )

  • Create a circle? Calculate the distance from the center point. Is it larger than the diameter of the circle, you are outside, otherwise you are inside.
  • Create a hexagon? Observe that you can create a hexagon from the intersection of 3 strips (of the same width) aligned at 60° angles. Are you inside of all of the 3 strips, you are inside the hexagon, otherwise you are outside.

I can’t point you to a concrete tutorial, and unfortunately few people post their setups for more complex textures here. For me it boils down to 2 things: If you want a known, well-defined shape, look up a suitable geometric description for it. If you want your own fun/creative kind of shape, you need to know the basic functions which are available to you and a feel about what will happen when you combine them in certain ways - and creativity about that.

A few things also maybe worth looking up to learn things are:

  • how the Voronoi texture works
  • how the Musgrave node works (there is a paper from the name-giving inventor about it)
  • fractals (like the Mandelbrot and Julia sets)

Hmm, maybe that was more rambling from me than useful info, but you see, I like to talk about this stuff :wink:

Check this youtube channel : Lance Phan.

Basically this guy made tutorials on procedural textures and recently he started a series teaching concepts in procedural textures and already made videos on stuff like the concept of space and value manipulation etc…

I think this might help you understand nodes a lot better.

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