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Highest priority:

  • Continue to refine the 'barbs' example, which broke some new ground.
  • Implement the continuous parametric transformations from 2020-05-07 in my notes. This will require some new abstractions.
  • Try some non-deterministic examples.
  • Get identical or near-identical meshes to ramhorn_branch from Python. (Should just be a matter of tweaking parameters.)
  • Look at performance.
    • Start at to_mesh_iter(). The cost of small appends/connects seems to be killing performance.
    • connect() is a big performance hot-spot: 85% of total time in one test, around 51% in extend(), 33% in clone(). It seems like I should be able to share geometry with the Rc (like noted above), defer copying until actually needed, and pre-allocate the vector to its size (which should be easy to compute).
  • See automata_scratch/examples.py and implement some of the tougher examples.
    • twisty_torus, spiral_nested_2, & spiral_nested_3 are all that remain. To do them, I need to compose transformations (not in the matrix sense), but I also probably need to produce RuleEvals which always have xf of identity transformation since the Python code does not 'inherit' transforms unless I tell it to.

Important but less critical:

  • Elegance & succinctness:

    • Clean up ramhorn_branch because it's ugly.
    • What patterns can I factor out? I do some things regularly, like: the clockwise boundaries, the zigzag connections.
    • Declarative macro to shorten this Tag::Parent, Tag::Body nonsense - and perhaps force to groups of 3? Does this have any value, though, over just making helper functions like p(...) and b(...)?
    • I'm near certain a declarative macros can simplify some bigger things like my patterns with closures (e.g. the Y combinator like method for recursive calls).
  • Docs on modules

  • Compute global scale factor, and perhaps pass it to a rule (to eventually be used for, perhaps, adaptive subdivision). Note that one can find the scale factors by taking the length of the first 3 columns of the transform matrix (supposedly).

  • swept-isocontour stuff from /mnt/dev/graphics_misc/isosurfaces_2018_2019/spiral*.py. This will probably require that I figure out parametric curves

  • Make an example that is more discrete-automata, less approximation-of-space-curve.

  • Catch-alls:

    • Grep for all TODOs in code, really.
    • Look at everything in README.md in automata_scratch.

If I'm bored:

  • Fix links in tri_mesh docs that use relative paths & do a PR?
  • Look in https://www.nalgebra.org/quick_reference/# for "pour obtain". Can I fix this somehow? Looks like a French-ism that made its way in.
  • Multithread! This looks very task-parallel anywhere that I branch.
  • Would being able to name a rule node (perhaps conditionally under some compile-time flag) help for debugging?
  • Use an actual logging framework.
  • Take a square. Wrap it around to a torus. Now add a twist (about the axis that is normal to the square). This is simple, but it looks pretty cool.
  • How can I take tangled things like the cinquefoil and produce more 'iterative' versions that still weave around?

Research Areas

  • When I have an iterated transform, that is basically transforming by M, MM=M^2, MMM=M^3, ..., and it seems to me that I should be able to compute its eigendecomposition and use this to compute fractional powers of the matrix. Couldn't I then determine the continuous function I'm approximating by taking the d/di (M^i)V - i.e. the partial derivative of the result of transforming a vector V with M^i? (See also: https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix#Functional_calculus and my 2020-04-20 paper notes. My 2020-04-24 org notes have some things too - this relates to dynamical systems and eigenvalues.) Later note: I have a feeling I was dead wrong about a bunch of this.

Reflections & Quick Notes

  • My old Python version composed rules in the opposite order and I think this made things more complicated. I didn't realize that I did it differently in this code, but it became much easier - particularly, more "inner" transformations are much easier to write because all that matters is that they work properly in the coordinate space they inherit.
  • Generalizing to space curves moves this away from the "discrete automata" roots, but it still ends up needing the machinery I made for discrete automata.
  • If you pre multiply a transformation: you are transforming the entire global space. If you post multiply: you are transforming the current local space.
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