Constraint-based three-dimensional dynamic geometry
Vectornaut
707618cdd3
Port the engine prototype to Rust, integrate it into the application prototype, and use it to enforce the constraints. ### Features To see the engine in action: 1. Add a constraint by shift-clicking to select two spheres in the outline view and then hitting the 🔗 button 2. Click a summary arrow to see the outline item for the new constraint 2. Set the constraint's Lorentz product by entering a value in the text field at the right end of the outline item * *The display should update as soon as you press* Enter *or focus away from the text field* The checkbox at the left end of a constraint outline item controls whether the constraint is active. Activating a constraint triggers a solution update. (Deactivating a constraint doesn't, since the remaining active constraints are still satisfied.) ### Precision The Julia prototype of the engine uses a generic scalar type, so you can pass in any type the linear algebra functions are implemented for. The examples use the [adjustable-precision](https://docs.julialang.org/en/v1/base/numbers/#Base.MPFR.setprecision) `BigFloat` type. In the Rust port of the engine, the scalar type is currently fixed at `f64`. Switching to generic scalars shouldn't be too hard, but I haven't looked into [which other types](https://www.nalgebra.org/docs/user_guide/generic_programming) the linear algebra functions are implemented for. ### Testing To confirm quantitatively that the Rust port of the engine is working, you can go to the `app-proto` folder and: * Run some automated tests by calling `cargo test`. * Inspect the optimization process in a few examples calling the `run-examples` script. The first example that prints is the same as the Irisawa hexlet example from the engine prototype. If you go into `engine-proto/gram-test`, launch Julia, and then ``` include("irisawa-hexlet.jl") for (step, scaled_loss) in enumerate(history_alt.scaled_loss) println(rpad(step-1, 4), " | ", scaled_loss) end ``` you should see that it prints basically the same loss history until the last few steps, when the lower default precision of the Rust engine really starts to show. ### A small engine revision The Rust port of the engine improves on the Julia prototype in one part of the constraint-solving routine: projecting the Hessian onto the subspace where the frozen entries stay constant. The Julia prototype does this by removing the rows and columns of the Hessian that correspond to the frozen entries, finding the Newton step from the resulting "compressed" Hessian, and then adding zero entries to the Newton step in the appropriate places. The Rust port instead replaces each frozen row and column with its corresponding standard unit vector, avoiding the finicky compressing and decompressing steps. To confirm that this version of the constraint-solving routine works the same as the original, I implemented it in Julia as `realize_gram_alt_proj`. The solutions we get from this routine match the ones we get from the original `realize_gram` to very high precision, and in the simplest examples (`sphere-in-tetrahedron.jl` and `tetrahedron-radius-ratio.jl`), the descent paths also match to very high precision. In a more complicated example (`irisawa-hexlet.jl`), the descent paths diverge about a quarter of the way into the search, even though they end up in the same place. Co-authored-by: Aaron Fenyes <aaron.fenyes@fareycircles.ooo> Reviewed-on: #15 Co-authored-by: Vectornaut <vectornaut@nobody@nowhere.net> Co-committed-by: Vectornaut <vectornaut@nobody@nowhere.net> |
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| app-proto | ||
| coffeetest | ||
| doc | ||
| engine-proto | ||
| notes | ||
| src | ||
| .gitignore | ||
| LICENSE | ||
| Makefile | ||
| package-lock.json | ||
| package.json | ||
| README.md | ||
dyna3
Abstract
Constraint-based three-dimensional dynamic geometry
Description
From a thorough web search, there does not seem to be a dynamic geometry software package which (a) began its life handling three dimensions, rather than just two, and (b) allows you to express the desired geometric configuration in terms of constraints on the entities (e.g. l and k are parallel, a, b, and c a collinear, etc.) rather than as a construction (e.g. l is the perpendicular bisector of a and b). The goal of the dyna3 project is to close this gap.
Note that currently this is just the barest beginnings of the project, more of a framework for developing dyna3 rather than anything useful.
Implementation goals
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Comfortable, intuitive UI
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Able to run in browser (so implemented in WASM-compatible language)
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Produce scalable graphics of 3D diagrams, and maybe STL files (or other fabricatable file format) as well.